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 = ['stage', 'xmomentum'] |
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55 | evolved_quantities = ['stage', 'xmomentum', 'elevation', 'height', 'velocity'] |
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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(['stage','xmomentum']) |
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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 | |
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95 | def check_integrity(self): |
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96 | |
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97 | #Check that we are solving the shallow water wave equation |
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98 | |
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99 | msg = 'First conserved quantity must be "stage"' |
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100 | assert self.conserved_quantities[0] == 'stage', msg |
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101 | msg = 'Second conserved quantity must be "xmomentum"' |
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102 | assert self.conserved_quantities[1] == 'xmomentum', msg |
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103 | |
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104 | msg = 'First evolved quantity must be "stage"' |
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105 | assert self.evolved_quantities[0] == 'stage', msg |
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106 | msg = 'Second evolved quantity must be "xmomentum"' |
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107 | assert self.evolved_quantities[1] == 'xmomentum', msg |
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108 | msg = 'Third evolved quantity must be "elevation"' |
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109 | assert self.evolved_quantities[2] == 'elevation', msg |
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110 | msg = 'Fourth evolved quantity must be "height"' |
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111 | assert self.evolved_quantities[3] == 'height', msg |
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112 | msg = 'Fifth evolved quantity must be "velocity"' |
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113 | assert self.evolved_quantities[4] == 'velocity', msg |
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114 | |
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115 | Generic_Domain.check_integrity(self) |
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116 | |
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117 | def compute_fluxes(self): |
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118 | #Call correct module function |
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119 | #(either from this module or C-extension) |
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120 | compute_fluxes_vel(self) |
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121 | |
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122 | def distribute_to_vertices_and_edges(self): |
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123 | #Call correct module function |
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124 | #(either from this module or C-extension) |
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125 | distribute_to_vertices_and_edges_limit_w_u(self) |
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126 | |
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127 | |
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128 | #=============== End of Shallow Water Domain =============================== |
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129 | #----------------------------------- |
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130 | # Compute fluxes interface |
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131 | #----------------------------------- |
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132 | def compute_fluxes(domain): |
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133 | """ |
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134 | Python version of compute fluxes (local_compute_fluxes) |
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135 | is available in test_shallow_water_vel_domain.py |
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136 | """ |
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137 | |
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138 | |
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139 | from Numeric import zeros, Float |
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140 | import sys |
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141 | |
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142 | |
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143 | timestep = float(sys.maxint) |
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144 | |
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145 | stage = domain.quantities['stage'] |
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146 | xmom = domain.quantities['xmomentum'] |
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147 | bed = domain.quantities['elevation'] |
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148 | |
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149 | |
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150 | from comp_flux_vel_ext import compute_fluxes_ext |
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151 | |
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152 | domain.flux_timestep = compute_fluxes_ext(timestep,domain,stage,xmom,bed) |
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153 | |
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154 | |
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155 | #----------------------------------- |
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156 | # Compute flux definition with vel |
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157 | #----------------------------------- |
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158 | def compute_fluxes_vel(domain): |
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159 | from Numeric import zeros, Float |
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160 | import sys |
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161 | |
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162 | |
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163 | timestep = float(sys.maxint) |
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164 | |
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165 | stage = domain.quantities['stage'] |
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166 | xmom = domain.quantities['xmomentum'] |
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167 | bed = domain.quantities['elevation'] |
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168 | height = domain.quantities['height'] |
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169 | velocity = domain.quantities['velocity'] |
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170 | |
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171 | |
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172 | from comp_flux_vel_ext import compute_fluxes_vel_ext |
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173 | |
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174 | domain.flux_timestep = compute_fluxes_vel_ext(timestep,domain,stage,xmom,bed,height,velocity) |
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175 | |
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176 | |
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177 | |
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178 | #-------------------------------------------------------------------------- |
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179 | def distribute_to_vertices_and_edges_limit_w_u(domain): |
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180 | """Distribution from centroids to vertices specific to the |
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181 | shallow water wave |
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182 | equation. |
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183 | |
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184 | It will ensure that h (w-z) is always non-negative even in the |
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185 | presence of steep bed-slopes by taking a weighted average between shallow |
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186 | and deep cases. |
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187 | |
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188 | In addition, all conserved quantities get distributed as per either a |
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189 | constant (order==1) or a piecewise linear function (order==2). |
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190 | |
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191 | FIXME: more explanation about removal of artificial variability etc |
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192 | |
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193 | Precondition: |
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194 | All quantities defined at centroids and bed elevation defined at |
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195 | vertices. |
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196 | |
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197 | Postcondition |
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198 | Conserved quantities defined at vertices |
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199 | |
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200 | """ |
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201 | |
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202 | #from config import optimised_gradient_limiter |
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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 Numeric import zeros, Float |
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209 | from 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 | h_V[:] = w_V - z_V |
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267 | for i in range(len(h_C)): |
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268 | for j in range(2): |
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269 | if h_V[i,j] < 0.0 : |
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270 | #print 'h_V[%d,%d] = %f \n' % (i,j,h_V[i,j]) |
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271 | dh = h_V[i,j] |
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272 | h_V[i,j] = 0.0 |
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273 | w_V[i,j] = z_V[i,j] |
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274 | h_V[i,(j+1)%2] = h_V[i,(j+1)%2] + dh |
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275 | w_V[i,(j+1)%2] = w_V[i,(j+1)%2] + dh |
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276 | |
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277 | uh_V[:] = u_V * h_V |
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278 | |
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279 | |
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280 | return |
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281 | |
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282 | #--------------------------------------------------------------------------- |
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283 | def distribute_to_vertices_and_edges_limit_w_uh(domain): |
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284 | """Distribution from centroids to vertices specific to the |
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285 | shallow water wave equation. |
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286 | |
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287 | In addition, all conserved quantities get distributed as per either a |
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288 | constant (order==1) or a piecewise linear function (order==2). |
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289 | |
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290 | Precondition: |
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291 | All quantities defined at centroids and bed elevation defined at |
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292 | vertices. |
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293 | |
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294 | Postcondition |
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295 | Conserved quantities defined at vertices |
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296 | |
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297 | """ |
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298 | |
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299 | import sys |
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300 | from Numeric import zeros, Float |
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301 | from config import epsilon, h0 |
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302 | |
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303 | N = domain.number_of_elements |
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304 | |
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305 | #Shortcuts |
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306 | Stage = domain.quantities['stage'] |
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307 | Xmom = domain.quantities['xmomentum'] |
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308 | Bed = domain.quantities['elevation'] |
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309 | Height = domain.quantities['height'] |
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310 | Velocity = domain.quantities['velocity'] |
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311 | |
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312 | #Arrays |
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313 | w_C = Stage.centroid_values |
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314 | uh_C = Xmom.centroid_values |
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315 | z_C = Bed.centroid_values |
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316 | h_C = Height.centroid_values |
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317 | u_C = Velocity.centroid_values |
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318 | |
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319 | |
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320 | for i in range(N): |
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321 | h_C[i] = w_C[i] - z_C[i] |
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322 | if h_C[i] <= 1.0e-6: |
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323 | #print 'h_C[%d]= %15.5e\n' % (i,h_C[i]) |
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324 | h_C[i] = 0.0 |
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325 | w_C[i] = z_C[i] |
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326 | uh_C[i] = 0.0 |
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327 | |
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328 | for name in [ 'stage', 'xmomentum']: |
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329 | Q = domain.quantities[name] |
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330 | if domain.order == 1: |
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331 | Q.extrapolate_first_order() |
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332 | elif domain.order == 2: |
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333 | Q.extrapolate_second_order() |
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334 | else: |
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335 | raise 'Unknown order' |
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336 | |
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337 | w_V = domain.quantities['stage'].vertex_values |
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338 | z_V = domain.quantities['elevation'].vertex_values |
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339 | h_V = domain.quantities['height'].vertex_values |
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340 | u_V = domain.quantities['velocity'].vertex_values |
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341 | uh_V = domain.quantities['xmomentum'].vertex_values |
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342 | |
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343 | h_V[:] = w_V - z_V |
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344 | |
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345 | for i in range(len(h_C)): |
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346 | for j in range(2): |
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347 | if h_V[i,j] < 0.0 : |
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348 | #print 'h_V[%d,%d] = %f \n' % (i,j,h_V[i,j]) |
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349 | dh = h_V[i,j] |
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350 | h_V[i,j] = 0.0 |
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351 | w_V[i,j] = z_V[i,j] |
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352 | h_V[i,(j+1)%2] = h_V[i,(j+1)%2] + dh |
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353 | w_V[i,(j+1)%2] = w_V[i,(j+1)%2] + dh |
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354 | u_V[i,j] = 0.0 |
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355 | if h_V[i,j] < h0: |
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356 | u_V[i,j] |
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357 | else: |
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358 | u_V[i,j] = uh_V[i,j]/(h_V[i,j] + h0/h_V[i,j]) |
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359 | |
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360 | |
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361 | #-------------------------------------------------------- |
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362 | #Boundaries - specific to the shallow_water_vel_domain |
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363 | #-------------------------------------------------------- |
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364 | class Reflective_boundary(Boundary): |
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365 | """Reflective boundary returns same conserved quantities as |
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366 | those present in its neighbour volume but reflected. |
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367 | |
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368 | This class is specific to the shallow water equation as it |
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369 | works with the momentum quantities assumed to be the second |
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370 | and third conserved quantities. |
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371 | """ |
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372 | |
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373 | def __init__(self, domain = None): |
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374 | Boundary.__init__(self) |
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375 | |
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376 | if domain is None: |
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377 | msg = 'Domain must be specified for reflective boundary' |
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378 | raise msg |
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379 | |
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380 | #Handy shorthands |
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381 | self.normals = domain.normals |
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382 | self.stage = domain.quantities['stage'].vertex_values |
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383 | self.xmom = domain.quantities['xmomentum'].vertex_values |
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384 | self.bed = domain.quantities['elevation'].vertex_values |
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385 | self.height = domain.quantities['height'].vertex_values |
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386 | self.velocity = domain.quantities['velocity'].vertex_values |
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387 | |
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388 | from Numeric import zeros, Float |
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389 | #self.conserved_quantities = zeros(3, Float) |
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390 | self.evolved_quantities = zeros(5, Float) |
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391 | |
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392 | def __repr__(self): |
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393 | return 'Reflective_boundary' |
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394 | |
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395 | |
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396 | def evaluate(self, vol_id, edge_id): |
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397 | """Reflective boundaries reverses the outward momentum |
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398 | of the volume they serve. |
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399 | """ |
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400 | |
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401 | q = self.evolved_quantities |
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402 | q[0] = self.stage[vol_id, edge_id] |
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403 | q[1] = -self.xmom[vol_id, edge_id] |
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404 | q[2] = self.bed[vol_id, edge_id] |
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405 | q[3] = self.height[vol_id, edge_id] |
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406 | q[4] = -self.velocity[vol_id, edge_id] |
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407 | |
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408 | #print "In Reflective q ",q |
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409 | |
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410 | |
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411 | return q |
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412 | |
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413 | class Dirichlet_boundary(Boundary): |
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414 | """Dirichlet boundary returns constant values for the |
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415 | conserved quantities |
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416 | """ |
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417 | |
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418 | |
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419 | def __init__(self, evolved_quantities=None): |
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420 | Boundary.__init__(self) |
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421 | |
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422 | if evolved_quantities is None: |
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423 | msg = 'Must specify one value for each evolved quantity' |
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424 | raise msg |
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425 | |
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426 | from Numeric import array, Float |
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427 | self.evolved_quantities=array(evolved_quantities).astype(Float) |
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428 | |
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429 | def __repr__(self): |
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430 | return 'Dirichlet boundary (%s)' %self.evolved_quantities |
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431 | |
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432 | def evaluate(self, vol_id=None, edge_id=None): |
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433 | return self.evolved_quantities |
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434 | |
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435 | |
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436 | #---------------------------- |
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437 | #Standard forcing terms: |
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438 | #--------------------------- |
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439 | def gravity(domain): |
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440 | """Apply gravitational pull in the presence of bed slope |
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441 | """ |
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442 | |
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443 | from util import gradient |
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444 | from Numeric import zeros, Float, array, sum |
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445 | |
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446 | |
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447 | |
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448 | Stage = domain.quantities['stage'] |
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449 | Xmom = domain.quantities['xmomentum'] |
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450 | Elevation = domain.quantities['elevation'] |
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451 | Height = domain.quantities['height'] |
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452 | |
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453 | xmom_ud = Xmom.explicit_update |
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454 | #stage_ud = Stage.explicit_update |
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455 | |
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456 | |
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457 | #h = Stage.vertex_values - Elevation.vertex_values |
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458 | h = Height.vertex_values |
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459 | b = Elevation.vertex_values |
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460 | w = Stage.vertex_values |
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461 | |
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462 | x = domain.get_vertex_coordinates() |
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463 | g = domain.g |
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464 | |
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465 | for k in range(domain.number_of_elements): |
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466 | avg_h = 0.5*(h[k,0] + h[k,1]) |
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467 | |
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468 | #Compute bed slope |
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469 | x0, x1 = x[k,:] |
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470 | b0, b1 = b[k,:] |
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471 | bx = gradient(x0, x1, b0, b1) |
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472 | |
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473 | #Update momentum (explicit update is reset to source values) |
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474 | xmom_ud[k] += -g*bx*avg_h |
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475 | #stage_ud[k] = 0.0 |
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476 | |
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477 | |
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478 | def manning_friction(domain): |
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479 | """Apply (Manning) friction to water momentum |
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480 | """ |
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481 | |
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482 | from math import sqrt |
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483 | |
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484 | w = domain.quantities['stage'].centroid_values |
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485 | z = domain.quantities['elevation'].centroid_values |
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486 | h = w-z |
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487 | |
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488 | uh = domain.quantities['xmomentum'].centroid_values |
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489 | #vh = domain.quantities['ymomentum'].centroid_values |
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490 | eta = domain.quantities['friction'].centroid_values |
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491 | |
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492 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
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493 | #ymom_update = domain.quantities['ymomentum'].semi_implicit_update |
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494 | |
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495 | N = domain.number_of_elements |
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496 | eps = domain.minimum_allowed_height |
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497 | g = domain.g |
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498 | |
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499 | for k in range(N): |
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500 | if eta[k] >= eps: |
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501 | if h[k] >= eps: |
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502 | #S = -g * eta[k]**2 * sqrt((uh[k]**2 + vh[k]**2)) |
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503 | S = -g * eta[k]**2 * uh[k] |
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504 | S /= h[k]**(7.0/3) |
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505 | |
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506 | #Update momentum |
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507 | xmom_update[k] += S*uh[k] |
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508 | #ymom_update[k] += S*vh[k] |
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509 | |
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510 | def linear_friction(domain): |
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511 | """Apply linear friction to water momentum |
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512 | |
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513 | Assumes quantity: 'linear_friction' to be present |
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514 | """ |
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515 | |
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516 | from math import sqrt |
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517 | |
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518 | w = domain.quantities['stage'].centroid_values |
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519 | z = domain.quantities['elevation'].centroid_values |
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520 | h = w-z |
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521 | |
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522 | uh = domain.quantities['xmomentum'].centroid_values |
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523 | tau = domain.quantities['linear_friction'].centroid_values |
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524 | |
---|
525 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
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526 | |
---|
527 | N = domain.number_of_elements |
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528 | eps = domain.minimum_allowed_height |
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529 | |
---|
530 | for k in range(N): |
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531 | if tau[k] >= eps: |
---|
532 | if h[k] >= eps: |
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533 | S = -tau[k]/h[k] |
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534 | |
---|
535 | #Update momentum |
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536 | xmom_update[k] += S*uh[k] |
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537 | |
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538 | |
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539 | |
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540 | def check_forcefield(f): |
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541 | """Check that f is either |
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542 | 1: a callable object f(t,x,y), where x and y are vectors |
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543 | and that it returns an array or a list of same length |
---|
544 | as x and y |
---|
545 | 2: a scalar |
---|
546 | """ |
---|
547 | |
---|
548 | from Numeric import ones, Float, array |
---|
549 | |
---|
550 | |
---|
551 | if callable(f): |
---|
552 | #N = 3 |
---|
553 | N = 2 |
---|
554 | #x = ones(3, Float) |
---|
555 | #y = ones(3, Float) |
---|
556 | x = ones(2, Float) |
---|
557 | #y = ones(2, Float) |
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558 | |
---|
559 | try: |
---|
560 | #q = f(1.0, x=x, y=y) |
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561 | q = f(1.0, x=x) |
---|
562 | except Exception, e: |
---|
563 | msg = 'Function %s could not be executed:\n%s' %(f, e) |
---|
564 | #FIXME: Reconsider this semantics |
---|
565 | raise msg |
---|
566 | |
---|
567 | try: |
---|
568 | q = array(q).astype(Float) |
---|
569 | except: |
---|
570 | msg = 'Return value from vector function %s could ' %f |
---|
571 | msg += 'not be converted into a Numeric array of floats.\n' |
---|
572 | msg += 'Specified function should return either list or array.' |
---|
573 | raise msg |
---|
574 | |
---|
575 | #Is this really what we want? |
---|
576 | msg = 'Return vector from function %s ' %f |
---|
577 | msg += 'must have same lenght as input vectors' |
---|
578 | assert len(q) == N, msg |
---|
579 | |
---|
580 | else: |
---|
581 | try: |
---|
582 | f = float(f) |
---|
583 | except: |
---|
584 | msg = 'Force field %s must be either a scalar' %f |
---|
585 | msg += ' or a vector function' |
---|
586 | raise msg |
---|
587 | return f |
---|
588 | |
---|