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 flow_1d.generic_1d.generic_domain import * |
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47 | from sww_boundary_conditions import * |
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48 | from sww_forcing_terms import * |
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49 | |
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50 | #Shallow water domain |
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51 | class Domain(Generic_domain): |
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52 | |
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53 | def __init__(self, coordinates, boundary = None, tagged_elements = None): |
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54 | |
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55 | conserved_quantities = ['stage', 'xmomentum'] |
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56 | evolved_quantities = ['stage', 'xmomentum', 'elevation', 'height', 'velocity'] |
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57 | other_quantities = ['friction'] |
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58 | Generic_domain.__init__(self, |
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59 | coordinates = coordinates, |
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60 | boundary = boundary, |
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61 | conserved_quantities = conserved_quantities, |
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62 | evolved_quantities = evolved_quantities, |
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63 | other_quantities = other_quantities, |
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64 | tagged_elements = tagged_elements) |
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65 | |
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66 | from flow_1d.config import minimum_allowed_height, g, h0 |
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67 | self.minimum_allowed_height = minimum_allowed_height |
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68 | self.g = g |
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69 | self.h0 = h0 |
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70 | |
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71 | #forcing terms not included in 1d domain ?WHy? |
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72 | self.forcing_terms.append(gravity) |
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73 | #self.forcing_terms.append(manning_friction) |
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74 | #print "\nI have Removed forcing terms line 64 1dsw" |
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75 | |
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76 | |
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77 | #Stored output |
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78 | self.store = True |
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79 | self.format = 'sww' |
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80 | self.smooth = True |
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81 | |
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82 | |
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83 | #Reduction operation for get_vertex_values |
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84 | from flow_1d.utilities.util import mean |
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85 | self.reduction = mean |
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86 | #self.reduction = min #Looks better near steep slopes |
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87 | |
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88 | self.set_quantities_to_be_stored(['stage','xmomentum']) |
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89 | |
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90 | self.__doc__ = 'sww_vel_domain' |
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91 | |
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92 | self.check_integrity() |
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93 | |
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94 | |
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95 | |
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96 | def check_integrity(self): |
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97 | |
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98 | #Check that we are solving the shallow water wave equation |
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99 | |
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100 | msg = 'First conserved quantity must be "stage"' |
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101 | assert self.conserved_quantities[0] == 'stage', msg |
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102 | msg = 'Second conserved quantity must be "xmomentum"' |
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103 | assert self.conserved_quantities[1] == 'xmomentum', msg |
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104 | |
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105 | msg = 'First evolved quantity must be "stage"' |
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106 | assert self.evolved_quantities[0] == 'stage', msg |
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107 | msg = 'Second evolved quantity must be "xmomentum"' |
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108 | assert self.evolved_quantities[1] == 'xmomentum', msg |
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109 | msg = 'Third evolved quantity must be "elevation"' |
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110 | assert self.evolved_quantities[2] == 'elevation', msg |
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111 | msg = 'Fourth evolved quantity must be "height"' |
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112 | assert self.evolved_quantities[3] == 'height', msg |
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113 | msg = 'Fifth evolved quantity must be "velocity"' |
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114 | assert self.evolved_quantities[4] == 'velocity', msg |
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115 | |
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116 | Generic_domain.check_integrity(self) |
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117 | |
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118 | def compute_fluxes(self): |
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119 | #Call correct module function |
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120 | #(either from this module or C-extension) |
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121 | compute_fluxes_vel(self) |
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122 | |
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123 | def distribute_to_vertices_and_edges(self): |
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124 | #Call correct module function |
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125 | #(either from this module or C-extension) |
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126 | distribute_to_vertices_and_edges_limit_w_u(self) |
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127 | |
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128 | |
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129 | #=============== End of Shallow Water Domain =============================== |
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130 | #----------------------------------- |
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131 | # Compute fluxes interface |
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132 | #----------------------------------- |
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133 | def compute_fluxes(domain): |
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134 | """ |
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135 | Python version of compute fluxes (local_compute_fluxes) |
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136 | is available in test_shallow_water_vel_domain.py |
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137 | """ |
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138 | |
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139 | |
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140 | from numpy import zeros |
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141 | import sys |
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142 | |
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143 | |
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144 | timestep = float(sys.maxint) |
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145 | |
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146 | stage = domain.quantities['stage'] |
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147 | xmom = domain.quantities['xmomentum'] |
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148 | bed = domain.quantities['elevation'] |
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149 | |
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150 | |
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151 | from flow_1d.sww_flow.sww_vel_comp_flux_ext import compute_fluxes_ext |
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152 | |
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153 | domain.flux_timestep = compute_fluxes_ext(timestep,domain,stage,xmom,bed) |
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154 | |
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155 | |
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156 | #----------------------------------- |
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157 | # Compute flux definition with vel |
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158 | #----------------------------------- |
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159 | def compute_fluxes_vel(domain): |
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160 | from Numeric import zeros, Float |
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161 | import sys |
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162 | |
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163 | |
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164 | timestep = float(sys.maxint) |
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165 | |
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166 | stage = domain.quantities['stage'] |
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167 | xmom = domain.quantities['xmomentum'] |
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168 | bed = domain.quantities['elevation'] |
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169 | height = domain.quantities['height'] |
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170 | velocity = domain.quantities['velocity'] |
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171 | |
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172 | |
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173 | from flow_1d.sww_flow.sww_vel_comp_flux_ext import compute_fluxes_vel_ext |
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174 | |
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175 | domain.flux_timestep = compute_fluxes_vel_ext(timestep,domain,stage,xmom,bed,height,velocity) |
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176 | |
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177 | |
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178 | |
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179 | #-------------------------------------------------------------------------- |
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180 | def distribute_to_vertices_and_edges_limit_w_u(domain): |
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181 | """Distribution from centroids to vertices specific to the |
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182 | shallow water wave |
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183 | equation. |
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184 | |
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185 | It will ensure that h (w-z) is always non-negative even in the |
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186 | presence of steep bed-slopes by taking a weighted average between shallow |
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187 | and deep cases. |
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188 | |
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189 | In addition, all conserved quantities get distributed as per either a |
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190 | constant (order==1) or a piecewise linear function (order==2). |
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191 | |
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192 | FIXME: more explanation about removal of artificial variability etc |
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193 | |
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194 | Precondition: |
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195 | All quantities defined at centroids and bed elevation defined at |
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196 | vertices. |
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197 | |
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198 | Postcondition |
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199 | Conserved quantities defined at vertices |
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200 | |
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201 | """ |
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202 | |
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203 | |
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204 | #Remove very thin layers of water |
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205 | #protect_against_infinitesimal_and_negative_heights(domain) |
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206 | |
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207 | import sys |
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208 | from numpy import zeros |
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209 | from flow_1d.config import epsilon, h0 |
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210 | |
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211 | N = domain.number_of_elements |
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212 | |
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213 | #Shortcuts |
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214 | Stage = domain.quantities['stage'] |
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215 | Xmom = domain.quantities['xmomentum'] |
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216 | Bed = domain.quantities['elevation'] |
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217 | Height = domain.quantities['height'] |
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218 | Velocity = domain.quantities['velocity'] |
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219 | |
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220 | #Arrays |
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221 | w_C = Stage.centroid_values |
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222 | uh_C = Xmom.centroid_values |
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223 | z_C = Bed.centroid_values |
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224 | h_C = Height.centroid_values |
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225 | u_C = Velocity.centroid_values |
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226 | |
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227 | #print id(h_C) |
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228 | ## for i in range(N): |
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229 | ## h_C[i] = w_C[i] - z_C[i] |
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230 | ## if h_C[i] <= 1.0e-12: |
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231 | ## #print 'h_C[%d]= %15.5e\n' % (i,h_C[i]) |
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232 | ## h_C[i] = 0.0 |
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233 | ## w_C[i] = z_C[i] |
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234 | ## #uh_C[i] = 0.0 |
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235 | |
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236 | ## # u_C[i] = 0.0 |
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237 | ## # else: |
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238 | ## # u_C[i] = uh_C[i]/h_C[i] |
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239 | |
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240 | h0 = 1.0e-12 |
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241 | for i in range(N): |
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242 | h_C[i] = w_C[i] - z_C[i] |
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243 | if h_C[i] < 1.0e-12: |
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244 | u_C[i] = 0.0 #Could have been negative |
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245 | h_C[i] = 0.0 |
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246 | w_C[i] = z_C[i] |
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247 | else: |
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248 | #u_C[i] = uh_C[i]/(h_C[i] + h0/h_C[i]) |
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249 | u_C[i] = uh_C[i]/h_C[i] |
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250 | |
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251 | for name in [ 'velocity', 'stage' ]: |
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252 | Q = domain.quantities[name] |
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253 | if domain.order == 1: |
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254 | Q.extrapolate_first_order() |
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255 | elif domain.order == 2: |
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256 | Q.extrapolate_second_order() |
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257 | else: |
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258 | raise 'Unknown order' |
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259 | |
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260 | w_V = domain.quantities['stage'].vertex_values |
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261 | z_V = domain.quantities['elevation'].vertex_values |
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262 | h_V = domain.quantities['height'].vertex_values |
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263 | u_V = domain.quantities['velocity'].vertex_values |
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264 | uh_V = domain.quantities['xmomentum'].vertex_values |
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265 | |
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266 | #print w_V |
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267 | #print z_V |
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268 | |
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269 | h_V[:,:] = w_V - z_V |
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270 | for i in range(len(h_C)): |
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271 | for j in range(2): |
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272 | if h_V[i,j] < 0.0 : |
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273 | #print 'h_V[%d,%d] = %f \n' % (i,j,h_V[i,j]) |
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274 | dh = h_V[i,j] |
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275 | h_V[i,j] = 0.0 |
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276 | w_V[i,j] = z_V[i,j] |
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277 | h_V[i,(j+1)%2] = h_V[i,(j+1)%2] + dh |
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278 | w_V[i,(j+1)%2] = w_V[i,(j+1)%2] + dh |
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279 | |
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280 | uh_V[:,:] = u_V * h_V |
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281 | |
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282 | |
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283 | return |
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284 | |
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285 | #--------------------------------------------------------------------------- |
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286 | def distribute_to_vertices_and_edges_limit_w_uh(domain): |
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287 | """Distribution from centroids to vertices specific to the |
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288 | shallow water wave equation. |
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289 | |
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290 | In addition, all conserved quantities get distributed as per either a |
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291 | constant (order==1) or a piecewise linear function (order==2). |
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292 | |
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293 | Precondition: |
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294 | All quantities defined at centroids and bed elevation defined at |
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295 | vertices. |
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296 | |
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297 | Postcondition |
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298 | Conserved quantities defined at vertices |
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299 | |
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300 | """ |
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301 | |
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302 | import sys |
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303 | from numpy import zeros |
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304 | from flow_1d.config import epsilon, h0 |
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305 | |
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306 | N = domain.number_of_elements |
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307 | |
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308 | #Shortcuts |
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309 | Stage = domain.quantities['stage'] |
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310 | Xmom = domain.quantities['xmomentum'] |
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311 | Bed = domain.quantities['elevation'] |
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312 | Height = domain.quantities['height'] |
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313 | Velocity = domain.quantities['velocity'] |
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314 | |
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315 | #Arrays |
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316 | w_C = Stage.centroid_values |
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317 | uh_C = Xmom.centroid_values |
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318 | z_C = Bed.centroid_values |
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319 | h_C = Height.centroid_values |
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320 | u_C = Velocity.centroid_values |
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321 | |
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322 | |
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323 | for i in range(N): |
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324 | h_C[i] = w_C[i] - z_C[i] |
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325 | if h_C[i] <= 1.0e-6: |
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326 | #print 'h_C[%d]= %15.5e\n' % (i,h_C[i]) |
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327 | h_C[i] = 0.0 |
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328 | w_C[i] = z_C[i] |
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329 | uh_C[i] = 0.0 |
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330 | |
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331 | for name in [ 'stage', 'xmomentum']: |
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332 | Q = domain.quantities[name] |
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333 | if domain.order == 1: |
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334 | Q.extrapolate_first_order() |
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335 | elif domain.order == 2: |
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336 | Q.extrapolate_second_order() |
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337 | else: |
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338 | raise 'Unknown order' |
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339 | |
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340 | w_V = domain.quantities['stage'].vertex_values |
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341 | z_V = domain.quantities['elevation'].vertex_values |
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342 | h_V = domain.quantities['height'].vertex_values |
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343 | u_V = domain.quantities['velocity'].vertex_values |
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344 | uh_V = domain.quantities['xmomentum'].vertex_values |
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345 | |
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346 | h_V[:,:] = w_V - z_V |
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347 | |
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348 | for i in range(len(h_C)): |
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349 | for j in range(2): |
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350 | if h_V[i,j] < 0.0 : |
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351 | #print 'h_V[%d,%d] = %f \n' % (i,j,h_V[i,j]) |
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352 | dh = h_V[i,j] |
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353 | h_V[i,j] = 0.0 |
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354 | w_V[i,j] = z_V[i,j] |
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355 | h_V[i,(j+1)%2] = h_V[i,(j+1)%2] + dh |
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356 | w_V[i,(j+1)%2] = w_V[i,(j+1)%2] + dh |
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357 | u_V[i,j] = 0.0 |
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358 | if h_V[i,j] < h0: |
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359 | u_V[i,j] |
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360 | else: |
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361 | u_V[i,j] = uh_V[i,j]/(h_V[i,j] + h0/h_V[i,j]) |
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362 | |
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363 | |
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