1 | """Class Domain - |
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2 | 1D interval domains for finite-volume computations of |
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3 | the shallow water wave equation. |
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4 | |
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5 | This module contains a specialisation of class Domain from module domain.py |
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6 | consisting of methods specific to the Shallow Water Wave Equation |
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7 | |
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8 | |
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9 | U_t + E_x = S |
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10 | |
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11 | where |
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12 | |
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13 | U = [w, uh] |
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14 | E = [uh, u^2h + gh^2/2] |
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15 | S represents source terms forcing the system |
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16 | (e.g. gravity, friction, wind stress, ...) |
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17 | |
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18 | and _t, _x, _y denote the derivative with respect to t, x and y respectiely. |
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19 | |
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20 | The quantities are |
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21 | |
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22 | symbol variable name explanation |
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23 | x x horizontal distance from origin [m] |
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24 | z elevation elevation of bed on which flow is modelled [m] |
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25 | h height water height above z [m] |
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26 | w stage absolute water level, w = z+h [m] |
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27 | u speed in the x direction [m/s] |
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28 | uh xmomentum momentum in the x direction [m^2/s] |
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29 | |
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30 | eta mannings friction coefficient [to appear] |
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31 | nu wind stress coefficient [to appear] |
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32 | |
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33 | The conserved quantities are w, uh |
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34 | |
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35 | For details see e.g. |
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36 | Christopher Zoppou and Stephen Roberts, |
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37 | Catastrophic Collapse of Water Supply Reservoirs in Urban Areas, |
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38 | Journal of Hydraulic Engineering, vol. 127, No. 7 July 1999 |
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39 | |
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40 | |
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41 | John Jakeman, Ole Nielsen, Stephen Roberts, Duncan Gray, Christopher Zoppou |
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42 | Geoscience Australia, 2006 |
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43 | """ |
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44 | |
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45 | |
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46 | from domain import * |
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47 | Generic_Domain = Domain #Rename |
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48 | |
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49 | #Shallow water domain |
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50 | class Domain(Generic_Domain): |
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51 | |
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52 | def __init__(self, coordinates, boundary = None, tagged_elements = None): |
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53 | |
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54 | conserved_quantities = ['area', 'discharge'] |
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55 | evolved_quantities = ['area', 'discharge', 'elevation', 'height', 'stage'] |
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56 | other_quantities = ['friction'] |
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57 | Generic_Domain.__init__(self, |
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58 | coordinates = coordinates, |
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59 | boundary = boundary, |
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60 | conserved_quantities = conserved_quantities, |
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61 | evolved_quantities = evolved_quantities, |
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62 | other_quantities = other_quantities, |
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63 | tagged_elements = tagged_elements) |
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64 | |
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65 | from config import minimum_allowed_height, g, h0 |
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66 | self.minimum_allowed_height = minimum_allowed_height |
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67 | self.g = g |
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68 | self.h0 = h0 |
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69 | |
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70 | #forcing terms not included in 1d domain ?WHy? |
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71 | self.forcing_terms.append(gravity) |
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72 | #self.forcing_terms.append(manning_friction) |
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73 | #print "\nI have Removed forcing terms line 64 1dsw" |
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74 | |
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75 | |
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76 | #Stored output |
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77 | self.store = True |
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78 | self.format = 'sww' |
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79 | self.smooth = True |
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80 | |
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81 | |
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82 | #Reduction operation for get_vertex_values |
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83 | from util import mean |
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84 | self.reduction = mean |
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85 | #self.reduction = min #Looks better near steep slopes |
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86 | |
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87 | self.set_quantities_to_be_stored(['area','discharge']) |
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88 | |
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89 | self.__doc__ = 'shallow_water_domain' |
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90 | |
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91 | # self.check_integrity() |
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92 | |
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93 | |
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94 | def check_integrity(self): |
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95 | |
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96 | #Check that we are solving the shallow water wave equation |
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97 | |
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98 | msg = 'First conserved quantity must be "stage"' |
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99 | assert self.conserved_quantities[0] == 'stage', msg |
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100 | msg = 'Second conserved quantity must be "xmomentum"' |
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101 | assert self.conserved_quantities[1] == 'xmomentum', msg |
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102 | |
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103 | msg = 'First evolved quantity must be "stage"' |
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104 | assert self.evolved_quantities[0] == 'stage', msg |
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105 | msg = 'Second evolved quantity must be "xmomentum"' |
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106 | assert self.evolved_quantities[1] == 'xmomentum', msg |
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107 | msg = 'Third evolved quantity must be "elevation"' |
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108 | assert self.evolved_quantities[2] == 'elevation', msg |
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109 | msg = 'Fourth evolved quantity must be "height"' |
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110 | assert self.evolved_quantities[3] == 'height', msg |
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111 | msg = 'Fifth evolved quantity must be "velocity"' |
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112 | assert self.evolved_quantities[4] == 'velocity', msg |
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113 | |
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114 | Generic_Domain.check_integrity(self) |
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115 | |
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116 | def compute_fluxes(self): |
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117 | #Call correct module function |
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118 | #(either from this module or C-extension) |
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119 | compute_fluxes_channel(self) |
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120 | |
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121 | def distribute_to_vertices_and_edges(self): |
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122 | #Call correct module function |
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123 | #(either from this module or C-extension) |
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124 | distribute_to_vertices_and_edges_limit_a_d(self) |
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125 | |
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126 | |
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127 | #=============== End of Shallow Water Domain =============================== |
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128 | #----------------------------------- |
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129 | # Compute fluxes interface |
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130 | #----------------------------------- |
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131 | def compute_fluxes(domain): |
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132 | """ |
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133 | Python version of compute fluxes (local_compute_fluxes) |
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134 | is available in test_shallow_water_vel_domain.py |
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135 | """ |
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136 | |
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137 | |
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138 | from Numeric import zeros, Float |
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139 | import sys |
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140 | |
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141 | |
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142 | timestep = float(sys.maxint) |
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143 | |
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144 | stage = domain.quantities['stage'] |
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145 | xmom = domain.quantities['xmomentum'] |
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146 | bed = domain.quantities['elevation'] |
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147 | |
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148 | |
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149 | #from comp_flux_vel_ext import compute_fluxes_ext |
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150 | |
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151 | #domain.flux_timestep = compute_fluxes_ext(timestep,domain,stage,xmom,bed) |
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152 | domain.flux_timestep = .1 |
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153 | |
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154 | #----------------------------------- |
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155 | # Compute flux definition with vel |
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156 | #----------------------------------- |
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157 | def compute_fluxes_vel(domain): |
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158 | from Numeric import zeros, Float |
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159 | import sys |
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160 | |
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161 | |
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162 | timestep = float(sys.maxint) |
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163 | |
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164 | stage = domain.quantities['stage'] |
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165 | xmom = domain.quantities['xmomentum'] |
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166 | bed = domain.quantities['elevation'] |
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167 | height = domain.quantities['height'] |
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168 | velocity = domain.quantities['velocity'] |
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169 | |
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170 | |
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171 | from comp_flux_vel_ext import compute_fluxes_vel_ext |
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172 | |
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173 | domain.flux_timestep = compute_fluxes_vel_ext(timestep,domain,stage,xmom,bed,height,velocity) |
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174 | |
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175 | #---------------------------------- |
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176 | # Compute fluxes channel |
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177 | #---------------------------------- |
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178 | def compute_fluxes_channel(domain): |
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179 | from Numeric import zeros, Float |
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180 | import sys |
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181 | |
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182 | timestep = float(sys.maxint) |
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183 | |
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184 | area = domain.quantities['area'] |
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185 | discharge = domain.quantities['discharge'] |
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186 | bed = domain.quantities['elevation'] |
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187 | height = domain.quantities['height'] |
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188 | stage = domain.quantities['stage'] |
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189 | |
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190 | #from channel_domain_ext import compute_fluxes_channel_ext |
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191 | |
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192 | # domain.flux_timestep = compute_fluxes_channel_ext(timestep,domain,area,discharge,bed,height,stage) |
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193 | # domain.quantities['area'].explicit_update=ones(410,Float) |
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194 | domain.flux_timestep = .1 |
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195 | #print area.vertex_values[0],area.vertex_values[1],area.vertex_values[2] |
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196 | for i in range(len(domain.coordinates)-1): |
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197 | fluxesl= channel_flux_func(domain,i-1) |
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198 | fluxesr= channel_flux_func(domain,i) |
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199 | #print domain.areas[i] |
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200 | #print -1*(fluxesl[1]-fluxesr[1]) |
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201 | #print height.centroid_values[200],height.vertex_values[200] |
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202 | #print fluxesl[0] |
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203 | print -1*(fluxesl[0]-fluxesr[0])*domain.areas[i] |
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204 | area.explicit_update[i]=-1*(fluxesl[0]-fluxesr[0])*domain.areas[i] |
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205 | discharge.explicit_update[i]=-(fluxesl[1]-fluxesr[1])*domain.areas[i] |
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206 | |
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207 | def channel_flux_func(domain, i): |
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208 | |
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209 | area = domain.quantities['area'] |
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210 | discharge = domain.quantities['discharge'] |
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211 | bed = domain.quantities['elevation'] |
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212 | height = domain.quantities['height'] |
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213 | stage = domain.quantities['stage'] |
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214 | |
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215 | flux_left0=0 |
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216 | flux_left1=0 |
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217 | flux_right0=0 |
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218 | flux_right1=0 |
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219 | flux0=0 |
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220 | flux1=0 |
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221 | # Crude numerical flux calculation |
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222 | from math import sqrt |
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223 | |
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224 | if i==0 or i==(len(domain.coordinates)-1): |
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225 | flux_left0=0 |
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226 | flux_left1=0 |
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227 | flux_right0=0 |
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228 | flux_right1=0 |
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229 | else: |
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230 | g=9.8 |
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231 | a_left = area.centroid_values[i-1] |
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232 | d_left = discharge.centroid_values[i-1] |
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233 | z_left = bed.centroid_values[i-1] |
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234 | h_left = height.centroid_values[i-1] |
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235 | w_left = stage.centroid_values[i-1] |
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236 | |
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237 | a_right = area.centroid_values[i] |
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238 | d_right = discharge.centroid_values[i] |
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239 | z_right = bed.centroid_values[i] |
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240 | h_right = height.centroid_values[i] |
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241 | w_right = stage.centroid_values[i] |
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242 | |
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243 | z=(z_left+z_right)/2 |
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244 | #hbarr=0.5*(height.vertex_values[i][1]+height.vertex_values[i][0]) |
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245 | #hbarl=0.5*(height.vertex_values[i-1][1]+height.vertex_values[i-1][0]) |
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246 | hbarr=0 |
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247 | hbarl=0 |
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248 | #print hbarl,h_left |
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249 | if a_left>1.0e-12: |
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250 | u_left=d_left/a_left |
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251 | else: |
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252 | u_left=0 |
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253 | if a_right>1.0e-12: |
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254 | u_right=d_right/a_right |
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255 | else: |
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256 | u_right=0 |
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257 | |
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258 | ## soundspeed_left = sqrt(g*h_left); |
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259 | ## soundspeed_right = sqrt(g*h_right); |
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260 | |
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261 | ## s_max = max(u_left+soundspeed_left,u_right+soundspeed_right) |
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262 | ## if s_max<0.0: |
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263 | ## s_max=0 |
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264 | ## s_min = min(u_left-soundspeed_left,u_right-soundspeed_right) |
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265 | ## if s_min>0.0: |
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266 | ## s_min=0 |
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267 | |
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268 | flux_left0 = d_left |
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269 | flux_right1= d_right |
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270 | if a_left<1.0e-12: |
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271 | flux_left11=0 |
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272 | else: |
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273 | flux_left11=d_left*d_left/a_left |
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274 | flux_left1=flux_left11+g*(calculateI(h_left,0)-calculateI(hbarl,0)) |
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275 | if a_right<1.0e-12: |
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276 | flux_right11=0 |
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277 | else: |
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278 | flux_right11=d_right*d_right/a_right |
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279 | flux_right1=flux_right11+g*(calculateI(h_right,0)-calculateI(hbarr,0)) |
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280 | #print g*(calculateI(h_right,0)-calculateI(hbarr,0)), g*(calculateI(h_left,0)-calculateI(hbarl,0)) |
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281 | |
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282 | flux0 = 0.5*(flux_left0+flux_right0) |
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283 | flux1 = 0.5*(flux_left1+flux_right1) |
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284 | return (flux0,flux1) |
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285 | |
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286 | def calculateI(H,z0): |
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287 | return H*H*0.5-z0*H+z0*z0*0.5 |
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288 | |
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289 | |
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290 | #-------------------------------------------------------------------------- |
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291 | def distribute_to_vertices_and_edges_limit_w_u(domain): |
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292 | """Distribution from centroids to vertices specific to the |
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293 | shallow water wave |
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294 | equation. |
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295 | |
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296 | It will ensure that h (w-z) is always non-negative even in the |
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297 | presence of steep bed-slopes by taking a weighted average between shallow |
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298 | and deep cases. |
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299 | |
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300 | In addition, all conserved quantities get distributed as per either a |
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301 | constant (order==1) or a piecewise linear function (order==2). |
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302 | |
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303 | FIXME: more explanation about removal of artificial variability etc |
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304 | |
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305 | Precondition: |
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306 | All quantities defined at centroids and bed elevation defined at |
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307 | vertices. |
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308 | |
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309 | Postcondition |
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310 | Conserved quantities defined at vertices |
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311 | |
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312 | """ |
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313 | |
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314 | #from config import optimised_gradient_limiter |
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315 | |
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316 | #Remove very thin layers of water |
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317 | #protect_against_infinitesimal_and_negative_heights(domain) |
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318 | |
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319 | import sys |
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320 | from Numeric import zeros, Float |
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321 | from config import epsilon, h0 |
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322 | |
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323 | N = domain.number_of_elements |
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324 | |
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325 | #Shortcuts |
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326 | Stage = domain.quantities['stage'] |
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327 | Xmom = domain.quantities['xmomentum'] |
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328 | Bed = domain.quantities['elevation'] |
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329 | Height = domain.quantities['height'] |
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330 | Velocity = domain.quantities['velocity'] |
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331 | |
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332 | #Arrays |
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333 | w_C = Stage.centroid_values |
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334 | uh_C = Xmom.centroid_values |
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335 | z_C = Bed.centroid_values |
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336 | h_C = Height.centroid_values |
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337 | u_C = Velocity.centroid_values |
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338 | |
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339 | #print id(h_C) |
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340 | for i in range(N): |
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341 | h_C[i] = w_C[i] - z_C[i] |
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342 | if h_C[i] <= 1.0e-12: |
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343 | #print 'h_C[%d]= %15.5e\n' % (i,h_C[i]) |
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344 | h_C[i] = 0.0 |
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345 | w_C[i] = z_C[i] |
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346 | #uh_C[i] = 0.0 |
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347 | |
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348 | # u_C[i] = 0.0 |
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349 | # else: |
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350 | # u_C[i] = uh_C[i]/h_C[i] |
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351 | |
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352 | h0 = 1.0e-12 |
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353 | for i in range(len(h_C)): |
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354 | if h_C[i] < 1.0e-12: |
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355 | u_C[i] = 0.0 #Could have been negative |
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356 | h_C[i] = 0.0 |
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357 | else: |
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358 | u_C[i] = uh_C[i]/(h_C[i] + h0/h_C[i]) |
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359 | #u_C[i] = uh_C[i]/h_C[i] |
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360 | |
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361 | for name in [ 'velocity', 'stage' ]: |
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362 | Q = domain.quantities[name] |
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363 | if domain.order == 1: |
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364 | Q.extrapolate_first_order() |
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365 | elif domain.order == 2: |
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366 | Q.extrapolate_second_order() |
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367 | else: |
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368 | raise 'Unknown order' |
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369 | |
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370 | w_V = domain.quantities['stage'].vertex_values |
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371 | z_V = domain.quantities['elevation'].vertex_values |
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372 | h_V = domain.quantities['height'].vertex_values |
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373 | u_V = domain.quantities['velocity'].vertex_values |
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374 | uh_V = domain.quantities['xmomentum'].vertex_values |
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375 | |
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376 | h_V[:] = w_V - z_V |
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377 | for i in range(len(h_C)): |
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378 | for j in range(2): |
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379 | if h_V[i,j] < 0.0 : |
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380 | #print 'h_V[%d,%d] = %f \n' % (i,j,h_V[i,j]) |
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381 | dh = h_V[i,j] |
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382 | h_V[i,j] = 0.0 |
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383 | w_V[i,j] = z_V[i,j] |
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384 | h_V[i,(j+1)%2] = h_V[i,(j+1)%2] + dh |
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385 | w_V[i,(j+1)%2] = w_V[i,(j+1)%2] + dh |
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386 | |
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387 | uh_V[:] = u_V * h_V |
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388 | |
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389 | |
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390 | return |
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391 | |
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392 | #--------------------------------------------------------------------------- |
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393 | def distribute_to_vertices_and_edges_limit_w_uh(domain): |
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394 | """Distribution from centroids to vertices specific to the |
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395 | shallow water wave equation. |
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396 | |
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397 | In addition, all conserved quantities get distributed as per either a |
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398 | constant (order==1) or a piecewise linear function (order==2). |
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399 | |
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400 | Precondition: |
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401 | All quantities defined at centroids and bed elevation defined at |
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402 | vertices. |
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403 | |
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404 | Postcondition |
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405 | Conserved quantities defined at vertices |
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406 | |
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407 | """ |
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408 | |
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409 | import sys |
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410 | from Numeric import zeros, Float |
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411 | from config import epsilon, h0 |
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412 | |
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413 | N = domain.number_of_elements |
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414 | |
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415 | #Shortcuts |
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416 | Stage = domain.quantities['stage'] |
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417 | Xmom = domain.quantities['xmomentum'] |
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418 | Bed = domain.quantities['elevation'] |
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419 | Height = domain.quantities['height'] |
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420 | Velocity = domain.quantities['velocity'] |
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421 | |
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422 | #Arrays |
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423 | w_C = Stage.centroid_values |
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424 | uh_C = Xmom.centroid_values |
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425 | z_C = Bed.centroid_values |
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426 | h_C = Height.centroid_values |
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427 | u_C = Velocity.centroid_values |
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428 | |
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429 | |
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430 | for i in range(N): |
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431 | h_C[i] = w_C[i] - z_C[i] |
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432 | if h_C[i] <= 1.0e-6: |
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433 | #print 'h_C[%d]= %15.5e\n' % (i,h_C[i]) |
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434 | h_C[i] = 0.0 |
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435 | w_C[i] = z_C[i] |
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436 | uh_C[i] = 0.0 |
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437 | |
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438 | for name in [ 'stage', 'xmomentum']: |
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439 | Q = domain.quantities[name] |
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440 | if domain.order == 1: |
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441 | Q.extrapolate_first_order() |
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442 | elif domain.order == 2: |
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443 | Q.extrapolate_second_order() |
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444 | else: |
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445 | raise 'Unknown order' |
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446 | |
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447 | w_V = domain.quantities['stage'].vertex_values |
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448 | z_V = domain.quantities['elevation'].vertex_values |
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449 | h_V = domain.quantities['height'].vertex_values |
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450 | u_V = domain.quantities['velocity'].vertex_values |
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451 | uh_V = domain.quantities['xmomentum'].vertex_values |
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452 | |
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453 | h_V[:] = w_V - z_V |
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454 | |
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455 | for i in range(len(h_C)): |
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456 | for j in range(2): |
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457 | if h_V[i,j] < 0.0 : |
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458 | #print 'h_V[%d,%d] = %f \n' % (i,j,h_V[i,j]) |
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459 | dh = h_V[i,j] |
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460 | h_V[i,j] = 0.0 |
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461 | w_V[i,j] = z_V[i,j] |
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462 | h_V[i,(j+1)%2] = h_V[i,(j+1)%2] + dh |
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463 | w_V[i,(j+1)%2] = w_V[i,(j+1)%2] + dh |
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464 | u_V[i,j] = 0.0 |
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465 | if h_V[i,j] < h0: |
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466 | u_V[i,j] |
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467 | else: |
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468 | u_V[i,j] = uh_V[i,j]/(h_V[i,j] + h0/h_V[i,j]) |
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469 | |
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470 | #--------------------------------------------------------------------------- |
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471 | def distribute_to_vertices_and_edges_limit_a_d(domain): |
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472 | """Distribution from centroids to vertices specific to the |
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473 | shallow water wave equation. |
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474 | |
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475 | In addition, all conserved quantities get distributed as per either a |
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476 | constant (order==1) or a piecewise linear function (order==2). |
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477 | |
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478 | Precondition: |
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479 | All quantities defined at centroids and bed elevation defined at |
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480 | vertices. |
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481 | |
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482 | Postcondition |
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483 | Conserved quantities defined at vertices |
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484 | |
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485 | """ |
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486 | |
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487 | import sys |
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488 | from Numeric import zeros, Float |
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489 | from config import epsilon, h0 |
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490 | |
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491 | N = domain.number_of_elements |
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492 | |
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493 | #Shortcuts |
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494 | Area = domain.quantities['area'] |
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495 | Discharge = domain.quantities['discharge'] |
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496 | Bed = domain.quantities['elevation'] |
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497 | Height = domain.quantities['height'] |
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498 | Stage = domain.quantities['stage'] |
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499 | |
---|
500 | #Arrays |
---|
501 | a_C = Area.centroid_values |
---|
502 | d_C = Discharge.centroid_values |
---|
503 | z_C = Bed.centroid_values |
---|
504 | h_C = Height.centroid_values |
---|
505 | w_C = Stage.centroid_values |
---|
506 | |
---|
507 | #work out stage |
---|
508 | for i in range(N): |
---|
509 | h_C[i] = w_C[i] - z_C[i] |
---|
510 | #make sure depth isn't zero |
---|
511 | if h_C[i] <= 1.0e-6: |
---|
512 | #print 'h_C[%d]= %15.5e\n' % (i,h_C[i]) |
---|
513 | h_C[i] = 0.0 |
---|
514 | w_C[i] = z_C[i] |
---|
515 | d_C[i] = 0.0 |
---|
516 | #distribute stage,discharge |
---|
517 | |
---|
518 | for name in [ 'area', 'discharge']: |
---|
519 | Q = domain.quantities[name] |
---|
520 | if domain.order == 1: |
---|
521 | Q.extrapolate_first_order() |
---|
522 | elif domain.order == 2: |
---|
523 | Q.extrapolate_second_order() |
---|
524 | else: |
---|
525 | raise 'Unknown order' |
---|
526 | |
---|
527 | a_V = domain.quantities['area'].vertex_values |
---|
528 | d_V = domain.quantities['discharge'].vertex_values |
---|
529 | h_V = domain.quantities['height'].vertex_values |
---|
530 | z_V = domain.quantities['elevation'].vertex_values |
---|
531 | w_V = domain.quantities['stage'].vertex_values |
---|
532 | #height at verticies |
---|
533 | h_V[:] = w_V - z_V |
---|
534 | |
---|
535 | ## for i in range(len(h_C)): |
---|
536 | ## for j in range(2): |
---|
537 | ## if h_V[i,j] < 0.0 : |
---|
538 | ## #print 'h_V[%d,%d] = %f \n' % (i,j,h_V[i,j]) |
---|
539 | ## dh = h_V[i,j] |
---|
540 | ## h_V[i,j] = 0.0 |
---|
541 | ## w_V[i,j] = z_V[i,j] |
---|
542 | ## h_V[i,(j+1)%2] = h_V[i,(j+1)%2] + dh |
---|
543 | ## w_V[i,(j+1)%2] = w_V[i,(j+1)%2] + dh |
---|
544 | ## u_V[i,j] = 0.0 |
---|
545 | ## if h_V[i,j] < h0: |
---|
546 | ## u_V[i,j] |
---|
547 | ## else: |
---|
548 | ## u_V[i,j] = uh_V[i,j]/(h_V[i,j] + h0/h_V[i,j] |
---|
549 | ## ) |
---|
550 | |
---|
551 | #-------------------------------------------------------- |
---|
552 | #Boundaries - specific to the shallow_water_vel_domain |
---|
553 | #-------------------------------------------------------- |
---|
554 | class Reflective_boundary(Boundary): |
---|
555 | """Reflective boundary returns same conserved quantities as |
---|
556 | those present in its neighbour volume but reflected. |
---|
557 | |
---|
558 | This class is specific to the shallow water equation as it |
---|
559 | works with the momentum quantities assumed to be the second |
---|
560 | and third conserved quantities. |
---|
561 | """ |
---|
562 | |
---|
563 | def __init__(self, domain = None): |
---|
564 | Boundary.__init__(self) |
---|
565 | |
---|
566 | if domain is None: |
---|
567 | msg = 'Domain must be specified for reflective boundary' |
---|
568 | raise msg |
---|
569 | |
---|
570 | #Handy shorthands |
---|
571 | self.normals = domain.normals |
---|
572 | self.stage = domain.quantities['stage'].vertex_values |
---|
573 | self.xmom = domain.quantities['xmomentum'].vertex_values |
---|
574 | self.bed = domain.quantities['elevation'].vertex_values |
---|
575 | self.height = domain.quantities['height'].vertex_values |
---|
576 | self.velocity = domain.quantities['velocity'].vertex_values |
---|
577 | |
---|
578 | from Numeric import zeros, Float |
---|
579 | #self.conserved_quantities = zeros(3, Float) |
---|
580 | self.evolved_quantities = zeros(5, Float) |
---|
581 | |
---|
582 | def __repr__(self): |
---|
583 | return 'Reflective_boundary' |
---|
584 | |
---|
585 | |
---|
586 | def evaluate(self, vol_id, edge_id): |
---|
587 | """Reflective boundaries reverses the outward momentum |
---|
588 | of the volume they serve. |
---|
589 | """ |
---|
590 | #Commenting out some quantities not currently keeping track of |
---|
591 | ## q = self.evolved_quantities |
---|
592 | ## q[0] = self.stage[vol_id, edge_id] |
---|
593 | ## q[1] = -self.xmom[vol_id, edge_id] |
---|
594 | ## q[2] = self.bed[vol_id, edge_id] |
---|
595 | ## q[3] = self.height[vol_id, edge_id] |
---|
596 | ## q[4] = -self.stage[stage_id, stage_id] |
---|
597 | |
---|
598 | #print "In Reflective q ",q |
---|
599 | |
---|
600 | |
---|
601 | return q |
---|
602 | |
---|
603 | class Dirichlet_boundary(Boundary): |
---|
604 | """Dirichlet boundary returns constant values for the |
---|
605 | conserved quantities |
---|
606 | """ |
---|
607 | |
---|
608 | |
---|
609 | def __init__(self, evolved_quantities=None): |
---|
610 | Boundary.__init__(self) |
---|
611 | |
---|
612 | if evolved_quantities is None: |
---|
613 | msg = 'Must specify one value for each evolved quantity' |
---|
614 | raise msg |
---|
615 | |
---|
616 | from Numeric import array, Float |
---|
617 | self.evolved_quantities=array(evolved_quantities).astype(Float) |
---|
618 | |
---|
619 | def __repr__(self): |
---|
620 | return 'Dirichlet boundary (%s)' %self.evolved_quantities |
---|
621 | |
---|
622 | def evaluate(self, vol_id=None, edge_id=None): |
---|
623 | return self.evolved_quantities |
---|
624 | |
---|
625 | #-------------------------------------------------------- |
---|
626 | #Boundaries for channel - specific to the channel domain |
---|
627 | #-------------------------------------------------------- |
---|
628 | class Reflective_boundary(Boundary): |
---|
629 | """Reflective boundary returns same conserved quantities as |
---|
630 | those present in its neighbour volume but reflected. |
---|
631 | |
---|
632 | This class is specific to the shallow water equation as it |
---|
633 | works with the momentum quantities assumed to be the second |
---|
634 | and third conserved quantities. |
---|
635 | """ |
---|
636 | |
---|
637 | def __init__(self, domain = None): |
---|
638 | Boundary.__init__(self) |
---|
639 | |
---|
640 | if domain is None: |
---|
641 | msg = 'Domain must be specified for reflective boundary' |
---|
642 | raise msg |
---|
643 | |
---|
644 | #Handy shorthands |
---|
645 | self.normals = domain.normals |
---|
646 | self.area = domain.quantities['area'].vertex_values |
---|
647 | self.discharge = domain.quantities['discharge'].vertex_values |
---|
648 | self.bed = domain.quantities['elevation'].vertex_values |
---|
649 | self.height = domain.quantities['height'].vertex_values |
---|
650 | self.stage = domain.quantities['stage'].vertex_values |
---|
651 | |
---|
652 | from Numeric import zeros, Float |
---|
653 | #self.conserved_quantities = zeros(3, Float) |
---|
654 | self.evolved_quantities = zeros(5, Float) |
---|
655 | |
---|
656 | def __repr__(self): |
---|
657 | return 'Reflective_boundary' |
---|
658 | |
---|
659 | |
---|
660 | def evaluate(self, vol_id, edge_id): |
---|
661 | """Reflective boundaries reverses the outward momentum |
---|
662 | of the volume they serve. |
---|
663 | """ |
---|
664 | |
---|
665 | q = self.evolved_quantities |
---|
666 | q[0] = self.area[vol_id, edge_id] |
---|
667 | q[1] = -self.discharge[vol_id, edge_id] |
---|
668 | q[2] = self.bed[vol_id, edge_id] |
---|
669 | q[3] = self.height[vol_id, edge_id] |
---|
670 | q[4] = self.stage[vol_id, edge_id] |
---|
671 | |
---|
672 | #print "In Reflective q ",q |
---|
673 | |
---|
674 | |
---|
675 | return q |
---|
676 | |
---|
677 | class Dirichlet_boundary(Boundary): |
---|
678 | """Dirichlet boundary returns constant values for the |
---|
679 | conserved quantities |
---|
680 | """ |
---|
681 | |
---|
682 | |
---|
683 | def __init__(self, evolved_quantities=None): |
---|
684 | Boundary.__init__(self) |
---|
685 | |
---|
686 | if evolved_quantities is None: |
---|
687 | msg = 'Must specify one value for each evolved quantity' |
---|
688 | raise msg |
---|
689 | |
---|
690 | from Numeric import array, Float |
---|
691 | self.evolved_quantities=array(evolved_quantities).astype(Float) |
---|
692 | |
---|
693 | def __repr__(self): |
---|
694 | return 'Dirichlet boundary (%s)' %self.evolved_quantities |
---|
695 | |
---|
696 | def evaluate(self, vol_id=None, edge_id=None): |
---|
697 | return self.evolved_quantities |
---|
698 | |
---|
699 | #---------------------------- |
---|
700 | #Standard forcing terms: |
---|
701 | #--------------------------- |
---|
702 | def gravity(domain): |
---|
703 | """Apply gravitational pull in the presence of bed slope |
---|
704 | """ |
---|
705 | |
---|
706 | from util import gradient |
---|
707 | from Numeric import zeros, Float, array, sum |
---|
708 | |
---|
709 | |
---|
710 | |
---|
711 | Area = domain.quantities['area'] |
---|
712 | Discharge = domain.quantities['discharge'] |
---|
713 | Elevation = domain.quantities['elevation'] |
---|
714 | Height = domain.quantities['height'] |
---|
715 | Stage = domain.quantities['stage'] |
---|
716 | |
---|
717 | discharge_ud = Discharge.explicit_update |
---|
718 | #stage_ud = Stage.explicit_update |
---|
719 | |
---|
720 | |
---|
721 | #h = Stage.vertex_values - Elevation.vertex_values |
---|
722 | h = Height.vertex_values |
---|
723 | b = Elevation.vertex_values |
---|
724 | w = Stage.vertex_values |
---|
725 | |
---|
726 | x = domain.get_vertex_coordinates() |
---|
727 | g = domain.g |
---|
728 | |
---|
729 | for k in range(domain.number_of_elements): |
---|
730 | avg_h = 0.5*(h[k,0] + h[k,1]) |
---|
731 | |
---|
732 | #Compute bed slope |
---|
733 | x0, x1 = x[k,:] |
---|
734 | b0, b1 = b[k,:] |
---|
735 | bx = gradient(x0, x1, b0, b1) |
---|
736 | |
---|
737 | #Update momentum (explicit update is reset to source values) |
---|
738 | discharge_ud[k] += -g*bx*avg_h |
---|
739 | #stage_ud[k] = 0.0 |
---|
740 | |
---|
741 | |
---|
742 | def manning_friction(domain): |
---|
743 | """Apply (Manning) friction to water momentum |
---|
744 | """ |
---|
745 | |
---|
746 | from math import sqrt |
---|
747 | |
---|
748 | w = domain.quantities['stage'].centroid_values |
---|
749 | z = domain.quantities['elevation'].centroid_values |
---|
750 | h = w-z |
---|
751 | |
---|
752 | uh = domain.quantities['xmomentum'].centroid_values |
---|
753 | #vh = domain.quantities['ymomentum'].centroid_values |
---|
754 | eta = domain.quantities['friction'].centroid_values |
---|
755 | |
---|
756 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
---|
757 | #ymom_update = domain.quantities['ymomentum'].semi_implicit_update |
---|
758 | |
---|
759 | N = domain.number_of_elements |
---|
760 | eps = domain.minimum_allowed_height |
---|
761 | g = domain.g |
---|
762 | |
---|
763 | for k in range(N): |
---|
764 | if eta[k] >= eps: |
---|
765 | if h[k] >= eps: |
---|
766 | #S = -g * eta[k]**2 * sqrt((uh[k]**2 + vh[k]**2)) |
---|
767 | S = -g * eta[k]**2 * uh[k] |
---|
768 | S /= h[k]**(7.0/3) |
---|
769 | |
---|
770 | #Update momentum |
---|
771 | xmom_update[k] += S*uh[k] |
---|
772 | #ymom_update[k] += S*vh[k] |
---|
773 | |
---|
774 | def linear_friction(domain): |
---|
775 | """Apply linear friction to water momentum |
---|
776 | |
---|
777 | Assumes quantity: 'linear_friction' to be present |
---|
778 | """ |
---|
779 | |
---|
780 | from math import sqrt |
---|
781 | |
---|
782 | w = domain.quantities['stage'].centroid_values |
---|
783 | z = domain.quantities['elevation'].centroid_values |
---|
784 | h = w-z |
---|
785 | |
---|
786 | uh = domain.quantities['xmomentum'].centroid_values |
---|
787 | tau = domain.quantities['linear_friction'].centroid_values |
---|
788 | |
---|
789 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
---|
790 | |
---|
791 | N = domain.number_of_elements |
---|
792 | eps = domain.minimum_allowed_height |
---|
793 | |
---|
794 | for k in range(N): |
---|
795 | if tau[k] >= eps: |
---|
796 | if h[k] >= eps: |
---|
797 | S = -tau[k]/h[k] |
---|
798 | |
---|
799 | #Update momentum |
---|
800 | xmom_update[k] += S*uh[k] |
---|
801 | |
---|
802 | |
---|
803 | |
---|
804 | def check_forcefield(f): |
---|
805 | """Check that f is either |
---|
806 | 1: a callable object f(t,x,y), where x and y are vectors |
---|
807 | and that it returns an array or a list of same length |
---|
808 | as x and y |
---|
809 | 2: a scalar |
---|
810 | """ |
---|
811 | |
---|
812 | from Numeric import ones, Float, array |
---|
813 | |
---|
814 | |
---|
815 | if callable(f): |
---|
816 | #N = 3 |
---|
817 | N = 2 |
---|
818 | #x = ones(3, Float) |
---|
819 | #y = ones(3, Float) |
---|
820 | x = ones(2, Float) |
---|
821 | #y = ones(2, Float) |
---|
822 | |
---|
823 | try: |
---|
824 | #q = f(1.0, x=x, y=y) |
---|
825 | q = f(1.0, x=x) |
---|
826 | except Exception, e: |
---|
827 | msg = 'Function %s could not be executed:\n%s' %(f, e) |
---|
828 | #FIXME: Reconsider this semantics |
---|
829 | raise msg |
---|
830 | |
---|
831 | try: |
---|
832 | q = array(q).astype(Float) |
---|
833 | except: |
---|
834 | msg = 'Return value from vector function %s could ' %f |
---|
835 | msg += 'not be converted into a Numeric array of floats.\n' |
---|
836 | msg += 'Specified function should return either list or array.' |
---|
837 | raise msg |
---|
838 | |
---|
839 | #Is this really what we want? |
---|
840 | msg = 'Return vector from function %s ' %f |
---|
841 | msg += 'must have same lenght as input vectors' |
---|
842 | assert len(q) == N, msg |
---|
843 | |
---|
844 | else: |
---|
845 | try: |
---|
846 | f = float(f) |
---|
847 | except: |
---|
848 | msg = 'Force field %s must be either a scalar' %f |
---|
849 | msg += ' or a vector function' |
---|
850 | raise msg |
---|
851 | return f |
---|
852 | |
---|