1 | #! /usr/bin/python |
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2 | |
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3 | |
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4 | |
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5 | __author__="Stephen Roberts" |
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6 | __date__ ="$05/06/2010 4:54:58 PM$" |
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7 | |
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8 | |
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9 | def compute_fluxes(domain): |
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10 | """Compute all fluxes and the timestep suitable for all volumes |
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11 | in domain. |
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12 | |
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13 | Compute total flux for each conserved quantity using "flux_function" |
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14 | |
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15 | Fluxes across each edge are scaled by edgelengths and summed up |
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16 | Resulting flux is then scaled by area and stored in |
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17 | explicit_update for each of the three conserved quantities |
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18 | stage, xmomentum and ymomentum |
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19 | |
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20 | The maximal allowable speed computed by the flux_function for each volume |
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21 | is converted to a timestep that must not be exceeded. The minimum of |
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22 | those is computed as the next overall timestep. |
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23 | |
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24 | Post conditions: |
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25 | domain.explicit_update is reset to computed flux values |
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26 | domain.timestep is set to the largest step satisfying all volumes. |
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27 | """ |
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28 | |
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29 | import sys |
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30 | import numpy |
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31 | |
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32 | N = domain.number_of_elements |
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33 | |
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34 | tmp0 = numpy.zeros(N,numpy.float) |
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35 | tmp1 = numpy.zeros(N,numpy.float) |
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36 | |
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37 | #Shortcuts |
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38 | Stage = domain.quantities['stage'] |
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39 | Xmom = domain.quantities['xmomentum'] |
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40 | Bed = domain.quantities['elevation'] |
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41 | |
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42 | #Arrays |
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43 | stage = Stage.vertex_values |
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44 | xmom = Xmom.vertex_values |
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45 | bed = Bed.vertex_values |
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46 | |
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47 | |
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48 | stage_bdry = Stage.boundary_values |
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49 | xmom_bdry = Xmom.boundary_values |
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50 | |
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51 | flux = numpy.zeros(2, numpy.float) #Work numpy.array for summing up fluxes |
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52 | ql = numpy.zeros(2, numpy.float) |
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53 | qr = numpy.zeros(2, numpy.float) |
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54 | |
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55 | #Loop |
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56 | timestep = float(sys.maxint) |
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57 | |
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58 | for k in range(N): |
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59 | |
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60 | flux[:,] = 0. #Reset work numpy.array |
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61 | #for i in range(3): |
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62 | for i in range(2): |
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63 | #Quantities inside volume facing neighbour i |
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64 | #ql[0] = stage[k, i] |
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65 | #ql[1] = xmom[k, i] |
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66 | ql = [stage[k, i], xmom[k, i]] |
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67 | zl = bed[k, i] |
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68 | |
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69 | #Quantities at neighbour on nearest face |
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70 | n = domain.neighbours[k,i] |
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71 | if n < 0: |
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72 | m = -n-1 #Convert negative flag to index |
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73 | qr[0] = stage_bdry[m] |
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74 | qr[1] = xmom_bdry[m] |
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75 | zr = zl #Extend bed elevation to boundary |
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76 | else: |
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77 | #m = domain.neighbour_edges[k,i] |
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78 | m = domain.neighbour_vertices[k,i] |
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79 | #print i, ' ' , m |
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80 | #qr = [stage[n, m], xmom[n, m], ymom[n, m]] |
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81 | qr[0] = stage[n, m] |
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82 | qr[1] = xmom[n, m] |
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83 | zr = bed[n, m] |
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84 | |
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85 | |
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86 | #Outward pointing normal vector |
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87 | normal = domain.normals[k, i] |
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88 | |
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89 | #Flux computation using provided function |
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90 | |
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91 | |
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92 | edgeflux, max_speed = flux_function(normal, ql, qr, zl, zr) |
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93 | |
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94 | #print 'edgeflux', edgeflux |
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95 | |
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96 | # THIS IS THE LINE TO DEAL WITH LEFT AND RIGHT FLUXES |
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97 | # flux = edgefluxleft - edgefluxright |
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98 | flux -= edgeflux |
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99 | #Update optimal_timestep |
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100 | try: |
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101 | #timestep = min(timestep, 0.5*domain.radii[k]/max_speed) |
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102 | timestep = min(timestep, domain.CFL*0.5*domain.areas[k]/max_speed) |
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103 | except ZeroDivisionError: |
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104 | pass |
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105 | |
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106 | #Normalise by area and store for when all conserved |
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107 | #quantities get updated |
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108 | flux /= domain.areas[k] |
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109 | |
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110 | #Stage.explicit_update[k] = flux[0] |
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111 | tmp0[k] = flux[0] |
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112 | tmp1[k] = flux[1] |
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113 | |
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114 | |
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115 | return tmp0, tmp1 |
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116 | |
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117 | |
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118 | def flux_function(normal, ql, qr, zl, zr): |
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119 | """Compute fluxes between volumes for the shallow water wave equation |
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120 | cast in terms of w = h+z using the 'central scheme' as described in |
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121 | |
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122 | Kurganov, Noelle, Petrova. 'Semidiscrete Central-Upwind Schemes For |
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123 | Hyperbolic Conservation Laws and Hamilton-Jacobi Equations'. |
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124 | Siam J. Sci. Comput. Vol. 23, No. 3, pp. 707-740. |
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125 | |
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126 | The implemented formula is given in equation (3.15) on page 714 |
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127 | |
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128 | Conserved quantities w, uh, are stored as elements 0 and 1 |
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129 | in the numerical vectors ql an qr. |
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130 | |
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131 | Bed elevations zl and zr. |
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132 | """ |
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133 | |
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134 | from anuga_1d.config import g, epsilon, h0 |
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135 | from math import sqrt |
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136 | import numpy |
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137 | |
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138 | #print 'ql',ql |
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139 | |
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140 | #Align momentums with x-axis |
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141 | #q_left = rotate(ql, normal, direction = 1) |
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142 | #q_right = rotate(qr, normal, direction = 1) |
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143 | q_left = ql |
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144 | q_left[1] = q_left[1]*normal |
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145 | q_right = qr |
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146 | q_right[1] = q_right[1]*normal |
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147 | |
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148 | #z = (zl+zr)/2 #Take average of field values |
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149 | z = 0.5*(zl+zr) #Take average of field values |
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150 | |
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151 | w_left = q_left[0] #w=h+z |
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152 | h_left = w_left-z |
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153 | uh_left = q_left[1] |
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154 | |
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155 | if h_left < epsilon: |
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156 | u_left = 0.0 #Could have been negative |
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157 | h_left = 0.0 |
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158 | else: |
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159 | u_left = uh_left/(h_left + h0/h_left) |
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160 | |
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161 | |
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162 | uh_left = u_left*h_left |
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163 | |
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164 | w_right = q_right[0] #w=h+z |
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165 | h_right = w_right-z |
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166 | uh_right = q_right[1] |
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167 | |
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168 | |
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169 | if h_right < epsilon: |
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170 | u_right = 0.0 #Could have been negative |
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171 | h_right = 0.0 |
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172 | else: |
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173 | u_right = uh_right/(h_right + h0/h_right) |
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174 | |
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175 | uh_right = u_right*h_right |
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176 | |
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177 | #vh_left = q_left[2] |
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178 | #vh_right = q_right[2] |
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179 | |
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180 | #print h_right |
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181 | #print u_right |
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182 | #print h_left |
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183 | #print u_right |
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184 | |
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185 | soundspeed_left = sqrt(g*h_left) |
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186 | soundspeed_right = sqrt(g*h_right) |
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187 | |
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188 | #Maximal wave speed |
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189 | s_max = max(u_left+soundspeed_left, u_right+soundspeed_right, 0) |
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190 | |
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191 | #Minimal wave speed |
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192 | s_min = min(u_left-soundspeed_left, u_right-soundspeed_right, 0) |
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193 | |
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194 | #Flux computation |
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195 | |
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196 | #flux_left = numpy.array([u_left*h_left, |
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197 | # u_left*uh_left + 0.5*g*h_left**2]) |
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198 | #flux_right = numpy.array([u_right*h_right, |
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199 | # u_right*uh_right + 0.5*g*h_right**2]) |
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200 | flux_left = numpy.array([u_left*h_left, |
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201 | u_left*uh_left + 0.5*g*h_left*h_left]) |
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202 | flux_right = numpy.array([u_right*h_right, |
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203 | u_right*uh_right + 0.5*g*h_right*h_right]) |
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204 | |
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205 | denom = s_max-s_min |
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206 | if denom == 0.0: |
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207 | edgeflux = numpy.array([0.0, 0.0]) |
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208 | max_speed = 0.0 |
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209 | else: |
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210 | edgeflux = (s_max*flux_left - s_min*flux_right)/denom |
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211 | edgeflux += s_max*s_min*(q_right-q_left)/denom |
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212 | |
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213 | edgeflux[1] = edgeflux[1]*normal |
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214 | |
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215 | max_speed = max(abs(s_max), abs(s_min)) |
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216 | |
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217 | return edgeflux, max_speed |
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218 | |
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219 | |
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220 | if __name__ == "__main__": |
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221 | print "Hello World"; |
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