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 Generic_domain from module |
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6 | generic_domain.py |
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7 | consisting of methods specific to Channel flow using the Shallow Water Wave Equation |
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8 | |
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9 | This particular modification of the Domain class implements the ability to |
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10 | vary the width of the 1D channel that the water flows in. As a result the |
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11 | conserved variables are different than previous implementations and so are the |
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12 | equations. |
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13 | |
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14 | U_t + E_x = S |
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15 | |
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16 | where |
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17 | |
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18 | U = [A, Q] = [b*h, u*b*h] |
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19 | E = [Q, Q^2/A + g*b*h^2/2] |
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20 | S represents source terms forcing the system |
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21 | (e.g. gravity, boundary_stree, friction, wind stress, ...) |
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22 | gravity = -g*b*h*z_x |
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23 | boundary_stress = 1/2*g*b_x*h^2 |
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24 | |
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25 | and _t, _x, _y denote the derivative with respect to t, x and y respectiely. |
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26 | |
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27 | The quantities are |
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28 | |
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29 | symbol variable name explanation |
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30 | A area Wetted area = b*h |
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31 | Q discharge flux of water = u*b*h |
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32 | x x horizontal distance from origin [m] |
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33 | z elevation elevation of bed on which flow is modelled [m] |
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34 | h height water height above z [m] |
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35 | w stage absolute water level, w = z+h [m] |
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36 | u speed in the x direction [m/s] |
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37 | uh xmomentum momentum in the x direction [m^2/s] |
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38 | b width width of channel |
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39 | eta mannings friction coefficient [to appear] |
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40 | nu wind stress coefficient [to appear] |
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41 | |
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42 | The conserved quantities are A, Q |
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43 | -------------------------------------------------------------------------- |
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44 | For details see e.g. |
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45 | Christopher Zoppou and Stephen Roberts, |
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46 | Catastrophic Collapse of Water Supply Reservoirs in Urban Areas, |
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47 | Journal of Hydraulic Engineering, vol. 127, No. 7 July 1999 |
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48 | |
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49 | |
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50 | John Jakeman, Ole Nielsen, Stephen Roberts, Duncan Gray, Christopher Zoppou, |
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51 | Padarn Wilson, Geoscience Australia, 2008 |
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52 | """ |
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53 | |
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54 | |
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55 | from anuga_1d.base.generic_domain import * |
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56 | import numpy |
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57 | |
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58 | |
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59 | #Shallow water domain |
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60 | class Domain(Generic_domain): |
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61 | |
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62 | def __init__(self, coordinates, boundary = None, tagged_elements = None): |
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63 | |
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64 | conserved_quantities = ['area', 'discharge'] |
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65 | evolved_quantities = ['area', 'discharge', 'elevation', 'height', 'velocity','width','stage'] |
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66 | other_quantities = ['friction'] |
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67 | Generic_domain.__init__(self, |
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68 | coordinates = coordinates, |
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69 | boundary = boundary, |
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70 | conserved_quantities = conserved_quantities, |
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71 | evolved_quantities = evolved_quantities, |
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72 | other_quantities = other_quantities, |
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73 | tagged_elements = tagged_elements) |
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74 | |
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75 | from anuga_1d.config import minimum_allowed_height, g, h0 |
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76 | self.minimum_allowed_height = minimum_allowed_height |
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77 | self.g = g |
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78 | self.h0 = h0 |
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79 | self.setstageflag = False |
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80 | self.discontinousb = False |
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81 | |
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82 | |
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83 | # forcing terms gravity and boundary stress are included in the flux calculation |
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84 | #self.forcing_terms.append(gravity) |
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85 | #self.forcing_terms.append(boundary_stress) |
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86 | #self.forcing_terms.append(manning_friction) |
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87 | |
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88 | |
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89 | |
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90 | #Stored output |
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91 | self.store = True |
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92 | self.format = 'sww' |
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93 | self.smooth = True |
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94 | |
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95 | |
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96 | #Reduction operation for get_vertex_values |
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97 | from anuga_1d.base.util import mean |
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98 | self.reduction = mean |
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99 | #self.reduction = min #Looks better near steep slopes |
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100 | |
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101 | self.set_quantities_to_be_stored(['area','discharge']) |
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102 | |
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103 | self.__doc__ = 'channel_domain' |
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104 | |
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105 | self.check_integrity() |
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106 | |
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107 | |
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108 | def check_integrity(self): |
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109 | |
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110 | #Check that we are solving the shallow water wave equation |
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111 | |
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112 | msg = 'First conserved quantity must be "area"' |
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113 | assert self.conserved_quantities[0] == 'area', msg |
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114 | msg = 'Second conserved quantity must be "discharge"' |
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115 | assert self.conserved_quantities[1] == 'discharge', msg |
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116 | |
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117 | msg = 'First evolved quantity must be "area"' |
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118 | assert self.evolved_quantities[0] == 'area', msg |
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119 | msg = 'Second evolved quantity must be "discharge"' |
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120 | assert self.evolved_quantities[1] == 'discharge', msg |
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121 | msg = 'Third evolved quantity must be "elevation"' |
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122 | assert self.evolved_quantities[2] == 'elevation', msg |
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123 | msg = 'Fourth evolved quantity must be "height"' |
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124 | assert self.evolved_quantities[3] == 'height', msg |
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125 | msg = 'Fifth evolved quantity must be "velocity"' |
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126 | assert self.evolved_quantities[4] == 'velocity', msg |
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127 | msg = 'Sixth evolved quantity must be "width"' |
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128 | assert self.evolved_quantities[5] == 'width', msg |
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129 | msg = 'Seventh evolved quantity must be "stage"' |
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130 | assert self.evolved_quantities[6] == 'stage', msg |
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131 | |
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132 | Generic_domain.check_integrity(self) |
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133 | |
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134 | def compute_fluxes(self): |
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135 | #Call correct module function |
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136 | #(either from this module or C-extension) |
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137 | compute_fluxes_channel(self) |
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138 | |
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139 | def distribute_to_vertices_and_edges(self): |
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140 | #Call correct module function |
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141 | #(either from this module or C-extension) |
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142 | #distribute_to_vertices_and_edges_limit_s_v_h(self) |
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143 | distribute_to_vertices_and_edges_limit_s_v(self) |
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144 | |
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145 | |
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146 | #=============== End of Channel Domain =============================== |
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147 | |
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148 | #----------------------------------- |
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149 | # Compute flux definition with channel |
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150 | #----------------------------------- |
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151 | def compute_fluxes_channel(domain): |
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152 | import sys |
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153 | timestep = float(sys.maxint) |
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154 | |
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155 | area = domain.quantities['area'] |
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156 | discharge = domain.quantities['discharge'] |
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157 | bed = domain.quantities['elevation'] |
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158 | height = domain.quantities['height'] |
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159 | velocity = domain.quantities['velocity'] |
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160 | width = domain.quantities['width'] |
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161 | |
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162 | |
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163 | from anuga_1d.channel.channel_domain_ext import compute_fluxes_channel_ext |
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164 | domain.flux_timestep = compute_fluxes_channel_ext(timestep,domain,area,discharge,bed,height,velocity,width) |
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165 | |
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166 | #----------------------------------------------------------------------- |
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167 | # Distribute to verticies with stage, velocity and channel geometry |
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168 | # reconstructed and then extrapolated. |
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169 | #----------------------------------------------------------------------- |
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170 | def distribute_to_vertices_and_edges_limit_s_v(domain): |
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171 | import sys |
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172 | from anuga_1d.config import epsilon, h0 |
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173 | |
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174 | N = domain.number_of_elements |
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175 | |
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176 | #Shortcuts |
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177 | area = domain.quantities['area'] |
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178 | discharge = domain.quantities['discharge'] |
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179 | bed = domain.quantities['elevation'] |
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180 | height = domain.quantities['height'] |
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181 | velocity = domain.quantities['velocity'] |
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182 | width = domain.quantities['width'] |
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183 | stage = domain.quantities['stage'] |
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184 | |
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185 | #Arrays |
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186 | a_C = area.centroid_values |
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187 | d_C = discharge.centroid_values |
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188 | z_C = bed.centroid_values |
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189 | h_C = height.centroid_values |
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190 | u_C = velocity.centroid_values |
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191 | b_C = width.centroid_values |
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192 | w_C = stage.centroid_values |
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193 | |
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194 | # Calculate height, velocity and stage. |
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195 | # Here we assume the conserved quantities and the channel geometry |
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196 | # (i.e. bed and width) have been accurately computed in the previous |
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197 | # timestep. |
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198 | h_C[:] = numpy.where(a_C > 0.0, a_C/(b_C + h0/b_C), 0.0) |
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199 | u_C[:] = numpy.where(a_C > 0.0, d_C/(a_C + h0/a_C), 0.0) |
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200 | |
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201 | w_C[:] = h_C + z_C |
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202 | |
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203 | # Extrapolate velocity and stage as well as channel geometry. |
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204 | for name in ['velocity', 'stage', 'elevation', 'width']: |
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205 | Q = domain.quantities[name] |
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206 | if domain.order == 1: |
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207 | Q.extrapolate_first_order() |
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208 | elif domain.order == 2: |
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209 | Q.extrapolate_second_order() |
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210 | else: |
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211 | raise 'Unknown order' |
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212 | |
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213 | # Stage, bed, width and velocity have been extrapolated |
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214 | w_V = stage.vertex_values |
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215 | u_V = velocity.vertex_values |
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216 | z_V = bed.vertex_values |
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217 | b_V = width.vertex_values |
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218 | |
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219 | # These quantites need to update vertex_values |
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220 | a_V = area.vertex_values |
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221 | h_V = height.vertex_values |
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222 | d_V = discharge.vertex_values |
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223 | |
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224 | # Calculate height and fix up negatives. The main idea here is |
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225 | # fix up the wet/dry interface. |
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226 | h_V[:,:] = w_V - z_V |
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227 | |
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228 | h_0 = numpy.where(h_V[:,0] < 0.0, 0.0, h_V[:,0]) |
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229 | h_1 = numpy.where(h_V[:,0] < 0.0, h_V[:,1]+h_V[:,0], h_V[:,1]) |
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230 | |
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231 | h_V[:,0] = h_0 |
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232 | h_V[:,1] = h_1 |
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233 | |
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234 | |
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235 | h_0 = numpy.where(h_V[:,1] < 0.0, h_V[:,1]+h_V[:,0], h_V[:,0]) |
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236 | h_1 = numpy.where(h_V[:,1] < 0.0, 0.0, h_V[:,1]) |
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237 | |
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238 | h_V[:,0] = h_0 |
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239 | h_V[:,1] = h_1 |
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240 | |
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241 | |
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242 | # Protect against negative and small heights. If we set h to zero |
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243 | # we better do the same with velocity (i.e. no water, no velocity). |
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244 | h_V[:,:] = numpy.where (h_V <= h0, 0.0, h_V) |
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245 | u_V[:,:] = numpy.where (h_V <= h0, 0.0, u_V) |
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246 | |
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247 | |
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248 | # Clean up conserved quantities |
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249 | w_V[:] = z_V + h_V |
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250 | a_V[:] = b_V * h_V |
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251 | d_V[:] = u_V * a_V |
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252 | |
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253 | |
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254 | return |
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255 | |
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256 | #----------------------------------------------------------------------- |
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257 | # Distribute to verticies with stage, height and velocity reconstructed |
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258 | # and then extrapolated. |
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259 | # In this method, we extrapolate the stage and height out to the vertices. |
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260 | # The bed, although given as initial data to the problem, is reconstructed |
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261 | # from the stage and height. This ensures consistency of the reconstructed |
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262 | # quantities (i.e. w = z + h) as well as protecting against negative |
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263 | # heights. |
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264 | #----------------------------------------------------------------------- |
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265 | def distribute_to_vertices_and_edges_limit_s_v_h(domain): |
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266 | import sys |
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267 | from anuga_1d.config import epsilon, h0 |
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268 | |
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269 | N = domain.number_of_elements |
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270 | |
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271 | #Shortcuts |
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272 | area = domain.quantities['area'] |
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273 | discharge = domain.quantities['discharge'] |
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274 | bed = domain.quantities['elevation'] |
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275 | height = domain.quantities['height'] |
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276 | velocity = domain.quantities['velocity'] |
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277 | width = domain.quantities['width'] |
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278 | stage = domain.quantities['stage'] |
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279 | |
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280 | #Arrays |
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281 | a_C = area.centroid_values |
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282 | d_C = discharge.centroid_values |
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283 | z_C = bed.centroid_values |
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284 | h_C = height.centroid_values |
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285 | u_C = velocity.centroid_values |
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286 | b_C = width.centroid_values |
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287 | w_C = stage.centroid_values |
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288 | |
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289 | # Construct h,u,w from the conserved quantities after protecting |
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290 | # conserved quantities from becoming too small. |
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291 | a_C[:] = numpy.where( (a_C>h0), a_C, 0.0 ) |
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292 | d_C[:] = numpy.where( (a_C>h0), d_C, 0.0 ) |
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293 | h_C[:] = numpy.where( (b_C>h0), a_C/(b_C + h0/b_C), 0.0 ) |
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294 | u_C[:] = numpy.where( (a_C>h0), d_C/(a_C + h0/a_C), 0.0 ) |
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295 | |
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296 | # Set the stage |
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297 | w_C[:] = h_C + z_C |
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298 | |
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299 | # Extrapolate "fundamental" quantities. |
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300 | # All other quantities will be reconstructed from these. |
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301 | for name in ['velocity', 'stage', 'height', 'width']: |
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302 | Q = domain.quantities[name] |
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303 | if domain.order == 1: |
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304 | Q.extrapolate_first_order() |
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305 | elif domain.order == 2: |
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306 | Q.extrapolate_second_order() |
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307 | else: |
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308 | raise 'Unknown order' |
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309 | |
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310 | # These quantities have been extrapolated. |
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311 | u_V = velocity.vertex_values |
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312 | w_V = stage.vertex_values |
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313 | h_V = height.vertex_values |
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314 | b_V = width.vertex_values |
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315 | |
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316 | # These need to be reconstructed |
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317 | a_V = area.vertex_values |
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318 | d_V = discharge.vertex_values |
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319 | z_V = bed.vertex_values |
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320 | |
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321 | # Reconstruct bed from stage and height. |
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322 | z_V[:] = w_V-h_V |
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323 | |
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324 | # Now reconstruct our conserved quantities from the above |
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325 | # reconstructed quantities. |
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326 | a_V[:] = b_V*h_V |
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327 | d_V[:] = u_V*a_V |
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328 | |
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329 | return |
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330 | |
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331 | |
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332 | #-------------------------------------------------------- |
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333 | #Boundaries - specific to the channel_domain |
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334 | #-------------------------------------------------------- |
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335 | class Reflective_boundary(Boundary): |
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336 | """Reflective boundary returns same conserved quantities as |
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337 | those present in its neighbour volume but reflected. |
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338 | |
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339 | This class is specific to the shallow water equation as it |
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340 | works with the momentum quantities assumed to be the second |
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341 | and third conserved quantities. |
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342 | """ |
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343 | |
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344 | def __init__(self, domain = None): |
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345 | Boundary.__init__(self) |
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346 | |
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347 | if domain is None: |
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348 | msg = 'Domain must be specified for reflective boundary' |
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349 | raise msg |
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350 | |
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351 | #Handy shorthands |
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352 | self.normals = domain.normals |
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353 | self.area = domain.quantities['area'].vertex_values |
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354 | self.discharge = domain.quantities['discharge'].vertex_values |
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355 | self.bed = domain.quantities['elevation'].vertex_values |
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356 | self.height = domain.quantities['height'].vertex_values |
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357 | self.velocity = domain.quantities['velocity'].vertex_values |
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358 | self.width = domain.quantities['width'].vertex_values |
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359 | self.stage = domain.quantities['stage'].vertex_values |
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360 | |
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361 | self.evolved_quantities = numpy.zeros(7, numpy.float) |
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362 | |
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363 | def __repr__(self): |
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364 | return 'Reflective_boundary' |
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365 | |
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366 | |
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367 | def evaluate(self, vol_id, edge_id): |
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368 | """Reflective boundaries reverses the outward momentum |
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369 | of the volume they serve. |
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370 | """ |
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371 | |
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372 | q = self.evolved_quantities |
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373 | q[0] = self.area[vol_id, edge_id] |
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374 | q[1] = -self.discharge[vol_id, edge_id] |
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375 | q[2] = self.bed[vol_id, edge_id] |
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376 | q[3] = self.height[vol_id, edge_id] |
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377 | q[4] = -self.velocity[vol_id, edge_id] |
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378 | q[5] = self.width[vol_id,edge_id] |
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379 | q[6] = self.stage[vol_id,edge_id] |
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380 | |
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381 | return q |
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382 | |
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383 | class Dirichlet_boundary(Boundary): |
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384 | """Dirichlet boundary returns constant values for the |
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385 | conserved quantities |
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386 | if k>5 and k<15: |
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387 | print discharge_ud[k],-g*zx*avg_h*avg_b |
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388 | discharge_ud[k] +=-g*zx*avg_h*avg_b """ |
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389 | |
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390 | |
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391 | def __init__(self, evolved_quantities=None): |
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392 | Boundary.__init__(self) |
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393 | |
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394 | if evolved_quantities is None: |
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395 | msg = 'Must specify one value for each evolved quantity' |
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396 | raise msg |
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397 | |
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398 | assert len(evolved_quantities) == 7 |
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399 | |
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400 | self.evolved_quantities=numpy.array(evolved_quantities,numpy.float) |
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401 | |
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402 | def __repr__(self): |
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403 | return 'Dirichlet boundary (%s)' %self.evolved_quantities |
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404 | |
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405 | def evaluate(self, vol_id=None, edge_id=None): |
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406 | return self.evolved_quantities |
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407 | |
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408 | |
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409 | #---------------------------- |
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410 | #Standard forcing terms: |
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411 | #--------------------------- |
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412 | def gravity(domain): |
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413 | """Apply gravitational pull in the presence of bed slope |
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414 | """ |
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415 | |
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416 | from util import gradient |
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417 | from Numeric import zeros, Float, array, sum |
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418 | |
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419 | |
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420 | |
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421 | Area = domain.quantities['area'] |
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422 | Discharge = domain.quantities['discharge'] |
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423 | Elevation = domain.quantities['elevation'] |
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424 | Height = domain.quantities['height'] |
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425 | Width = domain.quantities['width'] |
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426 | |
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427 | discharge_ud = Discharge.explicit_update |
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428 | |
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429 | |
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430 | |
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431 | h = Height.vertex_values |
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432 | b = Width.vertex_values |
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433 | a = Area.vertex_values |
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434 | z = Elevation.vertex_values |
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435 | |
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436 | x = domain.get_vertex_coordinates() |
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437 | g = domain.g |
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438 | for k in range(domain.number_of_elements): |
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439 | avg_h = 0.5*(h[k,0] + h[k,1]) |
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440 | avg_b = 0.5*(b[k,0] + b[k,1]) |
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441 | |
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442 | #Compute bed slope |
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443 | x0, x1 = x[k,:] |
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444 | z0, z1 = z[k,:] |
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445 | zx = gradient(x0, x1, z0, z1) |
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446 | |
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447 | #Update momentum (explicit update is reset to source values) |
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448 | discharge_ud[k]+= -g*zx*avg_h*avg_b |
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449 | |
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450 | |
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451 | def boundary_stress(domain): |
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452 | |
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453 | from util import gradient |
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454 | from Numeric import zeros, Float, array, sum |
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455 | |
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456 | Area = domain.quantities['area'] |
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457 | Discharge = domain.quantities['discharge'] |
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458 | Elevation = domain.quantities['elevation'] |
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459 | Height = domain.quantities['height'] |
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460 | Width = domain.quantities['width'] |
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461 | |
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462 | discharge_ud = Discharge.explicit_update |
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463 | |
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464 | h = Height.vertex_values |
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465 | b = Width.vertex_values |
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466 | a = Area.vertex_values |
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467 | z = Elevation.vertex_values |
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468 | |
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469 | x = domain.get_vertex_coordinates() |
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470 | g = domain.g |
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471 | |
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472 | for k in range(domain.number_of_elements): |
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473 | avg_h = 0.5*(h[k,0] + h[k,1]) |
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474 | |
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475 | |
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476 | #Compute bed slope |
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477 | x0, x1 = x[k,:] |
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478 | b0, b1 = b[k,:] |
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479 | bx = gradient(x0, x1, b0, b1) |
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480 | |
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481 | #Update momentum (explicit update is reset to source values) |
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482 | discharge_ud[k] += 0.5*g*bx*avg_h*avg_h |
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483 | #stage_ud[k] = 0.0 |
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484 | |
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485 | |
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486 | def manning_friction(domain): |
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487 | """Apply (Manning) friction to water momentum |
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488 | """ |
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489 | |
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490 | from math import sqrt |
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491 | |
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492 | w = domain.quantities['stage'].centroid_values |
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493 | z = domain.quantities['elevation'].centroid_values |
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494 | h = w-z |
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495 | |
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496 | uh = domain.quantities['xmomentum'].centroid_values |
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497 | eta = domain.quantities['friction'].centroid_values |
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498 | |
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499 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
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500 | |
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501 | N = domain.number_of_elements |
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502 | eps = domain.minimum_allowed_height |
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503 | g = domain.g |
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504 | |
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505 | for k in range(N): |
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506 | if eta[k] >= eps: |
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507 | if h[k] >= eps: |
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508 | #S = -g * eta[k]**2 * sqrt((uh[k]**2 + vh[k]**2)) |
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509 | S = -g * eta[k]**2 * uh[k] |
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510 | S /= h[k]**(7.0/3) |
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511 | |
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512 | #Update momentum |
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513 | xmom_update[k] += S*uh[k] |
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514 | #ymom_update[k] += S*vh[k] |
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515 | |
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516 | def linear_friction(domain): |
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517 | """Apply linear friction to water momentum |
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518 | |
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519 | Assumes quantity: 'linear_friction' to be present |
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520 | """ |
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521 | |
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522 | from math import sqrt |
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523 | |
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524 | w = domain.quantities['stage'].centroid_values |
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525 | z = domain.quantities['elevation'].centroid_values |
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526 | h = w-z |
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527 | |
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528 | uh = domain.quantities['xmomentum'].centroid_values |
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529 | tau = domain.quantities['linear_friction'].centroid_values |
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530 | |
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531 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
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532 | |
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533 | N = domain.number_of_elements |
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534 | eps = domain.minimum_allowed_height |
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535 | |
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536 | for k in range(N): |
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537 | if tau[k] >= eps: |
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538 | if h[k] >= eps: |
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539 | S = -tau[k]/h[k] |
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540 | |
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541 | #Update momentum |
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542 | xmom_update[k] += S*uh[k] |
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543 | |
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544 | |
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545 | |
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546 | |
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547 | def linearb(domain): |
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548 | |
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549 | bC = domain.quantities['width'].vertex_values |
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550 | |
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551 | for i in range(len(bC)-1): |
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552 | temp= 0.5*(bC[i,1]+bC[i+1,0]) |
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553 | bC[i,1]=temp |
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554 | bC[i+1,0]=temp |
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555 | |
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556 | |
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557 | |
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