1 | // Python - C extension module for shallow_water.py |
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2 | // |
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3 | // To compile (Python2.3): |
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4 | // gcc -c domain_ext.c -I/usr/include/python2.3 -o domain_ext.o -Wall -O |
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5 | // gcc -shared domain_ext.o -o domain_ext.so |
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6 | // |
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7 | // or use python compile.py |
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8 | // |
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9 | // See the module shallow_water_domain.py for more documentation on |
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10 | // how to use this module |
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11 | // |
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12 | // |
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13 | // Ole Nielsen, GA 2004 |
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14 | |
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15 | |
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16 | #include "Python.h" |
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17 | #include "numpy/arrayobject.h" |
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18 | #include "math.h" |
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19 | #include <stdio.h> |
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20 | |
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21 | // Shared code snippets |
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22 | #include "util_ext.h" |
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23 | |
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24 | |
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25 | const double pi = 3.14159265358979; |
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26 | |
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27 | // Computational function for rotation |
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28 | int _rotate(double *q, double n1, double n2) { |
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29 | /*Rotate the momentum component q (q[1], q[2]) |
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30 | from x,y coordinates to coordinates based on normal vector (n1, n2). |
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31 | |
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32 | Result is returned in array 3x1 r |
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33 | To rotate in opposite direction, call rotate with (q, n1, -n2) |
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34 | |
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35 | Contents of q are changed by this function */ |
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36 | |
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37 | |
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38 | double q1, q2; |
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39 | |
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40 | // Shorthands |
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41 | q1 = q[1]; // uh momentum |
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42 | q2 = q[2]; // vh momentum |
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43 | |
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44 | // Rotate |
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45 | q[1] = n1*q1 + n2*q2; |
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46 | q[2] = -n2*q1 + n1*q2; |
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47 | |
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48 | return 0; |
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49 | } |
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50 | |
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51 | int find_qmin_and_qmax(double dq0, double dq1, double dq2, |
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52 | double *qmin, double *qmax){ |
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53 | // Considering the centroid of an FV triangle and the vertices of its |
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54 | // auxiliary triangle, find |
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55 | // qmin=min(q)-qc and qmax=max(q)-qc, |
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56 | // where min(q) and max(q) are respectively min and max over the |
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57 | // four values (at the centroid of the FV triangle and the auxiliary |
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58 | // triangle vertices), |
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59 | // and qc is the centroid |
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60 | // dq0=q(vertex0)-q(centroid of FV triangle) |
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61 | // dq1=q(vertex1)-q(vertex0) |
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62 | // dq2=q(vertex2)-q(vertex0) |
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63 | |
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64 | if (dq0>=0.0){ |
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65 | if (dq1>=dq2){ |
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66 | if (dq1>=0.0) |
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67 | *qmax=dq0+dq1; |
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68 | else |
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69 | *qmax=dq0; |
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70 | |
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71 | *qmin=dq0+dq2; |
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72 | if (*qmin>=0.0) *qmin = 0.0; |
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73 | } |
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74 | else{// dq1<dq2 |
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75 | if (dq2>0) |
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76 | *qmax=dq0+dq2; |
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77 | else |
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78 | *qmax=dq0; |
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79 | |
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80 | *qmin=dq0+dq1; |
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81 | if (*qmin>=0.0) *qmin=0.0; |
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82 | } |
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83 | } |
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84 | else{//dq0<0 |
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85 | if (dq1<=dq2){ |
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86 | if (dq1<0.0) |
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87 | *qmin=dq0+dq1; |
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88 | else |
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89 | *qmin=dq0; |
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90 | |
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91 | *qmax=dq0+dq2; |
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92 | if (*qmax<=0.0) *qmax=0.0; |
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93 | } |
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94 | else{// dq1>dq2 |
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95 | if (dq2<0.0) |
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96 | *qmin=dq0+dq2; |
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97 | else |
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98 | *qmin=dq0; |
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99 | |
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100 | *qmax=dq0+dq1; |
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101 | if (*qmax<=0.0) *qmax=0.0; |
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102 | } |
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103 | } |
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104 | return 0; |
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105 | } |
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106 | |
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107 | int limit_gradient(double *dqv, double qmin, double qmax, double beta_w){ |
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108 | // Given provisional jumps dqv from the FV triangle centroid to its |
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109 | // vertices and jumps qmin (qmax) between the centroid of the FV |
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110 | // triangle and the minimum (maximum) of the values at the centroid of |
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111 | // the FV triangle and the auxiliary triangle vertices, |
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112 | // calculate a multiplicative factor phi by which the provisional |
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113 | // vertex jumps are to be limited |
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114 | |
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115 | int i; |
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116 | double r=1000.0, r0=1.0, phi=1.0; |
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117 | static double TINY = 1.0e-100; // to avoid machine accuracy problems. |
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118 | // FIXME: Perhaps use the epsilon used elsewhere. |
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119 | |
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120 | // Any provisional jump with magnitude < TINY does not contribute to |
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121 | // the limiting process. |
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122 | for (i=0;i<3;i++){ |
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123 | if (dqv[i]<-TINY) |
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124 | r0=qmin/dqv[i]; |
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125 | |
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126 | if (dqv[i]>TINY) |
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127 | r0=qmax/dqv[i]; |
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128 | |
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129 | r=min(r0,r); |
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130 | } |
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131 | |
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132 | phi=min(r*beta_w,1.0); |
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133 | for (i=0;i<3;i++) |
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134 | dqv[i]=dqv[i]*phi; |
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135 | |
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136 | return 0; |
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137 | } |
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138 | |
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139 | |
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140 | double compute_froude_number(double uh, |
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141 | double h, |
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142 | double g, |
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143 | double epsilon) { |
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144 | |
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145 | // Compute Froude number; v/sqrt(gh) |
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146 | // FIXME (Ole): Not currently in use |
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147 | |
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148 | double froude_number; |
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149 | |
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150 | //Compute Froude number (stability diagnostics) |
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151 | if (h > epsilon) { |
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152 | froude_number = uh/sqrt(g*h)/h; |
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153 | } else { |
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154 | froude_number = 0.0; |
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155 | // FIXME (Ole): What should it be when dry?? |
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156 | } |
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157 | |
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158 | return froude_number; |
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159 | } |
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160 | |
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161 | |
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162 | |
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163 | // Function to obtain speed from momentum and depth. |
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164 | // This is used by flux functions |
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165 | // Input parameters uh and h may be modified by this function. |
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166 | double _compute_speed(double *uh, |
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167 | double *h, |
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168 | double epsilon, |
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169 | double h0) { |
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170 | |
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171 | double u; |
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172 | |
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173 | |
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174 | if (*h < epsilon) { |
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175 | *h = 0.0; //Could have been negative |
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176 | u = 0.0; |
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177 | } else { |
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178 | u = *uh/(*h + h0/ *h); |
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179 | } |
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180 | |
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181 | |
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182 | // Adjust momentum to be consistent with speed |
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183 | *uh = u * *h; |
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184 | |
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185 | return u; |
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186 | } |
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187 | |
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188 | // Innermost flux function (using stage w=z+h) |
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189 | int _flux_function_central(double *q_left, double *q_right, |
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190 | double z_left, double z_right, |
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191 | double n1, double n2, |
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192 | double epsilon, double H0, double g, |
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193 | double *edgeflux, double *max_speed) { |
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194 | |
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195 | /*Compute fluxes between volumes for the shallow water wave equation |
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196 | cast in terms of the 'stage', w = h+z using |
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197 | the 'central scheme' as described in |
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198 | |
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199 | Kurganov, Noelle, Petrova. 'Semidiscrete Central-Upwind Schemes For |
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200 | Hyperbolic Conservation Laws and Hamilton-Jacobi Equations'. |
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201 | Siam J. Sci. Comput. Vol. 23, No. 3, pp. 707-740. |
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202 | |
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203 | The implemented formula is given in equation (3.15) on page 714 |
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204 | */ |
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205 | |
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206 | int i; |
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207 | |
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208 | double w_left, h_left, uh_left, vh_left, u_left; |
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209 | double w_right, h_right, uh_right, vh_right, u_right; |
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210 | double v_left, v_right; |
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211 | double s_min, s_max, soundspeed_left, soundspeed_right; |
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212 | double denom, z; |
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213 | |
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214 | // Workspace (allocate once, use many) |
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215 | static double q_left_rotated[3], q_right_rotated[3], flux_right[3], flux_left[3]; |
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216 | |
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217 | double h0 = H0*H0; // This ensures a good balance when h approaches H0. |
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218 | // But evidence suggests that h0 can be as little as |
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219 | // epsilon! |
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220 | |
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221 | // Copy conserved quantities to protect from modification |
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222 | for (i=0; i<3; i++) { |
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223 | q_left_rotated[i] = q_left[i]; |
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224 | q_right_rotated[i] = q_right[i]; |
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225 | } |
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226 | |
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227 | // Align x- and y-momentum with x-axis |
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228 | _rotate(q_left_rotated, n1, n2); |
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229 | _rotate(q_right_rotated, n1, n2); |
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230 | |
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231 | z = (z_left+z_right)/2; // Average elevation values. |
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232 | // Even though this will nominally allow for discontinuities |
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233 | // in the elevation data, there is currently no numerical |
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234 | // support for this so results may be strange near jumps in the bed. |
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235 | |
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236 | // Compute speeds in x-direction |
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237 | w_left = q_left_rotated[0]; |
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238 | h_left = w_left-z; |
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239 | uh_left = q_left_rotated[1]; |
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240 | u_left = _compute_speed(&uh_left, &h_left, epsilon, h0); |
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241 | |
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242 | w_right = q_right_rotated[0]; |
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243 | h_right = w_right-z; |
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244 | uh_right = q_right_rotated[1]; |
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245 | u_right = _compute_speed(&uh_right, &h_right, epsilon, h0); |
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246 | |
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247 | // Momentum in y-direction |
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248 | vh_left = q_left_rotated[2]; |
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249 | vh_right = q_right_rotated[2]; |
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250 | |
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251 | // Limit y-momentum if necessary |
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252 | v_left = _compute_speed(&vh_left, &h_left, epsilon, h0); |
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253 | v_right = _compute_speed(&vh_right, &h_right, epsilon, h0); |
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254 | |
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255 | // Maximal and minimal wave speeds |
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256 | soundspeed_left = sqrt(g*h_left); |
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257 | soundspeed_right = sqrt(g*h_right); |
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258 | |
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259 | s_max = max(u_left+soundspeed_left, u_right+soundspeed_right); |
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260 | if (s_max < 0.0) s_max = 0.0; |
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261 | |
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262 | s_min = min(u_left-soundspeed_left, u_right-soundspeed_right); |
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263 | if (s_min > 0.0) s_min = 0.0; |
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264 | |
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265 | |
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266 | // Flux formulas |
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267 | flux_left[0] = u_left*h_left; |
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268 | flux_left[1] = u_left*uh_left + 0.5*g*h_left*h_left; |
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269 | flux_left[2] = u_left*vh_left; |
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270 | |
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271 | flux_right[0] = u_right*h_right; |
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272 | flux_right[1] = u_right*uh_right + 0.5*g*h_right*h_right; |
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273 | flux_right[2] = u_right*vh_right; |
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274 | |
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275 | |
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276 | // Flux computation |
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277 | denom = s_max-s_min; |
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278 | if (denom < epsilon) { // FIXME (Ole): Try using H0 here |
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279 | for (i=0; i<3; i++) edgeflux[i] = 0.0; |
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280 | *max_speed = 0.0; |
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281 | } else { |
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282 | for (i=0; i<3; i++) { |
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283 | edgeflux[i] = s_max*flux_left[i] - s_min*flux_right[i]; |
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284 | edgeflux[i] += s_max*s_min*(q_right_rotated[i]-q_left_rotated[i]); |
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285 | edgeflux[i] /= denom; |
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286 | } |
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287 | |
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288 | // Maximal wavespeed |
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289 | *max_speed = max(fabs(s_max), fabs(s_min)); |
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290 | |
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291 | // Rotate back |
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292 | _rotate(edgeflux, n1, -n2); |
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293 | } |
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294 | |
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295 | return 0; |
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296 | } |
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297 | |
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298 | double erfcc(double x){ |
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299 | double z,t,result; |
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300 | |
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301 | z=fabs(x); |
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302 | t=1.0/(1.0+0.5*z); |
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303 | result=t*exp(-z*z-1.26551223+t*(1.00002368+t*(.37409196+ |
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304 | t*(.09678418+t*(-.18628806+t*(.27886807+t*(-1.13520398+ |
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305 | t*(1.48851587+t*(-.82215223+t*.17087277))))))))); |
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306 | if (x < 0.0) result = 2.0-result; |
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307 | |
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308 | return result; |
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309 | } |
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310 | |
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311 | |
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312 | |
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313 | // Computational function for flux computation (using stage w=z+h) |
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314 | int flux_function_kinetic(double *q_left, double *q_right, |
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315 | double z_left, double z_right, |
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316 | double n1, double n2, |
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317 | double epsilon, double H0, double g, |
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318 | double *edgeflux, double *max_speed) { |
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319 | |
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320 | /*Compute fluxes between volumes for the shallow water wave equation |
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321 | cast in terms of the 'stage', w = h+z using |
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322 | the 'central scheme' as described in |
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323 | |
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324 | Zhang et. al., Advances in Water Resources, 26(6), 2003, 635-647. |
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325 | */ |
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326 | |
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327 | int i; |
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328 | |
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329 | double w_left, h_left, uh_left, vh_left, u_left, F_left; |
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330 | double w_right, h_right, uh_right, vh_right, u_right, F_right; |
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331 | double s_min, s_max, soundspeed_left, soundspeed_right; |
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332 | double z; |
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333 | double q_left_rotated[3], q_right_rotated[3]; |
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334 | |
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335 | double h0 = H0*H0; //This ensures a good balance when h approaches H0. |
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336 | |
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337 | //Copy conserved quantities to protect from modification |
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338 | for (i=0; i<3; i++) { |
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339 | q_left_rotated[i] = q_left[i]; |
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340 | q_right_rotated[i] = q_right[i]; |
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341 | } |
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342 | |
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343 | //Align x- and y-momentum with x-axis |
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344 | _rotate(q_left_rotated, n1, n2); |
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345 | _rotate(q_right_rotated, n1, n2); |
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346 | |
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347 | z = (z_left+z_right)/2; //Take average of field values |
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348 | |
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349 | //Compute speeds in x-direction |
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350 | w_left = q_left_rotated[0]; |
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351 | h_left = w_left-z; |
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352 | uh_left = q_left_rotated[1]; |
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353 | u_left =_compute_speed(&uh_left, &h_left, epsilon, h0); |
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354 | |
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355 | w_right = q_right_rotated[0]; |
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356 | h_right = w_right-z; |
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357 | uh_right = q_right_rotated[1]; |
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358 | u_right =_compute_speed(&uh_right, &h_right, epsilon, h0); |
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359 | |
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360 | |
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361 | //Momentum in y-direction |
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362 | vh_left = q_left_rotated[2]; |
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363 | vh_right = q_right_rotated[2]; |
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364 | |
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365 | |
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366 | //Maximal and minimal wave speeds |
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367 | soundspeed_left = sqrt(g*h_left); |
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368 | soundspeed_right = sqrt(g*h_right); |
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369 | |
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370 | s_max = max(u_left+soundspeed_left, u_right+soundspeed_right); |
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371 | if (s_max < 0.0) s_max = 0.0; |
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372 | |
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373 | s_min = min(u_left-soundspeed_left, u_right-soundspeed_right); |
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374 | if (s_min > 0.0) s_min = 0.0; |
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375 | |
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376 | |
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377 | F_left = 0.0; |
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378 | F_right = 0.0; |
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379 | if (h_left > 0.0) F_left = u_left/sqrt(g*h_left); |
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380 | if (h_right > 0.0) F_right = u_right/sqrt(g*h_right); |
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381 | |
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382 | for (i=0; i<3; i++) edgeflux[i] = 0.0; |
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383 | *max_speed = 0.0; |
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384 | |
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385 | edgeflux[0] = h_left*u_left/2.0*erfcc(-F_left) + \ |
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386 | h_left*sqrt(g*h_left)/2.0/sqrt(pi)*exp(-(F_left*F_left)) + \ |
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387 | h_right*u_right/2.0*erfcc(F_right) - \ |
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388 | h_right*sqrt(g*h_right)/2.0/sqrt(pi)*exp(-(F_right*F_right)); |
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389 | |
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390 | edgeflux[1] = (h_left*u_left*u_left + g/2.0*h_left*h_left)/2.0*erfcc(-F_left) + \ |
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391 | u_left*h_left*sqrt(g*h_left)/2.0/sqrt(pi)*exp(-(F_left*F_left)) + \ |
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392 | (h_right*u_right*u_right + g/2.0*h_right*h_right)/2.0*erfcc(F_right) - \ |
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393 | u_right*h_right*sqrt(g*h_right)/2.0/sqrt(pi)*exp(-(F_right*F_right)); |
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394 | |
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395 | edgeflux[2] = vh_left*u_left/2.0*erfcc(-F_left) + \ |
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396 | vh_left*sqrt(g*h_left)/2.0/sqrt(pi)*exp(-(F_left*F_left)) + \ |
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397 | vh_right*u_right/2.0*erfcc(F_right) - \ |
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398 | vh_right*sqrt(g*h_right)/2.0/sqrt(pi)*exp(-(F_right*F_right)); |
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399 | |
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400 | //Maximal wavespeed |
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401 | *max_speed = max(fabs(s_max), fabs(s_min)); |
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402 | |
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403 | //Rotate back |
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404 | _rotate(edgeflux, n1, -n2); |
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405 | |
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406 | return 0; |
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407 | } |
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408 | |
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409 | |
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410 | |
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411 | |
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412 | void _manning_friction(double g, double eps, int N, |
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413 | double* w, double* z, |
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414 | double* uh, double* vh, |
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415 | double* eta, double* xmom, double* ymom) { |
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416 | |
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417 | int k; |
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418 | double S, h; |
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419 | |
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420 | for (k=0; k<N; k++) { |
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421 | if (eta[k] > eps) { |
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422 | h = w[k]-z[k]; |
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423 | if (h >= eps) { |
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424 | S = -g * eta[k]*eta[k] * sqrt((uh[k]*uh[k] + vh[k]*vh[k])); |
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425 | S /= pow(h, 7.0/3); //Expensive (on Ole's home computer) |
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426 | //S /= exp(7.0/3.0*log(h)); //seems to save about 15% over manning_friction |
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427 | //S /= h*h*(1 + h/3.0 - h*h/9.0); //FIXME: Could use a Taylor expansion |
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428 | |
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429 | |
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430 | //Update momentum |
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431 | xmom[k] += S*uh[k]; |
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432 | ymom[k] += S*vh[k]; |
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433 | } |
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434 | } |
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435 | } |
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436 | } |
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437 | |
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438 | |
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439 | /* |
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440 | void _manning_friction_explicit(double g, double eps, int N, |
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441 | double* w, double* z, |
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442 | double* uh, double* vh, |
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443 | double* eta, double* xmom, double* ymom) { |
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444 | |
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445 | int k; |
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446 | double S, h; |
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447 | |
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448 | for (k=0; k<N; k++) { |
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449 | if (eta[k] > eps) { |
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450 | h = w[k]-z[k]; |
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451 | if (h >= eps) { |
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452 | S = -g * eta[k]*eta[k] * sqrt((uh[k]*uh[k] + vh[k]*vh[k])); |
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453 | S /= pow(h, 7.0/3); //Expensive (on Ole's home computer) |
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454 | //S /= exp(7.0/3.0*log(h)); //seems to save about 15% over manning_friction |
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455 | //S /= h*h*(1 + h/3.0 - h*h/9.0); //FIXME: Could use a Taylor expansion |
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456 | |
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457 | |
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458 | //Update momentum |
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459 | xmom[k] += S*uh[k]; |
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460 | ymom[k] += S*vh[k]; |
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461 | } |
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462 | } |
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463 | } |
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464 | } |
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465 | */ |
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466 | |
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467 | |
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468 | |
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469 | |
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470 | double velocity_balance(double uh_i, |
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471 | double uh, |
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472 | double h_i, |
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473 | double h, |
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474 | double alpha, |
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475 | double epsilon) { |
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476 | // Find alpha such that speed at the vertex is within one |
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477 | // order of magnitude of the centroid speed |
---|
478 | |
---|
479 | // FIXME(Ole): Work in progress |
---|
480 | |
---|
481 | double a, b, estimate; |
---|
482 | double m=10; // One order of magnitude - allow for velocity deviations at vertices |
---|
483 | |
---|
484 | |
---|
485 | printf("alpha = %f, uh_i=%f, uh=%f, h_i=%f, h=%f\n", |
---|
486 | alpha, uh_i, uh, h_i, h); |
---|
487 | |
---|
488 | |
---|
489 | |
---|
490 | |
---|
491 | // Shorthands and determine inequality |
---|
492 | if (fabs(uh) < epsilon) { |
---|
493 | a = 1.0e10; // Limit |
---|
494 | } else { |
---|
495 | a = fabs(uh_i - uh)/fabs(uh); |
---|
496 | } |
---|
497 | |
---|
498 | if (h < epsilon) { |
---|
499 | b = 1.0e10; // Limit |
---|
500 | } else { |
---|
501 | b = m*fabs(h_i - h)/h; |
---|
502 | } |
---|
503 | |
---|
504 | printf("a %f, b %f\n", a, b); |
---|
505 | |
---|
506 | if (a > b) { |
---|
507 | estimate = (m-1)/(a-b); |
---|
508 | |
---|
509 | printf("Alpha %f, estimate %f\n", |
---|
510 | alpha, estimate); |
---|
511 | |
---|
512 | if (alpha < estimate) { |
---|
513 | printf("Adjusting alpha from %f to %f\n", |
---|
514 | alpha, estimate); |
---|
515 | alpha = estimate; |
---|
516 | } |
---|
517 | } else { |
---|
518 | |
---|
519 | if (h < h_i) { |
---|
520 | estimate = (m-1)/(a-b); |
---|
521 | |
---|
522 | printf("Alpha %f, estimate %f\n", |
---|
523 | alpha, estimate); |
---|
524 | |
---|
525 | if (alpha < estimate) { |
---|
526 | printf("Adjusting alpha from %f to %f\n", |
---|
527 | alpha, estimate); |
---|
528 | alpha = estimate; |
---|
529 | } |
---|
530 | } |
---|
531 | // Always fulfilled as alpha and m-1 are non negative |
---|
532 | } |
---|
533 | |
---|
534 | |
---|
535 | return alpha; |
---|
536 | } |
---|
537 | |
---|
538 | |
---|
539 | int _balance_deep_and_shallow(int N, |
---|
540 | double* wc, |
---|
541 | double* zc, |
---|
542 | double* wv, |
---|
543 | double* zv, |
---|
544 | double* hvbar, // Retire this |
---|
545 | double* xmomc, |
---|
546 | double* ymomc, |
---|
547 | double* xmomv, |
---|
548 | double* ymomv, |
---|
549 | double H0, |
---|
550 | int tight_slope_limiters, |
---|
551 | int use_centroid_velocities, |
---|
552 | double alpha_balance) { |
---|
553 | |
---|
554 | int k, k3, i; |
---|
555 | |
---|
556 | double dz, hmin, alpha, h_diff, hc_k; |
---|
557 | double epsilon = 1.0e-6; // FIXME: Temporary measure |
---|
558 | double hv[3]; // Depths at vertices |
---|
559 | double uc, vc; // Centroid speeds |
---|
560 | |
---|
561 | // Compute linear combination between w-limited stages and |
---|
562 | // h-limited stages close to the bed elevation. |
---|
563 | |
---|
564 | for (k=0; k<N; k++) { |
---|
565 | // Compute maximal variation in bed elevation |
---|
566 | // This quantitiy is |
---|
567 | // dz = max_i abs(z_i - z_c) |
---|
568 | // and it is independent of dimension |
---|
569 | // In the 1d case zc = (z0+z1)/2 |
---|
570 | // In the 2d case zc = (z0+z1+z2)/3 |
---|
571 | |
---|
572 | k3 = 3*k; |
---|
573 | hc_k = wc[k] - zc[k]; // Centroid value at triangle k |
---|
574 | |
---|
575 | dz = 0.0; |
---|
576 | if (tight_slope_limiters == 0) { |
---|
577 | // FIXME: Try with this one precomputed |
---|
578 | for (i=0; i<3; i++) { |
---|
579 | dz = max(dz, fabs(zv[k3+i]-zc[k])); |
---|
580 | } |
---|
581 | } |
---|
582 | |
---|
583 | // Calculate depth at vertices (possibly negative here!) |
---|
584 | hv[0] = wv[k3] - zv[k3]; |
---|
585 | hv[1] = wv[k3+1] - zv[k3+1]; |
---|
586 | hv[2] = wv[k3+2] - zv[k3+2]; |
---|
587 | |
---|
588 | // Calculate minimal depth across all three vertices |
---|
589 | hmin = min(hv[0], min(hv[1], hv[2])); |
---|
590 | |
---|
591 | //if (hmin < 0.0 ) { |
---|
592 | // printf("hmin = %f\n",hmin); |
---|
593 | //} |
---|
594 | |
---|
595 | |
---|
596 | // Create alpha in [0,1], where alpha==0 means using the h-limited |
---|
597 | // stage and alpha==1 means using the w-limited stage as |
---|
598 | // computed by the gradient limiter (both 1st or 2nd order) |
---|
599 | if (tight_slope_limiters == 0) { |
---|
600 | // If hmin > dz/alpha_balance then alpha = 1 and the bed will have no |
---|
601 | // effect |
---|
602 | // If hmin < 0 then alpha = 0 reverting to constant height above bed. |
---|
603 | // The parameter alpha_balance==2 by default |
---|
604 | |
---|
605 | |
---|
606 | if (dz > 0.0) { |
---|
607 | alpha = max( min( alpha_balance*hmin/dz, 1.0), 0.0 ); |
---|
608 | } else { |
---|
609 | alpha = 1.0; // Flat bed |
---|
610 | } |
---|
611 | //printf("Using old style limiter\n"); |
---|
612 | |
---|
613 | } else { |
---|
614 | |
---|
615 | // Tight Slope Limiter (2007) |
---|
616 | |
---|
617 | // Make alpha as large as possible but still ensure that |
---|
618 | // final depth is positive and that velocities at vertices |
---|
619 | // are controlled |
---|
620 | |
---|
621 | if (hmin < H0) { |
---|
622 | alpha = 1.0; |
---|
623 | for (i=0; i<3; i++) { |
---|
624 | |
---|
625 | h_diff = hc_k - hv[i]; |
---|
626 | if (h_diff <= 0) { |
---|
627 | // Deep water triangle is further away from bed than |
---|
628 | // shallow water (hbar < h). Any alpha will do |
---|
629 | |
---|
630 | } else { |
---|
631 | // Denominator is positive which means that we need some of the |
---|
632 | // h-limited stage. |
---|
633 | |
---|
634 | alpha = min(alpha, (hc_k - H0)/h_diff); |
---|
635 | } |
---|
636 | } |
---|
637 | |
---|
638 | // Ensure alpha in [0,1] |
---|
639 | if (alpha>1.0) alpha=1.0; |
---|
640 | if (alpha<0.0) alpha=0.0; |
---|
641 | |
---|
642 | } else { |
---|
643 | // Use w-limited stage exclusively in deeper water. |
---|
644 | alpha = 1.0; |
---|
645 | } |
---|
646 | } |
---|
647 | |
---|
648 | |
---|
649 | // Let |
---|
650 | // |
---|
651 | // wvi be the w-limited stage (wvi = zvi + hvi) |
---|
652 | // wvi- be the h-limited state (wvi- = zvi + hvi-) |
---|
653 | // |
---|
654 | // |
---|
655 | // where i=0,1,2 denotes the vertex ids |
---|
656 | // |
---|
657 | // Weighted balance between w-limited and h-limited stage is |
---|
658 | // |
---|
659 | // wvi := (1-alpha)*(zvi+hvi-) + alpha*(zvi+hvi) |
---|
660 | // |
---|
661 | // It follows that the updated wvi is |
---|
662 | // wvi := zvi + (1-alpha)*hvi- + alpha*hvi |
---|
663 | // |
---|
664 | // Momentum is balanced between constant and limited |
---|
665 | |
---|
666 | |
---|
667 | if (alpha < 1) { |
---|
668 | for (i=0; i<3; i++) { |
---|
669 | |
---|
670 | wv[k3+i] = zv[k3+i] + (1-alpha)*hc_k + alpha*hv[i]; |
---|
671 | |
---|
672 | // Update momentum at vertices |
---|
673 | if (use_centroid_velocities == 1) { |
---|
674 | // This is a simple, efficient and robust option |
---|
675 | // It uses first order approximation of velocities, but retains |
---|
676 | // the order used by stage. |
---|
677 | |
---|
678 | // Speeds at centroids |
---|
679 | if (hc_k > epsilon) { |
---|
680 | uc = xmomc[k]/hc_k; |
---|
681 | vc = ymomc[k]/hc_k; |
---|
682 | } else { |
---|
683 | uc = 0.0; |
---|
684 | vc = 0.0; |
---|
685 | } |
---|
686 | |
---|
687 | // Vertex momenta guaranteed to be consistent with depth guaranteeing |
---|
688 | // controlled speed |
---|
689 | hv[i] = wv[k3+i] - zv[k3+i]; // Recompute (balanced) vertex depth |
---|
690 | xmomv[k3+i] = uc*hv[i]; |
---|
691 | ymomv[k3+i] = vc*hv[i]; |
---|
692 | |
---|
693 | } else { |
---|
694 | // Update momentum as a linear combination of |
---|
695 | // xmomc and ymomc (shallow) and momentum |
---|
696 | // from extrapolator xmomv and ymomv (deep). |
---|
697 | // This assumes that values from xmomv and ymomv have |
---|
698 | // been established e.g. by the gradient limiter. |
---|
699 | |
---|
700 | // FIXME (Ole): I think this should be used with vertex momenta |
---|
701 | // computed above using centroid_velocities instead of xmomc |
---|
702 | // and ymomc as they'll be more representative first order |
---|
703 | // values. |
---|
704 | |
---|
705 | xmomv[k3+i] = (1-alpha)*xmomc[k] + alpha*xmomv[k3+i]; |
---|
706 | ymomv[k3+i] = (1-alpha)*ymomc[k] + alpha*ymomv[k3+i]; |
---|
707 | |
---|
708 | } |
---|
709 | } |
---|
710 | } |
---|
711 | } |
---|
712 | return 0; |
---|
713 | } |
---|
714 | |
---|
715 | |
---|
716 | |
---|
717 | |
---|
718 | int _protect(int N, |
---|
719 | double minimum_allowed_height, |
---|
720 | double maximum_allowed_speed, |
---|
721 | double epsilon, |
---|
722 | double* wc, |
---|
723 | double* zc, |
---|
724 | double* xmomc, |
---|
725 | double* ymomc) { |
---|
726 | |
---|
727 | int k; |
---|
728 | double hc; |
---|
729 | double u, v, reduced_speed; |
---|
730 | |
---|
731 | |
---|
732 | // Protect against initesimal and negative heights |
---|
733 | if (maximum_allowed_speed < epsilon) { |
---|
734 | for (k=0; k<N; k++) { |
---|
735 | hc = wc[k] - zc[k]; |
---|
736 | |
---|
737 | if (hc < minimum_allowed_height) { |
---|
738 | |
---|
739 | // Set momentum to zero and ensure h is non negative |
---|
740 | xmomc[k] = 0.0; |
---|
741 | ymomc[k] = 0.0; |
---|
742 | if (hc <= 0.0) wc[k] = zc[k]; |
---|
743 | } |
---|
744 | } |
---|
745 | } else { |
---|
746 | |
---|
747 | // Protect against initesimal and negative heights |
---|
748 | for (k=0; k<N; k++) { |
---|
749 | hc = wc[k] - zc[k]; |
---|
750 | |
---|
751 | if (hc < minimum_allowed_height) { |
---|
752 | |
---|
753 | //New code: Adjust momentum to guarantee speeds are physical |
---|
754 | // ensure h is non negative |
---|
755 | |
---|
756 | if (hc <= 0.0) { |
---|
757 | wc[k] = zc[k]; |
---|
758 | xmomc[k] = 0.0; |
---|
759 | ymomc[k] = 0.0; |
---|
760 | } else { |
---|
761 | //Reduce excessive speeds derived from division by small hc |
---|
762 | //FIXME (Ole): This may be unnecessary with new slope limiters |
---|
763 | //in effect. |
---|
764 | |
---|
765 | u = xmomc[k]/hc; |
---|
766 | if (fabs(u) > maximum_allowed_speed) { |
---|
767 | reduced_speed = maximum_allowed_speed * u/fabs(u); |
---|
768 | //printf("Speed (u) has been reduced from %.3f to %.3f\n", |
---|
769 | // u, reduced_speed); |
---|
770 | xmomc[k] = reduced_speed * hc; |
---|
771 | } |
---|
772 | |
---|
773 | v = ymomc[k]/hc; |
---|
774 | if (fabs(v) > maximum_allowed_speed) { |
---|
775 | reduced_speed = maximum_allowed_speed * v/fabs(v); |
---|
776 | //printf("Speed (v) has been reduced from %.3f to %.3f\n", |
---|
777 | // v, reduced_speed); |
---|
778 | ymomc[k] = reduced_speed * hc; |
---|
779 | } |
---|
780 | } |
---|
781 | } |
---|
782 | } |
---|
783 | } |
---|
784 | return 0; |
---|
785 | } |
---|
786 | |
---|
787 | |
---|
788 | |
---|
789 | int _assign_wind_field_values(int N, |
---|
790 | double* xmom_update, |
---|
791 | double* ymom_update, |
---|
792 | double* s_vec, |
---|
793 | double* phi_vec, |
---|
794 | double cw) { |
---|
795 | |
---|
796 | // Assign windfield values to momentum updates |
---|
797 | |
---|
798 | int k; |
---|
799 | double S, s, phi, u, v; |
---|
800 | |
---|
801 | for (k=0; k<N; k++) { |
---|
802 | |
---|
803 | s = s_vec[k]; |
---|
804 | phi = phi_vec[k]; |
---|
805 | |
---|
806 | //Convert to radians |
---|
807 | phi = phi*pi/180; |
---|
808 | |
---|
809 | //Compute velocity vector (u, v) |
---|
810 | u = s*cos(phi); |
---|
811 | v = s*sin(phi); |
---|
812 | |
---|
813 | //Compute wind stress |
---|
814 | S = cw * sqrt(u*u + v*v); |
---|
815 | xmom_update[k] += S*u; |
---|
816 | ymom_update[k] += S*v; |
---|
817 | } |
---|
818 | return 0; |
---|
819 | } |
---|
820 | |
---|
821 | |
---|
822 | |
---|
823 | /////////////////////////////////////////////////////////////////// |
---|
824 | // Gateways to Python |
---|
825 | |
---|
826 | |
---|
827 | |
---|
828 | PyObject *flux_function_central(PyObject *self, PyObject *args) { |
---|
829 | // |
---|
830 | // Gateway to innermost flux function. |
---|
831 | // This is only used by the unit tests as the c implementation is |
---|
832 | // normally called by compute_fluxes in this module. |
---|
833 | |
---|
834 | |
---|
835 | PyArrayObject *normal, *ql, *qr, *edgeflux; |
---|
836 | double g, epsilon, max_speed, H0, zl, zr; |
---|
837 | |
---|
838 | if (!PyArg_ParseTuple(args, "OOOddOddd", |
---|
839 | &normal, &ql, &qr, &zl, &zr, &edgeflux, |
---|
840 | &epsilon, &g, &H0)) { |
---|
841 | PyErr_SetString(PyExc_RuntimeError, "shallow_water_ext.c: flux_function_central could not parse input arguments"); |
---|
842 | return NULL; |
---|
843 | } |
---|
844 | |
---|
845 | |
---|
846 | _flux_function_central((double*) ql -> data, |
---|
847 | (double*) qr -> data, |
---|
848 | zl, |
---|
849 | zr, |
---|
850 | ((double*) normal -> data)[0], |
---|
851 | ((double*) normal -> data)[1], |
---|
852 | epsilon, H0, g, |
---|
853 | (double*) edgeflux -> data, |
---|
854 | &max_speed); |
---|
855 | |
---|
856 | return Py_BuildValue("d", max_speed); |
---|
857 | } |
---|
858 | |
---|
859 | |
---|
860 | |
---|
861 | PyObject *gravity(PyObject *self, PyObject *args) { |
---|
862 | // |
---|
863 | // gravity(g, h, v, x, xmom, ymom) |
---|
864 | // |
---|
865 | |
---|
866 | |
---|
867 | PyArrayObject *h, *v, *x, *xmom, *ymom; |
---|
868 | int k, N, k3, k6; |
---|
869 | double g, avg_h, zx, zy; |
---|
870 | double x0, y0, x1, y1, x2, y2, z0, z1, z2; |
---|
871 | //double epsilon; |
---|
872 | |
---|
873 | if (!PyArg_ParseTuple(args, "dOOOOO", |
---|
874 | &g, &h, &v, &x, |
---|
875 | &xmom, &ymom)) { |
---|
876 | //&epsilon)) { |
---|
877 | PyErr_SetString(PyExc_RuntimeError, "shallow_water_ext.c: gravity could not parse input arguments"); |
---|
878 | return NULL; |
---|
879 | } |
---|
880 | |
---|
881 | N = h -> dimensions[0]; |
---|
882 | for (k=0; k<N; k++) { |
---|
883 | k3 = 3*k; // base index |
---|
884 | |
---|
885 | // Get bathymetry |
---|
886 | z0 = ((double*) v -> data)[k3 + 0]; |
---|
887 | z1 = ((double*) v -> data)[k3 + 1]; |
---|
888 | z2 = ((double*) v -> data)[k3 + 2]; |
---|
889 | |
---|
890 | // Optimise for flat bed |
---|
891 | // Note (Ole): This didn't produce measurable speed up. |
---|
892 | // Revisit later |
---|
893 | //if (fabs(z0-z1)<epsilon && fabs(z1-z2)<epsilon) { |
---|
894 | // continue; |
---|
895 | //} |
---|
896 | |
---|
897 | // Get average depth from centroid values |
---|
898 | avg_h = ((double *) h -> data)[k]; |
---|
899 | |
---|
900 | // Compute bed slope |
---|
901 | k6 = 6*k; // base index |
---|
902 | |
---|
903 | x0 = ((double*) x -> data)[k6 + 0]; |
---|
904 | y0 = ((double*) x -> data)[k6 + 1]; |
---|
905 | x1 = ((double*) x -> data)[k6 + 2]; |
---|
906 | y1 = ((double*) x -> data)[k6 + 3]; |
---|
907 | x2 = ((double*) x -> data)[k6 + 4]; |
---|
908 | y2 = ((double*) x -> data)[k6 + 5]; |
---|
909 | |
---|
910 | |
---|
911 | _gradient(x0, y0, x1, y1, x2, y2, z0, z1, z2, &zx, &zy); |
---|
912 | |
---|
913 | // Update momentum |
---|
914 | ((double*) xmom -> data)[k] += -g*zx*avg_h; |
---|
915 | ((double*) ymom -> data)[k] += -g*zy*avg_h; |
---|
916 | } |
---|
917 | |
---|
918 | return Py_BuildValue(""); |
---|
919 | } |
---|
920 | |
---|
921 | |
---|
922 | PyObject *manning_friction(PyObject *self, PyObject *args) { |
---|
923 | // |
---|
924 | // manning_friction(g, eps, h, uh, vh, eta, xmom_update, ymom_update) |
---|
925 | // |
---|
926 | |
---|
927 | |
---|
928 | PyArrayObject *w, *z, *uh, *vh, *eta, *xmom, *ymom; |
---|
929 | int N; |
---|
930 | double g, eps; |
---|
931 | |
---|
932 | if (!PyArg_ParseTuple(args, "ddOOOOOOO", |
---|
933 | &g, &eps, &w, &z, &uh, &vh, &eta, |
---|
934 | &xmom, &ymom)) { |
---|
935 | PyErr_SetString(PyExc_RuntimeError, "shallow_water_ext.c: manning_friction could not parse input arguments"); |
---|
936 | return NULL; |
---|
937 | } |
---|
938 | |
---|
939 | |
---|
940 | N = w -> dimensions[0]; |
---|
941 | _manning_friction(g, eps, N, |
---|
942 | (double*) w -> data, |
---|
943 | (double*) z -> data, |
---|
944 | (double*) uh -> data, |
---|
945 | (double*) vh -> data, |
---|
946 | (double*) eta -> data, |
---|
947 | (double*) xmom -> data, |
---|
948 | (double*) ymom -> data); |
---|
949 | |
---|
950 | return Py_BuildValue(""); |
---|
951 | } |
---|
952 | |
---|
953 | |
---|
954 | /* |
---|
955 | PyObject *manning_friction_explicit(PyObject *self, PyObject *args) { |
---|
956 | // |
---|
957 | // manning_friction_explicit(g, eps, h, uh, vh, eta, xmom_update, ymom_update) |
---|
958 | // |
---|
959 | |
---|
960 | |
---|
961 | PyArrayObject *w, *z, *uh, *vh, *eta, *xmom, *ymom; |
---|
962 | int N; |
---|
963 | double g, eps; |
---|
964 | |
---|
965 | if (!PyArg_ParseTuple(args, "ddOOOOOOO", |
---|
966 | &g, &eps, &w, &z, &uh, &vh, &eta, |
---|
967 | &xmom, &ymom)) |
---|
968 | return NULL; |
---|
969 | |
---|
970 | N = w -> dimensions[0]; |
---|
971 | _manning_friction_explicit(g, eps, N, |
---|
972 | (double*) w -> data, |
---|
973 | (double*) z -> data, |
---|
974 | (double*) uh -> data, |
---|
975 | (double*) vh -> data, |
---|
976 | (double*) eta -> data, |
---|
977 | (double*) xmom -> data, |
---|
978 | (double*) ymom -> data); |
---|
979 | |
---|
980 | return Py_BuildValue(""); |
---|
981 | } |
---|
982 | */ |
---|
983 | |
---|
984 | |
---|
985 | |
---|
986 | // Computational routine |
---|
987 | int _extrapolate_second_order_sw(int number_of_elements, |
---|
988 | double epsilon, |
---|
989 | double minimum_allowed_height, |
---|
990 | double beta_w, |
---|
991 | double beta_w_dry, |
---|
992 | double beta_uh, |
---|
993 | double beta_uh_dry, |
---|
994 | double beta_vh, |
---|
995 | double beta_vh_dry, |
---|
996 | long* surrogate_neighbours, |
---|
997 | long* number_of_boundaries, |
---|
998 | double* centroid_coordinates, |
---|
999 | double* stage_centroid_values, |
---|
1000 | double* xmom_centroid_values, |
---|
1001 | double* ymom_centroid_values, |
---|
1002 | double* elevation_centroid_values, |
---|
1003 | double* vertex_coordinates, |
---|
1004 | double* stage_vertex_values, |
---|
1005 | double* xmom_vertex_values, |
---|
1006 | double* ymom_vertex_values, |
---|
1007 | double* elevation_vertex_values, |
---|
1008 | int optimise_dry_cells) { |
---|
1009 | |
---|
1010 | |
---|
1011 | |
---|
1012 | // Local variables |
---|
1013 | double a, b; // Gradient vector used to calculate vertex values from centroids |
---|
1014 | int k,k0,k1,k2,k3,k6,coord_index,i; |
---|
1015 | double x,y,x0,y0,x1,y1,x2,y2,xv0,yv0,xv1,yv1,xv2,yv2; // Vertices of the auxiliary triangle |
---|
1016 | double dx1,dx2,dy1,dy2,dxv0,dxv1,dxv2,dyv0,dyv1,dyv2,dq0,dq1,dq2,area2; |
---|
1017 | double dqv[3], qmin, qmax, hmin, hmax; |
---|
1018 | double hc, h0, h1, h2, beta_tmp, hfactor; |
---|
1019 | |
---|
1020 | |
---|
1021 | for (k=0; k<number_of_elements; k++) { |
---|
1022 | k3=k*3; |
---|
1023 | k6=k*6; |
---|
1024 | |
---|
1025 | |
---|
1026 | if (number_of_boundaries[k]==3){ |
---|
1027 | // No neighbours, set gradient on the triangle to zero |
---|
1028 | |
---|
1029 | stage_vertex_values[k3] = stage_centroid_values[k]; |
---|
1030 | stage_vertex_values[k3+1] = stage_centroid_values[k]; |
---|
1031 | stage_vertex_values[k3+2] = stage_centroid_values[k]; |
---|
1032 | xmom_vertex_values[k3] = xmom_centroid_values[k]; |
---|
1033 | xmom_vertex_values[k3+1] = xmom_centroid_values[k]; |
---|
1034 | xmom_vertex_values[k3+2] = xmom_centroid_values[k]; |
---|
1035 | ymom_vertex_values[k3] = ymom_centroid_values[k]; |
---|
1036 | ymom_vertex_values[k3+1] = ymom_centroid_values[k]; |
---|
1037 | ymom_vertex_values[k3+2] = ymom_centroid_values[k]; |
---|
1038 | |
---|
1039 | continue; |
---|
1040 | } |
---|
1041 | else { |
---|
1042 | // Triangle k has one or more neighbours. |
---|
1043 | // Get centroid and vertex coordinates of the triangle |
---|
1044 | |
---|
1045 | // Get the vertex coordinates |
---|
1046 | xv0 = vertex_coordinates[k6]; yv0=vertex_coordinates[k6+1]; |
---|
1047 | xv1 = vertex_coordinates[k6+2]; yv1=vertex_coordinates[k6+3]; |
---|
1048 | xv2 = vertex_coordinates[k6+4]; yv2=vertex_coordinates[k6+5]; |
---|
1049 | |
---|
1050 | // Get the centroid coordinates |
---|
1051 | coord_index=2*k; |
---|
1052 | x=centroid_coordinates[coord_index]; |
---|
1053 | y=centroid_coordinates[coord_index+1]; |
---|
1054 | |
---|
1055 | // Store x- and y- differentials for the vertices of |
---|
1056 | // triangle k relative to the centroid |
---|
1057 | dxv0=xv0-x; dxv1=xv1-x; dxv2=xv2-x; |
---|
1058 | dyv0=yv0-y; dyv1=yv1-y; dyv2=yv2-y; |
---|
1059 | } |
---|
1060 | |
---|
1061 | |
---|
1062 | |
---|
1063 | if (number_of_boundaries[k]<=1){ |
---|
1064 | |
---|
1065 | //============================================== |
---|
1066 | // Number of boundaries <= 1 |
---|
1067 | //============================================== |
---|
1068 | |
---|
1069 | |
---|
1070 | // If no boundaries, auxiliary triangle is formed |
---|
1071 | // from the centroids of the three neighbours |
---|
1072 | // If one boundary, auxiliary triangle is formed |
---|
1073 | // from this centroid and its two neighbours |
---|
1074 | |
---|
1075 | k0=surrogate_neighbours[k3]; |
---|
1076 | k1=surrogate_neighbours[k3+1]; |
---|
1077 | k2=surrogate_neighbours[k3+2]; |
---|
1078 | |
---|
1079 | // Get the auxiliary triangle's vertex coordinates |
---|
1080 | // (really the centroids of neighbouring triangles) |
---|
1081 | coord_index=2*k0; |
---|
1082 | x0=centroid_coordinates[coord_index]; |
---|
1083 | y0=centroid_coordinates[coord_index+1]; |
---|
1084 | |
---|
1085 | coord_index=2*k1; |
---|
1086 | x1=centroid_coordinates[coord_index]; |
---|
1087 | y1=centroid_coordinates[coord_index+1]; |
---|
1088 | |
---|
1089 | coord_index=2*k2; |
---|
1090 | x2=centroid_coordinates[coord_index]; |
---|
1091 | y2=centroid_coordinates[coord_index+1]; |
---|
1092 | |
---|
1093 | // Store x- and y- differentials for the vertices |
---|
1094 | // of the auxiliary triangle |
---|
1095 | dx1=x1-x0; dx2=x2-x0; |
---|
1096 | dy1=y1-y0; dy2=y2-y0; |
---|
1097 | |
---|
1098 | // Calculate 2*area of the auxiliary triangle |
---|
1099 | // The triangle is guaranteed to be counter-clockwise |
---|
1100 | area2 = dy2*dx1 - dy1*dx2; |
---|
1101 | |
---|
1102 | // If the mesh is 'weird' near the boundary, |
---|
1103 | // the triangle might be flat or clockwise: |
---|
1104 | if (area2<=0) { |
---|
1105 | PyErr_SetString(PyExc_RuntimeError, |
---|
1106 | "shallow_water_ext.c: negative triangle area encountered"); |
---|
1107 | return -1; |
---|
1108 | } |
---|
1109 | |
---|
1110 | // Calculate heights of neighbouring cells |
---|
1111 | hc = stage_centroid_values[k] - elevation_centroid_values[k]; |
---|
1112 | h0 = stage_centroid_values[k0] - elevation_centroid_values[k0]; |
---|
1113 | h1 = stage_centroid_values[k1] - elevation_centroid_values[k1]; |
---|
1114 | h2 = stage_centroid_values[k2] - elevation_centroid_values[k2]; |
---|
1115 | hmin = min(min(h0,min(h1,h2)),hc); |
---|
1116 | //hfactor = hc/(hc + 1.0); |
---|
1117 | |
---|
1118 | hfactor = 0.0; |
---|
1119 | if (hmin > 0.001 ) { |
---|
1120 | hfactor = (hmin-0.001)/(hmin+0.004); |
---|
1121 | } |
---|
1122 | |
---|
1123 | if (optimise_dry_cells) { |
---|
1124 | // Check if linear reconstruction is necessary for triangle k |
---|
1125 | // This check will exclude dry cells. |
---|
1126 | |
---|
1127 | hmax = max(h0,max(h1,h2)); |
---|
1128 | if (hmax < epsilon) { |
---|
1129 | continue; |
---|
1130 | } |
---|
1131 | } |
---|
1132 | |
---|
1133 | |
---|
1134 | //----------------------------------- |
---|
1135 | // stage |
---|
1136 | //----------------------------------- |
---|
1137 | |
---|
1138 | // Calculate the difference between vertex 0 of the auxiliary |
---|
1139 | // triangle and the centroid of triangle k |
---|
1140 | dq0=stage_centroid_values[k0]-stage_centroid_values[k]; |
---|
1141 | |
---|
1142 | // Calculate differentials between the vertices |
---|
1143 | // of the auxiliary triangle (centroids of neighbouring triangles) |
---|
1144 | dq1=stage_centroid_values[k1]-stage_centroid_values[k0]; |
---|
1145 | dq2=stage_centroid_values[k2]-stage_centroid_values[k0]; |
---|
1146 | |
---|
1147 | // Calculate the gradient of stage on the auxiliary triangle |
---|
1148 | a = dy2*dq1 - dy1*dq2; |
---|
1149 | a /= area2; |
---|
1150 | b = dx1*dq2 - dx2*dq1; |
---|
1151 | b /= area2; |
---|
1152 | |
---|
1153 | // Calculate provisional jumps in stage from the centroid |
---|
1154 | // of triangle k to its vertices, to be limited |
---|
1155 | dqv[0]=a*dxv0+b*dyv0; |
---|
1156 | dqv[1]=a*dxv1+b*dyv1; |
---|
1157 | dqv[2]=a*dxv2+b*dyv2; |
---|
1158 | |
---|
1159 | // Now we want to find min and max of the centroid and the |
---|
1160 | // vertices of the auxiliary triangle and compute jumps |
---|
1161 | // from the centroid to the min and max |
---|
1162 | find_qmin_and_qmax(dq0,dq1,dq2,&qmin,&qmax); |
---|
1163 | |
---|
1164 | // Playing with dry wet interface |
---|
1165 | //hmin = qmin; |
---|
1166 | //beta_tmp = beta_w_dry; |
---|
1167 | //if (hmin>minimum_allowed_height) |
---|
1168 | beta_tmp = beta_w_dry + (beta_w - beta_w_dry) * hfactor; |
---|
1169 | |
---|
1170 | //printf("min_alled_height = %f\n",minimum_allowed_height); |
---|
1171 | //printf("hmin = %f\n",hmin); |
---|
1172 | //printf("beta_w = %f\n",beta_w); |
---|
1173 | //printf("beta_tmp = %f\n",beta_tmp); |
---|
1174 | // Limit the gradient |
---|
1175 | limit_gradient(dqv,qmin,qmax,beta_tmp); |
---|
1176 | |
---|
1177 | for (i=0;i<3;i++) |
---|
1178 | stage_vertex_values[k3+i]=stage_centroid_values[k]+dqv[i]; |
---|
1179 | |
---|
1180 | |
---|
1181 | //----------------------------------- |
---|
1182 | // xmomentum |
---|
1183 | //----------------------------------- |
---|
1184 | |
---|
1185 | // Calculate the difference between vertex 0 of the auxiliary |
---|
1186 | // triangle and the centroid of triangle k |
---|
1187 | dq0=xmom_centroid_values[k0]-xmom_centroid_values[k]; |
---|
1188 | |
---|
1189 | // Calculate differentials between the vertices |
---|
1190 | // of the auxiliary triangle |
---|
1191 | dq1=xmom_centroid_values[k1]-xmom_centroid_values[k0]; |
---|
1192 | dq2=xmom_centroid_values[k2]-xmom_centroid_values[k0]; |
---|
1193 | |
---|
1194 | // Calculate the gradient of xmom on the auxiliary triangle |
---|
1195 | a = dy2*dq1 - dy1*dq2; |
---|
1196 | a /= area2; |
---|
1197 | b = dx1*dq2 - dx2*dq1; |
---|
1198 | b /= area2; |
---|
1199 | |
---|
1200 | // Calculate provisional jumps in stage from the centroid |
---|
1201 | // of triangle k to its vertices, to be limited |
---|
1202 | dqv[0]=a*dxv0+b*dyv0; |
---|
1203 | dqv[1]=a*dxv1+b*dyv1; |
---|
1204 | dqv[2]=a*dxv2+b*dyv2; |
---|
1205 | |
---|
1206 | // Now we want to find min and max of the centroid and the |
---|
1207 | // vertices of the auxiliary triangle and compute jumps |
---|
1208 | // from the centroid to the min and max |
---|
1209 | find_qmin_and_qmax(dq0,dq1,dq2,&qmin,&qmax); |
---|
1210 | //beta_tmp = beta_uh; |
---|
1211 | //if (hmin<minimum_allowed_height) |
---|
1212 | //beta_tmp = beta_uh_dry; |
---|
1213 | beta_tmp = beta_uh_dry + (beta_uh - beta_uh_dry) * hfactor; |
---|
1214 | |
---|
1215 | // Limit the gradient |
---|
1216 | limit_gradient(dqv,qmin,qmax,beta_tmp); |
---|
1217 | |
---|
1218 | for (i=0;i<3;i++) |
---|
1219 | xmom_vertex_values[k3+i]=xmom_centroid_values[k]+dqv[i]; |
---|
1220 | |
---|
1221 | |
---|
1222 | //----------------------------------- |
---|
1223 | // ymomentum |
---|
1224 | //----------------------------------- |
---|
1225 | |
---|
1226 | // Calculate the difference between vertex 0 of the auxiliary |
---|
1227 | // triangle and the centroid of triangle k |
---|
1228 | dq0=ymom_centroid_values[k0]-ymom_centroid_values[k]; |
---|
1229 | |
---|
1230 | // Calculate differentials between the vertices |
---|
1231 | // of the auxiliary triangle |
---|
1232 | dq1=ymom_centroid_values[k1]-ymom_centroid_values[k0]; |
---|
1233 | dq2=ymom_centroid_values[k2]-ymom_centroid_values[k0]; |
---|
1234 | |
---|
1235 | // Calculate the gradient of xmom on the auxiliary triangle |
---|
1236 | a = dy2*dq1 - dy1*dq2; |
---|
1237 | a /= area2; |
---|
1238 | b = dx1*dq2 - dx2*dq1; |
---|
1239 | b /= area2; |
---|
1240 | |
---|
1241 | // Calculate provisional jumps in stage from the centroid |
---|
1242 | // of triangle k to its vertices, to be limited |
---|
1243 | dqv[0]=a*dxv0+b*dyv0; |
---|
1244 | dqv[1]=a*dxv1+b*dyv1; |
---|
1245 | dqv[2]=a*dxv2+b*dyv2; |
---|
1246 | |
---|
1247 | // Now we want to find min and max of the centroid and the |
---|
1248 | // vertices of the auxiliary triangle and compute jumps |
---|
1249 | // from the centroid to the min and max |
---|
1250 | find_qmin_and_qmax(dq0,dq1,dq2,&qmin,&qmax); |
---|
1251 | |
---|
1252 | //beta_tmp = beta_vh; |
---|
1253 | // |
---|
1254 | //if (hmin<minimum_allowed_height) |
---|
1255 | //beta_tmp = beta_vh_dry; |
---|
1256 | beta_tmp = beta_vh_dry + (beta_vh - beta_vh_dry) * hfactor; |
---|
1257 | |
---|
1258 | // Limit the gradient |
---|
1259 | limit_gradient(dqv,qmin,qmax,beta_tmp); |
---|
1260 | |
---|
1261 | for (i=0;i<3;i++) |
---|
1262 | ymom_vertex_values[k3+i]=ymom_centroid_values[k]+dqv[i]; |
---|
1263 | |
---|
1264 | } // End number_of_boundaries <=1 |
---|
1265 | else{ |
---|
1266 | |
---|
1267 | //============================================== |
---|
1268 | // Number of boundaries == 2 |
---|
1269 | //============================================== |
---|
1270 | |
---|
1271 | // One internal neighbour and gradient is in direction of the neighbour's centroid |
---|
1272 | |
---|
1273 | // Find the only internal neighbour (k1?) |
---|
1274 | for (k2=k3;k2<k3+3;k2++){ |
---|
1275 | // Find internal neighbour of triangle k |
---|
1276 | // k2 indexes the edges of triangle k |
---|
1277 | |
---|
1278 | if (surrogate_neighbours[k2]!=k) |
---|
1279 | break; |
---|
1280 | } |
---|
1281 | |
---|
1282 | if ((k2==k3+3)) { |
---|
1283 | // If we didn't find an internal neighbour |
---|
1284 | PyErr_SetString(PyExc_RuntimeError, |
---|
1285 | "shallow_water_ext.c: Internal neighbour not found"); |
---|
1286 | return -1; |
---|
1287 | } |
---|
1288 | |
---|
1289 | k1=surrogate_neighbours[k2]; |
---|
1290 | |
---|
1291 | // The coordinates of the triangle are already (x,y). |
---|
1292 | // Get centroid of the neighbour (x1,y1) |
---|
1293 | coord_index=2*k1; |
---|
1294 | x1=centroid_coordinates[coord_index]; |
---|
1295 | y1=centroid_coordinates[coord_index+1]; |
---|
1296 | |
---|
1297 | // Compute x- and y- distances between the centroid of |
---|
1298 | // triangle k and that of its neighbour |
---|
1299 | dx1=x1-x; dy1=y1-y; |
---|
1300 | |
---|
1301 | // Set area2 as the square of the distance |
---|
1302 | area2=dx1*dx1+dy1*dy1; |
---|
1303 | |
---|
1304 | // Set dx2=(x1-x0)/((x1-x0)^2+(y1-y0)^2) |
---|
1305 | // and dy2=(y1-y0)/((x1-x0)^2+(y1-y0)^2) which |
---|
1306 | // respectively correspond to the x- and y- gradients |
---|
1307 | // of the conserved quantities |
---|
1308 | dx2=1.0/area2; |
---|
1309 | dy2=dx2*dy1; |
---|
1310 | dx2*=dx1; |
---|
1311 | |
---|
1312 | |
---|
1313 | //----------------------------------- |
---|
1314 | // stage |
---|
1315 | //----------------------------------- |
---|
1316 | |
---|
1317 | // Compute differentials |
---|
1318 | dq1=stage_centroid_values[k1]-stage_centroid_values[k]; |
---|
1319 | |
---|
1320 | // Calculate the gradient between the centroid of triangle k |
---|
1321 | // and that of its neighbour |
---|
1322 | a=dq1*dx2; |
---|
1323 | b=dq1*dy2; |
---|
1324 | |
---|
1325 | // Calculate provisional vertex jumps, to be limited |
---|
1326 | dqv[0]=a*dxv0+b*dyv0; |
---|
1327 | dqv[1]=a*dxv1+b*dyv1; |
---|
1328 | dqv[2]=a*dxv2+b*dyv2; |
---|
1329 | |
---|
1330 | // Now limit the jumps |
---|
1331 | if (dq1>=0.0){ |
---|
1332 | qmin=0.0; |
---|
1333 | qmax=dq1; |
---|
1334 | } |
---|
1335 | else{ |
---|
1336 | qmin=dq1; |
---|
1337 | qmax=0.0; |
---|
1338 | } |
---|
1339 | |
---|
1340 | // Limit the gradient |
---|
1341 | limit_gradient(dqv,qmin,qmax,beta_w); |
---|
1342 | |
---|
1343 | for (i=0;i<3;i++) |
---|
1344 | stage_vertex_values[k3+i]=stage_centroid_values[k]+dqv[i]; |
---|
1345 | |
---|
1346 | |
---|
1347 | //----------------------------------- |
---|
1348 | // xmomentum |
---|
1349 | //----------------------------------- |
---|
1350 | |
---|
1351 | // Compute differentials |
---|
1352 | dq1=xmom_centroid_values[k1]-xmom_centroid_values[k]; |
---|
1353 | |
---|
1354 | // Calculate the gradient between the centroid of triangle k |
---|
1355 | // and that of its neighbour |
---|
1356 | a=dq1*dx2; |
---|
1357 | b=dq1*dy2; |
---|
1358 | |
---|
1359 | // Calculate provisional vertex jumps, to be limited |
---|
1360 | dqv[0]=a*dxv0+b*dyv0; |
---|
1361 | dqv[1]=a*dxv1+b*dyv1; |
---|
1362 | dqv[2]=a*dxv2+b*dyv2; |
---|
1363 | |
---|
1364 | // Now limit the jumps |
---|
1365 | if (dq1>=0.0){ |
---|
1366 | qmin=0.0; |
---|
1367 | qmax=dq1; |
---|
1368 | } |
---|
1369 | else{ |
---|
1370 | qmin=dq1; |
---|
1371 | qmax=0.0; |
---|
1372 | } |
---|
1373 | |
---|
1374 | // Limit the gradient |
---|
1375 | limit_gradient(dqv,qmin,qmax,beta_w); |
---|
1376 | |
---|
1377 | for (i=0;i<3;i++) |
---|
1378 | xmom_vertex_values[k3+i]=xmom_centroid_values[k]+dqv[i]; |
---|
1379 | |
---|
1380 | |
---|
1381 | //----------------------------------- |
---|
1382 | // ymomentum |
---|
1383 | //----------------------------------- |
---|
1384 | |
---|
1385 | // Compute differentials |
---|
1386 | dq1=ymom_centroid_values[k1]-ymom_centroid_values[k]; |
---|
1387 | |
---|
1388 | // Calculate the gradient between the centroid of triangle k |
---|
1389 | // and that of its neighbour |
---|
1390 | a=dq1*dx2; |
---|
1391 | b=dq1*dy2; |
---|
1392 | |
---|
1393 | // Calculate provisional vertex jumps, to be limited |
---|
1394 | dqv[0]=a*dxv0+b*dyv0; |
---|
1395 | dqv[1]=a*dxv1+b*dyv1; |
---|
1396 | dqv[2]=a*dxv2+b*dyv2; |
---|
1397 | |
---|
1398 | // Now limit the jumps |
---|
1399 | if (dq1>=0.0){ |
---|
1400 | qmin=0.0; |
---|
1401 | qmax=dq1; |
---|
1402 | } |
---|
1403 | else{ |
---|
1404 | qmin=dq1; |
---|
1405 | qmax=0.0; |
---|
1406 | } |
---|
1407 | |
---|
1408 | // Limit the gradient |
---|
1409 | limit_gradient(dqv,qmin,qmax,beta_w); |
---|
1410 | |
---|
1411 | for (i=0;i<3;i++) |
---|
1412 | ymom_vertex_values[k3+i]=ymom_centroid_values[k]+dqv[i]; |
---|
1413 | |
---|
1414 | } // else [number_of_boundaries==2] |
---|
1415 | } // for k=0 to number_of_elements-1 |
---|
1416 | |
---|
1417 | return 0; |
---|
1418 | } |
---|
1419 | |
---|
1420 | |
---|
1421 | PyObject *extrapolate_second_order_sw(PyObject *self, PyObject *args) { |
---|
1422 | /*Compute the vertex values based on a linear reconstruction |
---|
1423 | on each triangle |
---|
1424 | |
---|
1425 | These values are calculated as follows: |
---|
1426 | 1) For each triangle not adjacent to a boundary, we consider the |
---|
1427 | auxiliary triangle formed by the centroids of its three |
---|
1428 | neighbours. |
---|
1429 | 2) For each conserved quantity, we integrate around the auxiliary |
---|
1430 | triangle's boundary the product of the quantity and the outward |
---|
1431 | normal vector. Dividing by the triangle area gives (a,b), the |
---|
1432 | average of the vector (q_x,q_y) on the auxiliary triangle. |
---|
1433 | We suppose that the linear reconstruction on the original |
---|
1434 | triangle has gradient (a,b). |
---|
1435 | 3) Provisional vertex jumps dqv[0,1,2] are computed and these are |
---|
1436 | then limited by calling the functions find_qmin_and_qmax and |
---|
1437 | limit_gradient |
---|
1438 | |
---|
1439 | Python call: |
---|
1440 | extrapolate_second_order_sw(domain.surrogate_neighbours, |
---|
1441 | domain.number_of_boundaries |
---|
1442 | domain.centroid_coordinates, |
---|
1443 | Stage.centroid_values |
---|
1444 | Xmom.centroid_values |
---|
1445 | Ymom.centroid_values |
---|
1446 | domain.vertex_coordinates, |
---|
1447 | Stage.vertex_values, |
---|
1448 | Xmom.vertex_values, |
---|
1449 | Ymom.vertex_values) |
---|
1450 | |
---|
1451 | Post conditions: |
---|
1452 | The vertices of each triangle have values from a |
---|
1453 | limited linear reconstruction |
---|
1454 | based on centroid values |
---|
1455 | |
---|
1456 | */ |
---|
1457 | PyArrayObject *surrogate_neighbours, |
---|
1458 | *number_of_boundaries, |
---|
1459 | *centroid_coordinates, |
---|
1460 | *stage_centroid_values, |
---|
1461 | *xmom_centroid_values, |
---|
1462 | *ymom_centroid_values, |
---|
1463 | *elevation_centroid_values, |
---|
1464 | *vertex_coordinates, |
---|
1465 | *stage_vertex_values, |
---|
1466 | *xmom_vertex_values, |
---|
1467 | *ymom_vertex_values, |
---|
1468 | *elevation_vertex_values; |
---|
1469 | |
---|
1470 | PyObject *domain; |
---|
1471 | |
---|
1472 | |
---|
1473 | double beta_w, beta_w_dry, beta_uh, beta_uh_dry, beta_vh, beta_vh_dry; |
---|
1474 | double minimum_allowed_height, epsilon; |
---|
1475 | int optimise_dry_cells, number_of_elements, e; |
---|
1476 | |
---|
1477 | // Provisional jumps from centroids to v'tices and safety factor re limiting |
---|
1478 | // by which these jumps are limited |
---|
1479 | // Convert Python arguments to C |
---|
1480 | if (!PyArg_ParseTuple(args, "OOOOOOOOOOOOOi", |
---|
1481 | &domain, |
---|
1482 | &surrogate_neighbours, |
---|
1483 | &number_of_boundaries, |
---|
1484 | ¢roid_coordinates, |
---|
1485 | &stage_centroid_values, |
---|
1486 | &xmom_centroid_values, |
---|
1487 | &ymom_centroid_values, |
---|
1488 | &elevation_centroid_values, |
---|
1489 | &vertex_coordinates, |
---|
1490 | &stage_vertex_values, |
---|
1491 | &xmom_vertex_values, |
---|
1492 | &ymom_vertex_values, |
---|
1493 | &elevation_vertex_values, |
---|
1494 | &optimise_dry_cells)) { |
---|
1495 | |
---|
1496 | PyErr_SetString(PyExc_RuntimeError, |
---|
1497 | "Input arguments to extrapolate_second_order_sw failed"); |
---|
1498 | return NULL; |
---|
1499 | } |
---|
1500 | |
---|
1501 | // Get the safety factor beta_w, set in the config.py file. |
---|
1502 | // This is used in the limiting process |
---|
1503 | |
---|
1504 | |
---|
1505 | beta_w = get_python_double(domain,"beta_w"); |
---|
1506 | beta_w_dry = get_python_double(domain,"beta_w_dry"); |
---|
1507 | beta_uh = get_python_double(domain,"beta_uh"); |
---|
1508 | beta_uh_dry = get_python_double(domain,"beta_uh_dry"); |
---|
1509 | beta_vh = get_python_double(domain,"beta_vh"); |
---|
1510 | beta_vh_dry = get_python_double(domain,"beta_vh_dry"); |
---|
1511 | |
---|
1512 | minimum_allowed_height = get_python_double(domain,"minimum_allowed_height"); |
---|
1513 | epsilon = get_python_double(domain,"epsilon"); |
---|
1514 | |
---|
1515 | number_of_elements = stage_centroid_values -> dimensions[0]; |
---|
1516 | |
---|
1517 | // Call underlying computational routine |
---|
1518 | e = _extrapolate_second_order_sw(number_of_elements, |
---|
1519 | epsilon, |
---|
1520 | minimum_allowed_height, |
---|
1521 | beta_w, |
---|
1522 | beta_w_dry, |
---|
1523 | beta_uh, |
---|
1524 | beta_uh_dry, |
---|
1525 | beta_vh, |
---|
1526 | beta_vh_dry, |
---|
1527 | (long*) surrogate_neighbours -> data, |
---|
1528 | (long*) number_of_boundaries -> data, |
---|
1529 | (double*) centroid_coordinates -> data, |
---|
1530 | (double*) stage_centroid_values -> data, |
---|
1531 | (double*) xmom_centroid_values -> data, |
---|
1532 | (double*) ymom_centroid_values -> data, |
---|
1533 | (double*) elevation_centroid_values -> data, |
---|
1534 | (double*) vertex_coordinates -> data, |
---|
1535 | (double*) stage_vertex_values -> data, |
---|
1536 | (double*) xmom_vertex_values -> data, |
---|
1537 | (double*) ymom_vertex_values -> data, |
---|
1538 | (double*) elevation_vertex_values -> data, |
---|
1539 | optimise_dry_cells); |
---|
1540 | if (e == -1) { |
---|
1541 | // Use error string set inside computational routine |
---|
1542 | return NULL; |
---|
1543 | } |
---|
1544 | |
---|
1545 | |
---|
1546 | return Py_BuildValue(""); |
---|
1547 | |
---|
1548 | }// extrapolate_second-order_sw |
---|
1549 | |
---|
1550 | |
---|
1551 | |
---|
1552 | |
---|
1553 | PyObject *rotate(PyObject *self, PyObject *args, PyObject *kwargs) { |
---|
1554 | // |
---|
1555 | // r = rotate(q, normal, direction=1) |
---|
1556 | // |
---|
1557 | // Where q is assumed to be a Float numeric array of length 3 and |
---|
1558 | // normal a Float numeric array of length 2. |
---|
1559 | |
---|
1560 | // FIXME(Ole): I don't think this is used anymore |
---|
1561 | |
---|
1562 | PyObject *Q, *Normal; |
---|
1563 | PyArrayObject *q, *r, *normal; |
---|
1564 | |
---|
1565 | static char *argnames[] = {"q", "normal", "direction", NULL}; |
---|
1566 | int dimensions[1], i, direction=1; |
---|
1567 | double n1, n2; |
---|
1568 | |
---|
1569 | // Convert Python arguments to C |
---|
1570 | if (!PyArg_ParseTupleAndKeywords(args, kwargs, "OO|i", argnames, |
---|
1571 | &Q, &Normal, &direction)) { |
---|
1572 | PyErr_SetString(PyExc_RuntimeError, "shallow_water_ext.c: rotate could not parse input arguments"); |
---|
1573 | return NULL; |
---|
1574 | } |
---|
1575 | |
---|
1576 | // Input checks (convert sequences into numeric arrays) |
---|
1577 | q = (PyArrayObject *) |
---|
1578 | PyArray_ContiguousFromObject(Q, PyArray_DOUBLE, 0, 0); |
---|
1579 | normal = (PyArrayObject *) |
---|
1580 | PyArray_ContiguousFromObject(Normal, PyArray_DOUBLE, 0, 0); |
---|
1581 | |
---|
1582 | |
---|
1583 | if (normal -> dimensions[0] != 2) { |
---|
1584 | PyErr_SetString(PyExc_RuntimeError, "Normal vector must have 2 components"); |
---|
1585 | return NULL; |
---|
1586 | } |
---|
1587 | |
---|
1588 | // Allocate space for return vector r (don't DECREF) |
---|
1589 | dimensions[0] = 3; |
---|
1590 | r = (PyArrayObject *) PyArray_FromDims(1, dimensions, PyArray_DOUBLE); |
---|
1591 | |
---|
1592 | // Copy |
---|
1593 | for (i=0; i<3; i++) { |
---|
1594 | ((double *) (r -> data))[i] = ((double *) (q -> data))[i]; |
---|
1595 | } |
---|
1596 | |
---|
1597 | // Get normal and direction |
---|
1598 | n1 = ((double *) normal -> data)[0]; |
---|
1599 | n2 = ((double *) normal -> data)[1]; |
---|
1600 | if (direction == -1) n2 = -n2; |
---|
1601 | |
---|
1602 | // Rotate |
---|
1603 | _rotate((double *) r -> data, n1, n2); |
---|
1604 | |
---|
1605 | // Release numeric arrays |
---|
1606 | Py_DECREF(q); |
---|
1607 | Py_DECREF(normal); |
---|
1608 | |
---|
1609 | // Return result using PyArray to avoid memory leak |
---|
1610 | return PyArray_Return(r); |
---|
1611 | } |
---|
1612 | |
---|
1613 | |
---|
1614 | // Computational function for flux computation |
---|
1615 | double _compute_fluxes_central(int number_of_elements, |
---|
1616 | double timestep, |
---|
1617 | double epsilon, |
---|
1618 | double H0, |
---|
1619 | double g, |
---|
1620 | long* neighbours, |
---|
1621 | long* neighbour_edges, |
---|
1622 | double* normals, |
---|
1623 | double* edgelengths, |
---|
1624 | double* radii, |
---|
1625 | double* areas, |
---|
1626 | long* tri_full_flag, |
---|
1627 | double* stage_edge_values, |
---|
1628 | double* xmom_edge_values, |
---|
1629 | double* ymom_edge_values, |
---|
1630 | double* bed_edge_values, |
---|
1631 | double* stage_boundary_values, |
---|
1632 | double* xmom_boundary_values, |
---|
1633 | double* ymom_boundary_values, |
---|
1634 | double* stage_explicit_update, |
---|
1635 | double* xmom_explicit_update, |
---|
1636 | double* ymom_explicit_update, |
---|
1637 | long* already_computed_flux, |
---|
1638 | double* max_speed_array, |
---|
1639 | int optimise_dry_cells) { |
---|
1640 | |
---|
1641 | // Local variables |
---|
1642 | double max_speed, length, area, zl, zr; |
---|
1643 | int k, i, m, n; |
---|
1644 | int ki, nm=0, ki2; // Index shorthands |
---|
1645 | |
---|
1646 | // Workspace (making them static actually made function slightly slower (Ole)) |
---|
1647 | double ql[3], qr[3], edgeflux[3]; // Work array for summing up fluxes |
---|
1648 | |
---|
1649 | static long call=1; // Static local variable flagging already computed flux |
---|
1650 | |
---|
1651 | |
---|
1652 | // Start computation |
---|
1653 | call++; // Flag 'id' of flux calculation for this timestep |
---|
1654 | |
---|
1655 | // Set explicit_update to zero for all conserved_quantities. |
---|
1656 | // This assumes compute_fluxes called before forcing terms |
---|
1657 | for (k=0; k<number_of_elements; k++) { |
---|
1658 | stage_explicit_update[k]=0.0; |
---|
1659 | xmom_explicit_update[k]=0.0; |
---|
1660 | ymom_explicit_update[k]=0.0; |
---|
1661 | } |
---|
1662 | |
---|
1663 | // For all triangles |
---|
1664 | for (k=0; k<number_of_elements; k++) { |
---|
1665 | |
---|
1666 | // Loop through neighbours and compute edge flux for each |
---|
1667 | for (i=0; i<3; i++) { |
---|
1668 | ki = k*3+i; // Linear index (triangle k, edge i) |
---|
1669 | |
---|
1670 | if (already_computed_flux[ki] == call) |
---|
1671 | // We've already computed the flux across this edge |
---|
1672 | continue; |
---|
1673 | |
---|
1674 | |
---|
1675 | ql[0] = stage_edge_values[ki]; |
---|
1676 | ql[1] = xmom_edge_values[ki]; |
---|
1677 | ql[2] = ymom_edge_values[ki]; |
---|
1678 | zl = bed_edge_values[ki]; |
---|
1679 | |
---|
1680 | // Quantities at neighbour on nearest face |
---|
1681 | n = neighbours[ki]; |
---|
1682 | if (n < 0) { |
---|
1683 | // Neighbour is a boundary condition |
---|
1684 | m = -n-1; // Convert negative flag to boundary index |
---|
1685 | |
---|
1686 | qr[0] = stage_boundary_values[m]; |
---|
1687 | qr[1] = xmom_boundary_values[m]; |
---|
1688 | qr[2] = ymom_boundary_values[m]; |
---|
1689 | zr = zl; // Extend bed elevation to boundary |
---|
1690 | } else { |
---|
1691 | // Neighbour is a real element |
---|
1692 | m = neighbour_edges[ki]; |
---|
1693 | nm = n*3+m; // Linear index (triangle n, edge m) |
---|
1694 | |
---|
1695 | qr[0] = stage_edge_values[nm]; |
---|
1696 | qr[1] = xmom_edge_values[nm]; |
---|
1697 | qr[2] = ymom_edge_values[nm]; |
---|
1698 | zr = bed_edge_values[nm]; |
---|
1699 | } |
---|
1700 | |
---|
1701 | |
---|
1702 | if (optimise_dry_cells) { |
---|
1703 | // Check if flux calculation is necessary across this edge |
---|
1704 | // This check will exclude dry cells. |
---|
1705 | // This will also optimise cases where zl != zr as |
---|
1706 | // long as both are dry |
---|
1707 | |
---|
1708 | if ( fabs(ql[0] - zl) < epsilon && |
---|
1709 | fabs(qr[0] - zr) < epsilon ) { |
---|
1710 | // Cell boundary is dry |
---|
1711 | |
---|
1712 | already_computed_flux[ki] = call; // #k Done |
---|
1713 | if (n>=0) |
---|
1714 | already_computed_flux[nm] = call; // #n Done |
---|
1715 | |
---|
1716 | max_speed = 0.0; |
---|
1717 | continue; |
---|
1718 | } |
---|
1719 | } |
---|
1720 | |
---|
1721 | |
---|
1722 | // Outward pointing normal vector (domain.normals[k, 2*i:2*i+2]) |
---|
1723 | ki2 = 2*ki; //k*6 + i*2 |
---|
1724 | |
---|
1725 | // Edge flux computation (triangle k, edge i) |
---|
1726 | _flux_function_central(ql, qr, zl, zr, |
---|
1727 | normals[ki2], normals[ki2+1], |
---|
1728 | epsilon, H0, g, |
---|
1729 | edgeflux, &max_speed); |
---|
1730 | |
---|
1731 | |
---|
1732 | // Multiply edgeflux by edgelength |
---|
1733 | length = edgelengths[ki]; |
---|
1734 | edgeflux[0] *= length; |
---|
1735 | edgeflux[1] *= length; |
---|
1736 | edgeflux[2] *= length; |
---|
1737 | |
---|
1738 | |
---|
1739 | // Update triangle k with flux from edge i |
---|
1740 | stage_explicit_update[k] -= edgeflux[0]; |
---|
1741 | xmom_explicit_update[k] -= edgeflux[1]; |
---|
1742 | ymom_explicit_update[k] -= edgeflux[2]; |
---|
1743 | |
---|
1744 | already_computed_flux[ki] = call; // #k Done |
---|
1745 | |
---|
1746 | |
---|
1747 | // Update neighbour n with same flux but reversed sign |
---|
1748 | if (n>=0) { |
---|
1749 | stage_explicit_update[n] += edgeflux[0]; |
---|
1750 | xmom_explicit_update[n] += edgeflux[1]; |
---|
1751 | ymom_explicit_update[n] += edgeflux[2]; |
---|
1752 | |
---|
1753 | already_computed_flux[nm] = call; // #n Done |
---|
1754 | } |
---|
1755 | |
---|
1756 | |
---|
1757 | // Update timestep based on edge i and possibly neighbour n |
---|
1758 | if (tri_full_flag[k] == 1) { |
---|
1759 | if (max_speed > epsilon) { |
---|
1760 | |
---|
1761 | // Apply CFL condition for triangles joining this edge (triangle k and triangle n) |
---|
1762 | |
---|
1763 | // CFL for triangle k |
---|
1764 | timestep = min(timestep, radii[k]/max_speed); |
---|
1765 | |
---|
1766 | if (n>=0) |
---|
1767 | // Apply CFL condition for neigbour n (which is on the ith edge of triangle k) |
---|
1768 | timestep = min(timestep, radii[n]/max_speed); |
---|
1769 | |
---|
1770 | // Ted Rigby's suggested less conservative version |
---|
1771 | //if (n>=0) { |
---|
1772 | // timestep = min(timestep, (radii[k]+radii[n])/max_speed); |
---|
1773 | //} else { |
---|
1774 | // timestep = min(timestep, radii[k]/max_speed); |
---|
1775 | // } |
---|
1776 | } |
---|
1777 | } |
---|
1778 | |
---|
1779 | } // End edge i (and neighbour n) |
---|
1780 | |
---|
1781 | |
---|
1782 | // Normalise triangle k by area and store for when all conserved |
---|
1783 | // quantities get updated |
---|
1784 | area = areas[k]; |
---|
1785 | stage_explicit_update[k] /= area; |
---|
1786 | xmom_explicit_update[k] /= area; |
---|
1787 | ymom_explicit_update[k] /= area; |
---|
1788 | |
---|
1789 | |
---|
1790 | // Keep track of maximal speeds |
---|
1791 | max_speed_array[k] = max_speed; |
---|
1792 | |
---|
1793 | } // End triangle k |
---|
1794 | |
---|
1795 | |
---|
1796 | |
---|
1797 | return timestep; |
---|
1798 | } |
---|
1799 | |
---|
1800 | //========================================================================= |
---|
1801 | // Python Glue |
---|
1802 | //========================================================================= |
---|
1803 | |
---|
1804 | PyObject *compute_fluxes_ext_central_new(PyObject *self, PyObject *args) { |
---|
1805 | /*Compute all fluxes and the timestep suitable for all volumes |
---|
1806 | in domain. |
---|
1807 | |
---|
1808 | Compute total flux for each conserved quantity using "flux_function_central" |
---|
1809 | |
---|
1810 | Fluxes across each edge are scaled by edgelengths and summed up |
---|
1811 | Resulting flux is then scaled by area and stored in |
---|
1812 | explicit_update for each of the three conserved quantities |
---|
1813 | stage, xmomentum and ymomentum |
---|
1814 | |
---|
1815 | The maximal allowable speed computed by the flux_function for each volume |
---|
1816 | is converted to a timestep that must not be exceeded. The minimum of |
---|
1817 | those is computed as the next overall timestep. |
---|
1818 | |
---|
1819 | Python call: |
---|
1820 | timestep = compute_fluxes(timestep, domain, stage, xmom, ymom, bed) |
---|
1821 | |
---|
1822 | |
---|
1823 | Post conditions: |
---|
1824 | domain.explicit_update is reset to computed flux values |
---|
1825 | returns timestep which is the largest step satisfying all volumes. |
---|
1826 | |
---|
1827 | |
---|
1828 | */ |
---|
1829 | |
---|
1830 | PyObject |
---|
1831 | *domain, |
---|
1832 | *stage, |
---|
1833 | *xmom, |
---|
1834 | *ymom, |
---|
1835 | *bed; |
---|
1836 | |
---|
1837 | PyArrayObject |
---|
1838 | *neighbours, |
---|
1839 | *neighbour_edges, |
---|
1840 | *normals, |
---|
1841 | *edgelengths, |
---|
1842 | *radii, |
---|
1843 | *areas, |
---|
1844 | *tri_full_flag, |
---|
1845 | *stage_edge_values, |
---|
1846 | *xmom_edge_values, |
---|
1847 | *ymom_edge_values, |
---|
1848 | *bed_edge_values, |
---|
1849 | *stage_boundary_values, |
---|
1850 | *xmom_boundary_values, |
---|
1851 | *ymom_boundary_values, |
---|
1852 | *stage_explicit_update, |
---|
1853 | *xmom_explicit_update, |
---|
1854 | *ymom_explicit_update, |
---|
1855 | *already_computed_flux, //Tracks whether the flux across an edge has already been computed |
---|
1856 | *max_speed_array; //Keeps track of max speeds for each triangle |
---|
1857 | |
---|
1858 | |
---|
1859 | double timestep, epsilon, H0, g; |
---|
1860 | int optimise_dry_cells; |
---|
1861 | |
---|
1862 | // Convert Python arguments to C |
---|
1863 | if (!PyArg_ParseTuple(args, "dOOOO", ×tep, &domain, &stage, &xmom, &ymom, &bed )) { |
---|
1864 | PyErr_SetString(PyExc_RuntimeError, "Input arguments failed"); |
---|
1865 | return NULL; |
---|
1866 | } |
---|
1867 | |
---|
1868 | epsilon = get_python_double(domain,"epsilon"); |
---|
1869 | H0 = get_python_double(domain,"H0"); |
---|
1870 | g = get_python_double(domain,"g"); |
---|
1871 | optimise_dry_cells = get_python_integer(domain,"optimse_dry_cells"); |
---|
1872 | |
---|
1873 | neighbours = get_consecutive_array(domain, "neighbours"); |
---|
1874 | neighbour_edges = get_consecutive_array(domain, "neighbour_edges"); |
---|
1875 | normals = get_consecutive_array(domain, "normals"); |
---|
1876 | edgelengths = get_consecutive_array(domain, "edge_lengths"); |
---|
1877 | radii = get_consecutive_array(domain, "radii"); |
---|
1878 | areas = get_consecutive_array(domain, "areas"); |
---|
1879 | tri_full_flag = get_consecutive_array(domain, "tri_full_flag"); |
---|
1880 | already_computed_flux = get_consecutive_array(domain, "already_computed_flux"); |
---|
1881 | max_speed_array = get_consecutive_array(domain, "max_speed"); |
---|
1882 | |
---|
1883 | stage_edge_values = get_consecutive_array(stage, "edge_values"); |
---|
1884 | xmom_edge_values = get_consecutive_array(xmom, "edge_values"); |
---|
1885 | ymom_edge_values = get_consecutive_array(ymom, "edge_values"); |
---|
1886 | bed_edge_values = get_consecutive_array(bed, "edge_values"); |
---|
1887 | |
---|
1888 | stage_boundary_values = get_consecutive_array(stage, "boundary_values"); |
---|
1889 | xmom_boundary_values = get_consecutive_array(xmom, "boundary_values"); |
---|
1890 | ymom_boundary_values = get_consecutive_array(ymom, "boundary_values"); |
---|
1891 | |
---|
1892 | stage_explicit_update = get_consecutive_array(stage, "explicit_update"); |
---|
1893 | xmom_explicit_update = get_consecutive_array(xmom, "explicit_update"); |
---|
1894 | ymom_explicit_update = get_consecutive_array(ymom, "explicit_update"); |
---|
1895 | |
---|
1896 | |
---|
1897 | int number_of_elements = stage_edge_values -> dimensions[0]; |
---|
1898 | |
---|
1899 | // Call underlying flux computation routine and update |
---|
1900 | // the explicit update arrays |
---|
1901 | timestep = _compute_fluxes_central(number_of_elements, |
---|
1902 | timestep, |
---|
1903 | epsilon, |
---|
1904 | H0, |
---|
1905 | g, |
---|
1906 | (long*) neighbours -> data, |
---|
1907 | (long*) neighbour_edges -> data, |
---|
1908 | (double*) normals -> data, |
---|
1909 | (double*) edgelengths -> data, |
---|
1910 | (double*) radii -> data, |
---|
1911 | (double*) areas -> data, |
---|
1912 | (long*) tri_full_flag -> data, |
---|
1913 | (double*) stage_edge_values -> data, |
---|
1914 | (double*) xmom_edge_values -> data, |
---|
1915 | (double*) ymom_edge_values -> data, |
---|
1916 | (double*) bed_edge_values -> data, |
---|
1917 | (double*) stage_boundary_values -> data, |
---|
1918 | (double*) xmom_boundary_values -> data, |
---|
1919 | (double*) ymom_boundary_values -> data, |
---|
1920 | (double*) stage_explicit_update -> data, |
---|
1921 | (double*) xmom_explicit_update -> data, |
---|
1922 | (double*) ymom_explicit_update -> data, |
---|
1923 | (long*) already_computed_flux -> data, |
---|
1924 | (double*) max_speed_array -> data, |
---|
1925 | optimise_dry_cells); |
---|
1926 | |
---|
1927 | Py_DECREF(neighbours); |
---|
1928 | Py_DECREF(neighbour_edges); |
---|
1929 | Py_DECREF(normals); |
---|
1930 | Py_DECREF(edgelengths); |
---|
1931 | Py_DECREF(radii); |
---|
1932 | Py_DECREF(areas); |
---|
1933 | Py_DECREF(tri_full_flag); |
---|
1934 | Py_DECREF(already_computed_flux); |
---|
1935 | Py_DECREF(max_speed_array); |
---|
1936 | Py_DECREF(stage_edge_values); |
---|
1937 | Py_DECREF(xmom_edge_values); |
---|
1938 | Py_DECREF(ymom_edge_values); |
---|
1939 | Py_DECREF(bed_edge_values); |
---|
1940 | Py_DECREF(stage_boundary_values); |
---|
1941 | Py_DECREF(xmom_boundary_values); |
---|
1942 | Py_DECREF(ymom_boundary_values); |
---|
1943 | Py_DECREF(stage_explicit_update); |
---|
1944 | Py_DECREF(xmom_explicit_update); |
---|
1945 | Py_DECREF(ymom_explicit_update); |
---|
1946 | |
---|
1947 | |
---|
1948 | // Return updated flux timestep |
---|
1949 | return Py_BuildValue("d", timestep); |
---|
1950 | } |
---|
1951 | |
---|
1952 | |
---|
1953 | |
---|
1954 | |
---|
1955 | |
---|
1956 | |
---|
1957 | PyObject *compute_fluxes_ext_central(PyObject *self, PyObject *args) { |
---|
1958 | /*Compute all fluxes and the timestep suitable for all volumes |
---|
1959 | in domain. |
---|
1960 | |
---|
1961 | Compute total flux for each conserved quantity using "flux_function_central" |
---|
1962 | |
---|
1963 | Fluxes across each edge are scaled by edgelengths and summed up |
---|
1964 | Resulting flux is then scaled by area and stored in |
---|
1965 | explicit_update for each of the three conserved quantities |
---|
1966 | stage, xmomentum and ymomentum |
---|
1967 | |
---|
1968 | The maximal allowable speed computed by the flux_function for each volume |
---|
1969 | is converted to a timestep that must not be exceeded. The minimum of |
---|
1970 | those is computed as the next overall timestep. |
---|
1971 | |
---|
1972 | Python call: |
---|
1973 | domain.timestep = compute_fluxes(timestep, |
---|
1974 | domain.epsilon, |
---|
1975 | domain.H0, |
---|
1976 | domain.g, |
---|
1977 | domain.neighbours, |
---|
1978 | domain.neighbour_edges, |
---|
1979 | domain.normals, |
---|
1980 | domain.edgelengths, |
---|
1981 | domain.radii, |
---|
1982 | domain.areas, |
---|
1983 | tri_full_flag, |
---|
1984 | Stage.edge_values, |
---|
1985 | Xmom.edge_values, |
---|
1986 | Ymom.edge_values, |
---|
1987 | Bed.edge_values, |
---|
1988 | Stage.boundary_values, |
---|
1989 | Xmom.boundary_values, |
---|
1990 | Ymom.boundary_values, |
---|
1991 | Stage.explicit_update, |
---|
1992 | Xmom.explicit_update, |
---|
1993 | Ymom.explicit_update, |
---|
1994 | already_computed_flux, |
---|
1995 | optimise_dry_cells) |
---|
1996 | |
---|
1997 | |
---|
1998 | Post conditions: |
---|
1999 | domain.explicit_update is reset to computed flux values |
---|
2000 | domain.timestep is set to the largest step satisfying all volumes. |
---|
2001 | |
---|
2002 | |
---|
2003 | */ |
---|
2004 | |
---|
2005 | |
---|
2006 | PyArrayObject *neighbours, *neighbour_edges, |
---|
2007 | *normals, *edgelengths, *radii, *areas, |
---|
2008 | *tri_full_flag, |
---|
2009 | *stage_edge_values, |
---|
2010 | *xmom_edge_values, |
---|
2011 | *ymom_edge_values, |
---|
2012 | *bed_edge_values, |
---|
2013 | *stage_boundary_values, |
---|
2014 | *xmom_boundary_values, |
---|
2015 | *ymom_boundary_values, |
---|
2016 | *stage_explicit_update, |
---|
2017 | *xmom_explicit_update, |
---|
2018 | *ymom_explicit_update, |
---|
2019 | *already_computed_flux, //Tracks whether the flux across an edge has already been computed |
---|
2020 | *max_speed_array; //Keeps track of max speeds for each triangle |
---|
2021 | |
---|
2022 | |
---|
2023 | double timestep, epsilon, H0, g; |
---|
2024 | int optimise_dry_cells; |
---|
2025 | |
---|
2026 | // Convert Python arguments to C |
---|
2027 | if (!PyArg_ParseTuple(args, "ddddOOOOOOOOOOOOOOOOOOOi", |
---|
2028 | ×tep, |
---|
2029 | &epsilon, |
---|
2030 | &H0, |
---|
2031 | &g, |
---|
2032 | &neighbours, |
---|
2033 | &neighbour_edges, |
---|
2034 | &normals, |
---|
2035 | &edgelengths, &radii, &areas, |
---|
2036 | &tri_full_flag, |
---|
2037 | &stage_edge_values, |
---|
2038 | &xmom_edge_values, |
---|
2039 | &ymom_edge_values, |
---|
2040 | &bed_edge_values, |
---|
2041 | &stage_boundary_values, |
---|
2042 | &xmom_boundary_values, |
---|
2043 | &ymom_boundary_values, |
---|
2044 | &stage_explicit_update, |
---|
2045 | &xmom_explicit_update, |
---|
2046 | &ymom_explicit_update, |
---|
2047 | &already_computed_flux, |
---|
2048 | &max_speed_array, |
---|
2049 | &optimise_dry_cells)) { |
---|
2050 | PyErr_SetString(PyExc_RuntimeError, "Input arguments failed"); |
---|
2051 | return NULL; |
---|
2052 | } |
---|
2053 | |
---|
2054 | |
---|
2055 | int number_of_elements = stage_edge_values -> dimensions[0]; |
---|
2056 | |
---|
2057 | // Call underlying flux computation routine and update |
---|
2058 | // the explicit update arrays |
---|
2059 | timestep = _compute_fluxes_central(number_of_elements, |
---|
2060 | timestep, |
---|
2061 | epsilon, |
---|
2062 | H0, |
---|
2063 | g, |
---|
2064 | (long*) neighbours -> data, |
---|
2065 | (long*) neighbour_edges -> data, |
---|
2066 | (double*) normals -> data, |
---|
2067 | (double*) edgelengths -> data, |
---|
2068 | (double*) radii -> data, |
---|
2069 | (double*) areas -> data, |
---|
2070 | (long*) tri_full_flag -> data, |
---|
2071 | (double*) stage_edge_values -> data, |
---|
2072 | (double*) xmom_edge_values -> data, |
---|
2073 | (double*) ymom_edge_values -> data, |
---|
2074 | (double*) bed_edge_values -> data, |
---|
2075 | (double*) stage_boundary_values -> data, |
---|
2076 | (double*) xmom_boundary_values -> data, |
---|
2077 | (double*) ymom_boundary_values -> data, |
---|
2078 | (double*) stage_explicit_update -> data, |
---|
2079 | (double*) xmom_explicit_update -> data, |
---|
2080 | (double*) ymom_explicit_update -> data, |
---|
2081 | (long*) already_computed_flux -> data, |
---|
2082 | (double*) max_speed_array -> data, |
---|
2083 | optimise_dry_cells); |
---|
2084 | |
---|
2085 | // Return updated flux timestep |
---|
2086 | return Py_BuildValue("d", timestep); |
---|
2087 | } |
---|
2088 | |
---|
2089 | |
---|
2090 | |
---|
2091 | |
---|
2092 | |
---|
2093 | PyObject *compute_fluxes_ext_kinetic(PyObject *self, PyObject *args) { |
---|
2094 | /*Compute all fluxes and the timestep suitable for all volumes |
---|
2095 | in domain. |
---|
2096 | |
---|
2097 | THIS IS AN EXPERIMENTAL FUNCTION - NORMALLY flux_function_central IS USED. |
---|
2098 | |
---|
2099 | Compute total flux for each conserved quantity using "flux_function_kinetic" |
---|
2100 | |
---|
2101 | Fluxes across each edge are scaled by edgelengths and summed up |
---|
2102 | Resulting flux is then scaled by area and stored in |
---|
2103 | explicit_update for each of the three conserved quantities |
---|
2104 | stage, xmomentum and ymomentum |
---|
2105 | |
---|
2106 | The maximal allowable speed computed by the flux_function for each volume |
---|
2107 | is converted to a timestep that must not be exceeded. The minimum of |
---|
2108 | those is computed as the next overall timestep. |
---|
2109 | |
---|
2110 | Python call: |
---|
2111 | domain.timestep = compute_fluxes(timestep, |
---|
2112 | domain.epsilon, |
---|
2113 | domain.H0, |
---|
2114 | domain.g, |
---|
2115 | domain.neighbours, |
---|
2116 | domain.neighbour_edges, |
---|
2117 | domain.normals, |
---|
2118 | domain.edgelengths, |
---|
2119 | domain.radii, |
---|
2120 | domain.areas, |
---|
2121 | Stage.edge_values, |
---|
2122 | Xmom.edge_values, |
---|
2123 | Ymom.edge_values, |
---|
2124 | Bed.edge_values, |
---|
2125 | Stage.boundary_values, |
---|
2126 | Xmom.boundary_values, |
---|
2127 | Ymom.boundary_values, |
---|
2128 | Stage.explicit_update, |
---|
2129 | Xmom.explicit_update, |
---|
2130 | Ymom.explicit_update, |
---|
2131 | already_computed_flux) |
---|
2132 | |
---|
2133 | |
---|
2134 | Post conditions: |
---|
2135 | domain.explicit_update is reset to computed flux values |
---|
2136 | domain.timestep is set to the largest step satisfying all volumes. |
---|
2137 | |
---|
2138 | |
---|
2139 | */ |
---|
2140 | |
---|
2141 | |
---|
2142 | PyArrayObject *neighbours, *neighbour_edges, |
---|
2143 | *normals, *edgelengths, *radii, *areas, |
---|
2144 | *tri_full_flag, |
---|
2145 | *stage_edge_values, |
---|
2146 | *xmom_edge_values, |
---|
2147 | *ymom_edge_values, |
---|
2148 | *bed_edge_values, |
---|
2149 | *stage_boundary_values, |
---|
2150 | *xmom_boundary_values, |
---|
2151 | *ymom_boundary_values, |
---|
2152 | *stage_explicit_update, |
---|
2153 | *xmom_explicit_update, |
---|
2154 | *ymom_explicit_update, |
---|
2155 | *already_computed_flux; // Tracks whether the flux across an edge has already been computed |
---|
2156 | |
---|
2157 | |
---|
2158 | // Local variables |
---|
2159 | double timestep, max_speed, epsilon, g, H0; |
---|
2160 | double normal[2], ql[3], qr[3], zl, zr; |
---|
2161 | double edgeflux[3]; //Work arrays for summing up fluxes |
---|
2162 | |
---|
2163 | int number_of_elements, k, i, m, n; |
---|
2164 | int ki, nm=0, ki2; //Index shorthands |
---|
2165 | static long call=1; |
---|
2166 | |
---|
2167 | |
---|
2168 | // Convert Python arguments to C |
---|
2169 | if (!PyArg_ParseTuple(args, "ddddOOOOOOOOOOOOOOOOOO", |
---|
2170 | ×tep, |
---|
2171 | &epsilon, |
---|
2172 | &H0, |
---|
2173 | &g, |
---|
2174 | &neighbours, |
---|
2175 | &neighbour_edges, |
---|
2176 | &normals, |
---|
2177 | &edgelengths, &radii, &areas, |
---|
2178 | &tri_full_flag, |
---|
2179 | &stage_edge_values, |
---|
2180 | &xmom_edge_values, |
---|
2181 | &ymom_edge_values, |
---|
2182 | &bed_edge_values, |
---|
2183 | &stage_boundary_values, |
---|
2184 | &xmom_boundary_values, |
---|
2185 | &ymom_boundary_values, |
---|
2186 | &stage_explicit_update, |
---|
2187 | &xmom_explicit_update, |
---|
2188 | &ymom_explicit_update, |
---|
2189 | &already_computed_flux)) { |
---|
2190 | PyErr_SetString(PyExc_RuntimeError, "Input arguments failed"); |
---|
2191 | return NULL; |
---|
2192 | } |
---|
2193 | number_of_elements = stage_edge_values -> dimensions[0]; |
---|
2194 | call++;//a static local variable to which already_computed_flux is compared |
---|
2195 | //set explicit_update to zero for all conserved_quantities. |
---|
2196 | //This assumes compute_fluxes called before forcing terms |
---|
2197 | for (k=0; k<number_of_elements; k++) { |
---|
2198 | ((double *) stage_explicit_update -> data)[k]=0.0; |
---|
2199 | ((double *) xmom_explicit_update -> data)[k]=0.0; |
---|
2200 | ((double *) ymom_explicit_update -> data)[k]=0.0; |
---|
2201 | } |
---|
2202 | //Loop through neighbours and compute edge flux for each |
---|
2203 | for (k=0; k<number_of_elements; k++) { |
---|
2204 | for (i=0; i<3; i++) { |
---|
2205 | ki = k*3+i; |
---|
2206 | if (((long *) already_computed_flux->data)[ki]==call)//we've already computed the flux across this edge |
---|
2207 | continue; |
---|
2208 | ql[0] = ((double *) stage_edge_values -> data)[ki]; |
---|
2209 | ql[1] = ((double *) xmom_edge_values -> data)[ki]; |
---|
2210 | ql[2] = ((double *) ymom_edge_values -> data)[ki]; |
---|
2211 | zl = ((double *) bed_edge_values -> data)[ki]; |
---|
2212 | |
---|
2213 | //Quantities at neighbour on nearest face |
---|
2214 | n = ((long *) neighbours -> data)[ki]; |
---|
2215 | if (n < 0) { |
---|
2216 | m = -n-1; //Convert negative flag to index |
---|
2217 | qr[0] = ((double *) stage_boundary_values -> data)[m]; |
---|
2218 | qr[1] = ((double *) xmom_boundary_values -> data)[m]; |
---|
2219 | qr[2] = ((double *) ymom_boundary_values -> data)[m]; |
---|
2220 | zr = zl; //Extend bed elevation to boundary |
---|
2221 | } else { |
---|
2222 | m = ((long *) neighbour_edges -> data)[ki]; |
---|
2223 | nm = n*3+m; |
---|
2224 | qr[0] = ((double *) stage_edge_values -> data)[nm]; |
---|
2225 | qr[1] = ((double *) xmom_edge_values -> data)[nm]; |
---|
2226 | qr[2] = ((double *) ymom_edge_values -> data)[nm]; |
---|
2227 | zr = ((double *) bed_edge_values -> data)[nm]; |
---|
2228 | } |
---|
2229 | // Outward pointing normal vector |
---|
2230 | // normal = domain.normals[k, 2*i:2*i+2] |
---|
2231 | ki2 = 2*ki; //k*6 + i*2 |
---|
2232 | normal[0] = ((double *) normals -> data)[ki2]; |
---|
2233 | normal[1] = ((double *) normals -> data)[ki2+1]; |
---|
2234 | //Edge flux computation |
---|
2235 | flux_function_kinetic(ql, qr, zl, zr, |
---|
2236 | normal[0], normal[1], |
---|
2237 | epsilon, H0, g, |
---|
2238 | edgeflux, &max_speed); |
---|
2239 | //update triangle k |
---|
2240 | ((long *) already_computed_flux->data)[ki]=call; |
---|
2241 | ((double *) stage_explicit_update -> data)[k] -= edgeflux[0]*((double *) edgelengths -> data)[ki]; |
---|
2242 | ((double *) xmom_explicit_update -> data)[k] -= edgeflux[1]*((double *) edgelengths -> data)[ki]; |
---|
2243 | ((double *) ymom_explicit_update -> data)[k] -= edgeflux[2]*((double *) edgelengths -> data)[ki]; |
---|
2244 | //update the neighbour n |
---|
2245 | if (n>=0){ |
---|
2246 | ((long *) already_computed_flux->data)[nm]=call; |
---|
2247 | ((double *) stage_explicit_update -> data)[n] += edgeflux[0]*((double *) edgelengths -> data)[nm]; |
---|
2248 | ((double *) xmom_explicit_update -> data)[n] += edgeflux[1]*((double *) edgelengths -> data)[nm]; |
---|
2249 | ((double *) ymom_explicit_update -> data)[n] += edgeflux[2]*((double *) edgelengths -> data)[nm]; |
---|
2250 | } |
---|
2251 | ///for (j=0; j<3; j++) { |
---|
2252 | ///flux[j] -= edgeflux[j]*((double *) edgelengths -> data)[ki]; |
---|
2253 | ///} |
---|
2254 | //Update timestep |
---|
2255 | //timestep = min(timestep, domain.radii[k]/max_speed) |
---|
2256 | //FIXME: SR Add parameter for CFL condition |
---|
2257 | if ( ((long *) tri_full_flag -> data)[k] == 1) { |
---|
2258 | if (max_speed > epsilon) { |
---|
2259 | timestep = min(timestep, ((double *) radii -> data)[k]/max_speed); |
---|
2260 | //maxspeed in flux_function is calculated as max(|u+a|,|u-a|) |
---|
2261 | if (n>=0) |
---|
2262 | timestep = min(timestep, ((double *) radii -> data)[n]/max_speed); |
---|
2263 | } |
---|
2264 | } |
---|
2265 | } // end for i |
---|
2266 | //Normalise by area and store for when all conserved |
---|
2267 | //quantities get updated |
---|
2268 | ((double *) stage_explicit_update -> data)[k] /= ((double *) areas -> data)[k]; |
---|
2269 | ((double *) xmom_explicit_update -> data)[k] /= ((double *) areas -> data)[k]; |
---|
2270 | ((double *) ymom_explicit_update -> data)[k] /= ((double *) areas -> data)[k]; |
---|
2271 | } //end for k |
---|
2272 | return Py_BuildValue("d", timestep); |
---|
2273 | } |
---|
2274 | |
---|
2275 | PyObject *protect(PyObject *self, PyObject *args) { |
---|
2276 | // |
---|
2277 | // protect(minimum_allowed_height, maximum_allowed_speed, wc, zc, xmomc, ymomc) |
---|
2278 | |
---|
2279 | |
---|
2280 | PyArrayObject |
---|
2281 | *wc, //Stage at centroids |
---|
2282 | *zc, //Elevation at centroids |
---|
2283 | *xmomc, //Momentums at centroids |
---|
2284 | *ymomc; |
---|
2285 | |
---|
2286 | |
---|
2287 | int N; |
---|
2288 | double minimum_allowed_height, maximum_allowed_speed, epsilon; |
---|
2289 | |
---|
2290 | // Convert Python arguments to C |
---|
2291 | if (!PyArg_ParseTuple(args, "dddOOOO", |
---|
2292 | &minimum_allowed_height, |
---|
2293 | &maximum_allowed_speed, |
---|
2294 | &epsilon, |
---|
2295 | &wc, &zc, &xmomc, &ymomc)) { |
---|
2296 | PyErr_SetString(PyExc_RuntimeError, "shallow_water_ext.c: protect could not parse input arguments"); |
---|
2297 | return NULL; |
---|
2298 | } |
---|
2299 | |
---|
2300 | N = wc -> dimensions[0]; |
---|
2301 | |
---|
2302 | _protect(N, |
---|
2303 | minimum_allowed_height, |
---|
2304 | maximum_allowed_speed, |
---|
2305 | epsilon, |
---|
2306 | (double*) wc -> data, |
---|
2307 | (double*) zc -> data, |
---|
2308 | (double*) xmomc -> data, |
---|
2309 | (double*) ymomc -> data); |
---|
2310 | |
---|
2311 | return Py_BuildValue(""); |
---|
2312 | } |
---|
2313 | |
---|
2314 | |
---|
2315 | |
---|
2316 | PyObject *balance_deep_and_shallow(PyObject *self, PyObject *args) { |
---|
2317 | // Compute linear combination between stage as computed by |
---|
2318 | // gradient-limiters limiting using w, and stage computed by |
---|
2319 | // gradient-limiters limiting using h (h-limiter). |
---|
2320 | // The former takes precedence when heights are large compared to the |
---|
2321 | // bed slope while the latter takes precedence when heights are |
---|
2322 | // relatively small. Anything in between is computed as a balanced |
---|
2323 | // linear combination in order to avoid numerical disturbances which |
---|
2324 | // would otherwise appear as a result of hard switching between |
---|
2325 | // modes. |
---|
2326 | // |
---|
2327 | // balance_deep_and_shallow(wc, zc, wv, zv, |
---|
2328 | // xmomc, ymomc, xmomv, ymomv) |
---|
2329 | |
---|
2330 | |
---|
2331 | PyArrayObject |
---|
2332 | *wc, //Stage at centroids |
---|
2333 | *zc, //Elevation at centroids |
---|
2334 | *wv, //Stage at vertices |
---|
2335 | *zv, //Elevation at vertices |
---|
2336 | *hvbar, //h-Limited depths at vertices |
---|
2337 | *xmomc, //Momentums at centroids and vertices |
---|
2338 | *ymomc, |
---|
2339 | *xmomv, |
---|
2340 | *ymomv; |
---|
2341 | |
---|
2342 | PyObject *domain, *Tmp; |
---|
2343 | |
---|
2344 | double alpha_balance = 2.0; |
---|
2345 | double H0; |
---|
2346 | |
---|
2347 | int N, tight_slope_limiters, use_centroid_velocities; //, err; |
---|
2348 | |
---|
2349 | // Convert Python arguments to C |
---|
2350 | if (!PyArg_ParseTuple(args, "OOOOOOOOOO", |
---|
2351 | &domain, |
---|
2352 | &wc, &zc, |
---|
2353 | &wv, &zv, &hvbar, |
---|
2354 | &xmomc, &ymomc, &xmomv, &ymomv)) { |
---|
2355 | PyErr_SetString(PyExc_RuntimeError, |
---|
2356 | "shallow_water_ext.c: balance_deep_and_shallow could not parse input arguments"); |
---|
2357 | return NULL; |
---|
2358 | } |
---|
2359 | |
---|
2360 | |
---|
2361 | // FIXME (Ole): I tested this without GetAttrString and got time down |
---|
2362 | // marginally from 4.0s to 3.8s. Consider passing everything in |
---|
2363 | // through ParseTuple and profile. |
---|
2364 | |
---|
2365 | // Pull out parameters |
---|
2366 | Tmp = PyObject_GetAttrString(domain, "alpha_balance"); |
---|
2367 | if (!Tmp) { |
---|
2368 | PyErr_SetString(PyExc_RuntimeError, "shallow_water_ext.c: balance_deep_and_shallow could not obtain object alpha_balance from domain"); |
---|
2369 | return NULL; |
---|
2370 | } |
---|
2371 | alpha_balance = PyFloat_AsDouble(Tmp); |
---|
2372 | Py_DECREF(Tmp); |
---|
2373 | |
---|
2374 | |
---|
2375 | Tmp = PyObject_GetAttrString(domain, "H0"); |
---|
2376 | if (!Tmp) { |
---|
2377 | PyErr_SetString(PyExc_RuntimeError, "shallow_water_ext.c: balance_deep_and_shallow could not obtain object H0 from domain"); |
---|
2378 | return NULL; |
---|
2379 | } |
---|
2380 | H0 = PyFloat_AsDouble(Tmp); |
---|
2381 | Py_DECREF(Tmp); |
---|
2382 | |
---|
2383 | |
---|
2384 | Tmp = PyObject_GetAttrString(domain, "tight_slope_limiters"); |
---|
2385 | if (!Tmp) { |
---|
2386 | PyErr_SetString(PyExc_RuntimeError, "shallow_water_ext.c: balance_deep_and_shallow could not obtain object tight_slope_limiters from domain"); |
---|
2387 | return NULL; |
---|
2388 | } |
---|
2389 | tight_slope_limiters = PyInt_AsLong(Tmp); |
---|
2390 | Py_DECREF(Tmp); |
---|
2391 | |
---|
2392 | |
---|
2393 | Tmp = PyObject_GetAttrString(domain, "use_centroid_velocities"); |
---|
2394 | if (!Tmp) { |
---|
2395 | PyErr_SetString(PyExc_RuntimeError, "shallow_water_ext.c: balance_deep_and_shallow could not obtain object use_centroid_velocities from domain"); |
---|
2396 | return NULL; |
---|
2397 | } |
---|
2398 | use_centroid_velocities = PyInt_AsLong(Tmp); |
---|
2399 | Py_DECREF(Tmp); |
---|
2400 | |
---|
2401 | |
---|
2402 | |
---|
2403 | N = wc -> dimensions[0]; |
---|
2404 | _balance_deep_and_shallow(N, |
---|
2405 | (double*) wc -> data, |
---|
2406 | (double*) zc -> data, |
---|
2407 | (double*) wv -> data, |
---|
2408 | (double*) zv -> data, |
---|
2409 | (double*) hvbar -> data, |
---|
2410 | (double*) xmomc -> data, |
---|
2411 | (double*) ymomc -> data, |
---|
2412 | (double*) xmomv -> data, |
---|
2413 | (double*) ymomv -> data, |
---|
2414 | H0, |
---|
2415 | (int) tight_slope_limiters, |
---|
2416 | (int) use_centroid_velocities, |
---|
2417 | alpha_balance); |
---|
2418 | |
---|
2419 | |
---|
2420 | return Py_BuildValue(""); |
---|
2421 | } |
---|
2422 | |
---|
2423 | |
---|
2424 | |
---|
2425 | |
---|
2426 | PyObject *assign_windfield_values(PyObject *self, PyObject *args) { |
---|
2427 | // |
---|
2428 | // assign_windfield_values(xmom_update, ymom_update, |
---|
2429 | // s_vec, phi_vec, self.const) |
---|
2430 | |
---|
2431 | |
---|
2432 | |
---|
2433 | PyArrayObject //(one element per triangle) |
---|
2434 | *s_vec, //Speeds |
---|
2435 | *phi_vec, //Bearings |
---|
2436 | *xmom_update, //Momentum updates |
---|
2437 | *ymom_update; |
---|
2438 | |
---|
2439 | |
---|
2440 | int N; |
---|
2441 | double cw; |
---|
2442 | |
---|
2443 | // Convert Python arguments to C |
---|
2444 | if (!PyArg_ParseTuple(args, "OOOOd", |
---|
2445 | &xmom_update, |
---|
2446 | &ymom_update, |
---|
2447 | &s_vec, &phi_vec, |
---|
2448 | &cw)) { |
---|
2449 | PyErr_SetString(PyExc_RuntimeError, "shallow_water_ext.c: assign_windfield_values could not parse input arguments"); |
---|
2450 | return NULL; |
---|
2451 | } |
---|
2452 | |
---|
2453 | |
---|
2454 | N = xmom_update -> dimensions[0]; |
---|
2455 | |
---|
2456 | _assign_wind_field_values(N, |
---|
2457 | (double*) xmom_update -> data, |
---|
2458 | (double*) ymom_update -> data, |
---|
2459 | (double*) s_vec -> data, |
---|
2460 | (double*) phi_vec -> data, |
---|
2461 | cw); |
---|
2462 | |
---|
2463 | return Py_BuildValue(""); |
---|
2464 | } |
---|
2465 | |
---|
2466 | |
---|
2467 | |
---|
2468 | |
---|
2469 | //------------------------------- |
---|
2470 | // Method table for python module |
---|
2471 | //------------------------------- |
---|
2472 | static struct PyMethodDef MethodTable[] = { |
---|
2473 | /* The cast of the function is necessary since PyCFunction values |
---|
2474 | * only take two PyObject* parameters, and rotate() takes |
---|
2475 | * three. |
---|
2476 | */ |
---|
2477 | |
---|
2478 | {"rotate", (PyCFunction)rotate, METH_VARARGS | METH_KEYWORDS, "Print out"}, |
---|
2479 | {"extrapolate_second_order_sw", extrapolate_second_order_sw, METH_VARARGS, "Print out"}, |
---|
2480 | {"compute_fluxes_ext_central", compute_fluxes_ext_central, METH_VARARGS, "Print out"}, |
---|
2481 | {"compute_fluxes_ext_central_new", compute_fluxes_ext_central_new, METH_VARARGS, "Print out"}, |
---|
2482 | {"compute_fluxes_ext_kinetic", compute_fluxes_ext_kinetic, METH_VARARGS, "Print out"}, |
---|
2483 | {"gravity", gravity, METH_VARARGS, "Print out"}, |
---|
2484 | {"manning_friction", manning_friction, METH_VARARGS, "Print out"}, |
---|
2485 | {"flux_function_central", flux_function_central, METH_VARARGS, "Print out"}, |
---|
2486 | {"balance_deep_and_shallow", balance_deep_and_shallow, |
---|
2487 | METH_VARARGS, "Print out"}, |
---|
2488 | {"protect", protect, METH_VARARGS | METH_KEYWORDS, "Print out"}, |
---|
2489 | {"assign_windfield_values", assign_windfield_values, |
---|
2490 | METH_VARARGS | METH_KEYWORDS, "Print out"}, |
---|
2491 | {NULL, NULL} |
---|
2492 | }; |
---|
2493 | |
---|
2494 | // Module initialisation |
---|
2495 | void initshallow_water_ext(void){ |
---|
2496 | Py_InitModule("shallow_water_ext", MethodTable); |
---|
2497 | |
---|
2498 | import_array(); // Necessary for handling of NumPY structures |
---|
2499 | } |
---|