1 | """Finite-volume computations of the shallow water wave equation. |
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2 | |
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3 | Title: ANGUA shallow_water_domain - 2D triangular domains for finite-volume |
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4 | computations of the shallow water wave equation. |
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5 | |
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6 | |
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7 | Author: Ole Nielsen (Ole.Nielsen@ga.gov.au), |
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8 | Stephen Roberts (Stephen.Roberts@anu.edu.au), |
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9 | Duncan Gray (Duncan.Gray@ga.gov.au), etc |
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10 | |
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11 | CreationDate: 2004 |
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12 | |
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13 | Description: |
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14 | This module contains a specialisation of class Domain from |
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15 | module domain.py consisting of methods specific to the |
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16 | Shallow Water Wave Equation |
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17 | |
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18 | U_t + E_x + G_y = S |
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19 | |
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20 | where |
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21 | |
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22 | U = [w, uh, vh] |
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23 | E = [uh, u^2h + gh^2/2, uvh] |
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24 | G = [vh, uvh, v^2h + gh^2/2] |
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25 | S represents source terms forcing the system |
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26 | (e.g. gravity, friction, wind stress, ...) |
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27 | |
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28 | and _t, _x, _y denote the derivative with respect to t, x and y |
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29 | respectively. |
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30 | |
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31 | |
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32 | The quantities are |
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33 | |
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34 | symbol variable name explanation |
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35 | x x horizontal distance from origin [m] |
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36 | y y vertical distance from origin [m] |
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37 | z elevation elevation of bed on which flow is modelled [m] |
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38 | h height water height above z [m] |
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39 | w stage absolute water level, w = z+h [m] |
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40 | u speed in the x direction [m/s] |
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41 | v speed in the y direction [m/s] |
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42 | uh xmomentum momentum in the x direction [m^2/s] |
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43 | vh ymomentum momentum in the y direction [m^2/s] |
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44 | |
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45 | eta mannings friction coefficient [to appear] |
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46 | nu wind stress coefficient [to appear] |
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47 | |
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48 | The conserved quantities are w, uh, vh |
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49 | |
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50 | Reference: |
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51 | Catastrophic Collapse of Water Supply Reservoirs in Urban Areas, |
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52 | Christopher Zoppou and Stephen Roberts, |
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53 | Journal of Hydraulic Engineering, vol. 127, No. 7 July 1999 |
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54 | |
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55 | Hydrodynamic modelling of coastal inundation. |
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56 | Nielsen, O., S. Roberts, D. Gray, A. McPherson and A. Hitchman |
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57 | In Zerger, A. and Argent, R.M. (eds) MODSIM 2005 International Congress on |
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58 | Modelling and Simulation. Modelling and Simulation Society of Australia and |
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59 | New Zealand, December 2005, pp. 518-523. ISBN: 0-9758400-2-9. |
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60 | http://www.mssanz.org.au/modsim05/papers/nielsen.pdf |
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61 | |
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62 | |
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63 | SeeAlso: |
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64 | TRAC administration of ANUGA (User Manuals etc) at |
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65 | https://datamining.anu.edu.au/anuga and Subversion repository at |
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66 | $HeadURL: anuga_core/source/anuga/shallow_water/shallow_water_domain.py $ |
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67 | |
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68 | Constraints: See GPL license in the user guide |
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69 | Version: 1.0 ($Revision: 4254 $) |
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70 | ModifiedBy: |
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71 | $Author: duncan $ |
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72 | $Date: 2007-02-12 06:18:20 +0000 (Mon, 12 Feb 2007) $ |
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73 | |
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74 | """ |
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75 | |
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76 | #Subversion keywords: |
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77 | # |
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78 | #$LastChangedDate: 2007-02-12 06:18:20 +0000 (Mon, 12 Feb 2007) $ |
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79 | #$LastChangedRevision: 4254 $ |
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80 | #$LastChangedBy: duncan $ |
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81 | |
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82 | from Numeric import zeros, ones, Float, array, sum, size |
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83 | from Numeric import compress, arange |
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84 | |
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85 | |
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86 | from anuga.abstract_2d_finite_volumes.domain import Domain as Generic_Domain |
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87 | from anuga.abstract_2d_finite_volumes.generic_boundary_conditions\ |
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88 | import Boundary |
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89 | from anuga.abstract_2d_finite_volumes.generic_boundary_conditions\ |
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90 | import File_boundary |
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91 | from anuga.abstract_2d_finite_volumes.generic_boundary_conditions\ |
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92 | import Dirichlet_boundary |
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93 | from anuga.abstract_2d_finite_volumes.generic_boundary_conditions\ |
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94 | import Time_boundary |
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95 | from anuga.abstract_2d_finite_volumes.generic_boundary_conditions\ |
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96 | import Transmissive_boundary |
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97 | |
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98 | from anuga.utilities.numerical_tools import gradient, mean |
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99 | from anuga.config import minimum_storable_height |
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100 | from anuga.config import minimum_allowed_height, maximum_allowed_speed |
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101 | from anuga.config import g, beta_h, beta_w, beta_w_dry,\ |
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102 | beta_uh, beta_uh_dry, beta_vh, beta_vh_dry, limit2007 |
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103 | from anuga.config import alpha_balance |
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104 | |
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105 | |
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106 | #Shallow water domain |
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107 | class Domain(Generic_Domain): |
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108 | |
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109 | def __init__(self, |
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110 | coordinates=None, |
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111 | vertices=None, |
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112 | boundary=None, |
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113 | tagged_elements=None, |
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114 | geo_reference=None, |
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115 | use_inscribed_circle=False, |
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116 | mesh_filename=None, |
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117 | use_cache=False, |
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118 | verbose=False, |
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119 | full_send_dict=None, |
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120 | ghost_recv_dict=None, |
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121 | processor=0, |
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122 | numproc=1, |
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123 | number_of_full_nodes=None, |
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124 | number_of_full_triangles=None): |
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125 | |
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126 | |
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127 | conserved_quantities = ['stage', 'xmomentum', 'ymomentum'] |
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128 | other_quantities = ['elevation', 'friction'] |
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129 | Generic_Domain.__init__(self, |
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130 | coordinates, |
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131 | vertices, |
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132 | boundary, |
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133 | conserved_quantities, |
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134 | other_quantities, |
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135 | tagged_elements, |
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136 | geo_reference, |
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137 | use_inscribed_circle, |
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138 | mesh_filename, |
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139 | use_cache, |
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140 | verbose, |
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141 | full_send_dict, |
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142 | ghost_recv_dict, |
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143 | processor, |
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144 | numproc, |
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145 | number_of_full_nodes=number_of_full_nodes, |
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146 | number_of_full_triangles=number_of_full_triangles) |
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147 | |
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148 | self.minimum_allowed_height = minimum_allowed_height |
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149 | self.H0 = minimum_allowed_height # Minimal height for flux computation |
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150 | self.maximum_allowed_speed = maximum_allowed_speed |
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151 | self.g = g |
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152 | self.beta_w = beta_w |
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153 | self.beta_w_dry = beta_w_dry |
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154 | self.beta_uh = beta_uh |
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155 | self.beta_uh_dry = beta_uh_dry |
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156 | self.beta_vh = beta_vh |
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157 | self.beta_vh_dry = beta_vh_dry |
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158 | self.beta_h = beta_h |
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159 | self.alpha_balance = alpha_balance |
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160 | |
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161 | self.limit2007 = limit2007 |
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162 | |
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163 | self.flux_function = flux_function_central |
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164 | #self.flux_function = flux_function_kinetic |
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165 | |
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166 | self.forcing_terms.append(manning_friction) |
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167 | self.forcing_terms.append(gravity) |
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168 | |
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169 | #Stored output |
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170 | self.store = True |
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171 | self.format = 'sww' |
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172 | self.set_store_vertices_uniquely(False) |
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173 | self.minimum_storable_height = minimum_storable_height |
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174 | self.quantities_to_be_stored = ['stage','xmomentum','ymomentum'] |
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175 | |
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176 | |
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177 | def set_all_limiters(self, beta): |
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178 | """Shorthand to assign one constant value [0,1[ to all limiters. |
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179 | 0 Corresponds to first order, where as larger values make use of |
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180 | the second order scheme. |
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181 | """ |
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182 | |
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183 | self.beta_w = beta |
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184 | self.beta_w_dry = beta |
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185 | self.beta_uh = beta |
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186 | self.beta_uh_dry = beta |
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187 | self.beta_vh = beta |
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188 | self.beta_vh_dry = beta |
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189 | self.beta_h = beta |
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190 | |
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191 | |
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192 | def set_store_vertices_uniquely(self, flag, reduction=None): |
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193 | """Decide whether vertex values should be stored uniquely as |
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194 | computed in the model or whether they should be reduced to one |
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195 | value per vertex using self.reduction. |
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196 | """ |
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197 | |
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198 | # FIXME (Ole): how about using the word continuous vertex values? |
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199 | self.smooth = not flag |
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200 | |
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201 | #Reduction operation for get_vertex_values |
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202 | if reduction is None: |
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203 | self.reduction = mean |
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204 | #self.reduction = min #Looks better near steep slopes |
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205 | |
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206 | |
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207 | def set_minimum_storable_height(self, minimum_storable_height): |
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208 | """ |
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209 | Set the minimum depth that will be recognised when writing |
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210 | to an sww file. This is useful for removing thin water layers |
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211 | that seems to be caused by friction creep. |
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212 | |
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213 | The minimum allowed sww depth is in meters. |
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214 | """ |
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215 | self.minimum_storable_height = minimum_storable_height |
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216 | |
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217 | |
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218 | def set_maximum_allowed_speed(self, maximum_allowed_speed): |
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219 | """ |
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220 | Set the maximum particle speed that is allowed in water |
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221 | shallower than minimum_allowed_height. This is useful for |
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222 | controlling speeds in very thin layers of water and at the same time |
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223 | allow some movement avoiding pooling of water. |
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224 | |
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225 | """ |
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226 | self.maximum_allowed_speed = maximum_allowed_speed |
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227 | |
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228 | |
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229 | def set_points_file_block_line_size(self,points_file_block_line_size): |
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230 | """ |
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231 | Set the minimum depth that will be recognised when writing |
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232 | to an sww file. This is useful for removing thin water layers |
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233 | that seems to be caused by friction creep. |
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234 | |
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235 | The minimum allowed sww depth is in meters. |
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236 | """ |
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237 | self.points_file_block_line_size = points_file_block_line_size |
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238 | |
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239 | def set_quantities_to_be_stored(self, q): |
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240 | """Specify which quantities will be stored in the sww file. |
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241 | |
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242 | q must be either: |
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243 | - the name of a quantity |
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244 | - a list of quantity names |
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245 | - None |
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246 | |
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247 | In the two first cases, the named quantities will be stored at |
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248 | each yieldstep (This is in addition to the quantities elevation |
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249 | and friction) |
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250 | |
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251 | If q is None, storage will be switched off altogether. |
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252 | """ |
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253 | |
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254 | |
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255 | if q is None: |
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256 | self.quantities_to_be_stored = [] |
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257 | self.store = False |
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258 | return |
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259 | |
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260 | if isinstance(q, basestring): |
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261 | q = [q] # Turn argument into a list |
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262 | |
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263 | #Check correcness |
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264 | for quantity_name in q: |
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265 | msg = 'Quantity %s is not a valid conserved quantity'\ |
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266 | %quantity_name |
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267 | |
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268 | assert quantity_name in self.conserved_quantities, msg |
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269 | |
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270 | self.quantities_to_be_stored = q |
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271 | |
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272 | |
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273 | |
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274 | def get_wet_elements(self, indices=None): |
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275 | """Return indices for elements where h > minimum_allowed_height |
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276 | |
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277 | Optional argument: |
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278 | indices is the set of element ids that the operation applies to. |
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279 | |
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280 | Usage: |
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281 | indices = get_wet_elements() |
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282 | |
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283 | Note, centroid values are used for this operation |
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284 | """ |
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285 | |
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286 | # Water depth below which it is considered to be 0 in the model |
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287 | # FIXME (Ole): Allow this to be specified as a keyword argument as well |
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288 | from anuga.config import minimum_allowed_height |
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289 | |
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290 | |
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291 | elevation = self.get_quantity('elevation').\ |
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292 | get_values(location='centroids', indices=indices) |
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293 | stage = self.get_quantity('stage').\ |
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294 | get_values(location='centroids', indices=indices) |
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295 | depth = stage - elevation |
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296 | |
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297 | # Select indices for which depth > 0 |
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298 | wet_indices = compress(depth > minimum_allowed_height, |
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299 | arange(len(depth))) |
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300 | return wet_indices |
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301 | |
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302 | |
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303 | def get_maximum_inundation_elevation(self, indices=None): |
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304 | """Return highest elevation where h > 0 |
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305 | |
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306 | Optional argument: |
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307 | indices is the set of element ids that the operation applies to. |
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308 | |
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309 | Usage: |
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310 | q = get_maximum_inundation_elevation() |
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311 | |
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312 | Note, centroid values are used for this operation |
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313 | """ |
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314 | |
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315 | wet_elements = self.get_wet_elements(indices) |
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316 | return self.get_quantity('elevation').\ |
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317 | get_maximum_value(indices=wet_elements) |
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318 | |
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319 | |
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320 | def get_maximum_inundation_location(self, indices=None): |
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321 | """Return highest elevation where h > 0 |
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322 | |
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323 | Optional argument: |
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324 | indices is the set of element ids that the operation applies to. |
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325 | |
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326 | Usage: |
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327 | q = get_maximum_inundation_elevation() |
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328 | |
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329 | Note, centroid values are used for this operation |
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330 | """ |
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331 | |
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332 | wet_elements = self.get_wet_elements(indices) |
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333 | return self.get_quantity('elevation').\ |
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334 | get_maximum_location(indices=wet_elements) |
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335 | |
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336 | def check_integrity(self): |
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337 | Generic_Domain.check_integrity(self) |
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338 | |
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339 | #Check that we are solving the shallow water wave equation |
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340 | |
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341 | msg = 'First conserved quantity must be "stage"' |
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342 | assert self.conserved_quantities[0] == 'stage', msg |
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343 | msg = 'Second conserved quantity must be "xmomentum"' |
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344 | assert self.conserved_quantities[1] == 'xmomentum', msg |
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345 | msg = 'Third conserved quantity must be "ymomentum"' |
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346 | assert self.conserved_quantities[2] == 'ymomentum', msg |
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347 | |
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348 | def extrapolate_second_order_sw(self): |
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349 | #Call correct module function |
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350 | #(either from this module or C-extension) |
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351 | extrapolate_second_order_sw(self) |
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352 | |
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353 | def compute_fluxes(self): |
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354 | #Call correct module function |
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355 | #(either from this module or C-extension) |
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356 | compute_fluxes(self) |
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357 | |
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358 | def distribute_to_vertices_and_edges(self): |
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359 | #Call correct module function |
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360 | #(either from this module or C-extension) |
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361 | distribute_to_vertices_and_edges(self) |
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362 | |
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363 | |
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364 | #FIXME: Under construction |
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365 | # def set_defaults(self): |
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366 | # """Set default values for uninitialised quantities. |
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367 | # This is specific to the shallow water wave equation |
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368 | # Defaults for 'elevation', 'friction', 'xmomentum' and 'ymomentum' |
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369 | # are 0.0. Default for 'stage' is whatever the value of 'elevation'. |
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370 | # """ |
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371 | |
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372 | # for name in self.other_quantities + self.conserved_quantities: |
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373 | # print name |
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374 | # print self.quantities.keys() |
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375 | # if not self.quantities.has_key(name): |
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376 | # if name == 'stage': |
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377 | |
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378 | # if self.quantities.has_key('elevation'): |
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379 | # z = self.quantities['elevation'].vertex_values |
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380 | # self.set_quantity(name, z) |
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381 | # else: |
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382 | # self.set_quantity(name, 0.0) |
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383 | # else: |
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384 | # self.set_quantity(name, 0.0) |
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385 | |
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386 | |
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387 | |
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388 | # #Lift negative heights up |
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389 | # #z = self.quantities['elevation'].vertex_values |
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390 | # #w = self.quantities['stage'].vertex_values |
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391 | |
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392 | # #h = w-z |
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393 | |
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394 | # #for k in range(h.shape[0]): |
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395 | # # for i in range(3): |
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396 | # # if h[k, i] < 0.0: |
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397 | # # w[k, i] = z[k, i] |
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398 | |
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399 | |
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400 | # #self.quantities['stage'].interpolate() |
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401 | |
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402 | |
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403 | def evolve(self, |
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404 | yieldstep = None, |
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405 | finaltime = None, |
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406 | duration = None, |
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407 | skip_initial_step = False): |
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408 | """Specialisation of basic evolve method from parent class |
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409 | """ |
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410 | |
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411 | #Call check integrity here rather than from user scripts |
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412 | #self.check_integrity() |
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413 | |
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414 | msg = 'Parameter beta_h must be in the interval [0, 1[' |
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415 | assert 0 <= self.beta_h <= 1.0, msg |
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416 | msg = 'Parameter beta_w must be in the interval [0, 1[' |
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417 | assert 0 <= self.beta_w <= 1.0, msg |
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418 | |
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419 | |
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420 | #Initial update of vertex and edge values before any storage |
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421 | #and or visualisation |
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422 | self.distribute_to_vertices_and_edges() |
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423 | |
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424 | if self.store is True and self.time == 0.0: |
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425 | self.initialise_storage() |
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426 | #print 'Storing results in ' + self.writer.filename |
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427 | else: |
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428 | pass |
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429 | #print 'Results will not be stored.' |
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430 | #print 'To store results set domain.store = True' |
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431 | #FIXME: Diagnostic output should be controlled by |
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432 | # a 'verbose' flag living in domain (or in a parent class) |
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433 | |
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434 | #Call basic machinery from parent class |
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435 | for t in Generic_Domain.evolve(self, |
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436 | yieldstep=yieldstep, |
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437 | finaltime=finaltime, |
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438 | duration=duration, |
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439 | skip_initial_step=skip_initial_step): |
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440 | |
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441 | #Store model data, e.g. for subsequent visualisation |
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442 | if self.store is True: |
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443 | self.store_timestep(self.quantities_to_be_stored) |
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444 | |
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445 | #FIXME: Could maybe be taken from specified list |
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446 | #of 'store every step' quantities |
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447 | |
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448 | #Pass control on to outer loop for more specific actions |
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449 | yield(t) |
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450 | |
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451 | def initialise_storage(self): |
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452 | """Create and initialise self.writer object for storing data. |
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453 | Also, save x,y and bed elevation |
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454 | """ |
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455 | |
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456 | from anuga.shallow_water.data_manager import get_dataobject |
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457 | |
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458 | #Initialise writer |
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459 | self.writer = get_dataobject(self, mode = 'w') |
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460 | |
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461 | #Store vertices and connectivity |
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462 | self.writer.store_connectivity() |
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463 | |
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464 | |
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465 | def store_timestep(self, name): |
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466 | """Store named quantity and time. |
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467 | |
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468 | Precondition: |
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469 | self.write has been initialised |
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470 | """ |
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471 | self.writer.store_timestep(name) |
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472 | |
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473 | |
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474 | #=============== End of Shallow Water Domain =============================== |
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475 | |
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476 | |
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477 | |
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478 | #Rotation of momentum vector |
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479 | def rotate(q, normal, direction = 1): |
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480 | """Rotate the momentum component q (q[1], q[2]) |
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481 | from x,y coordinates to coordinates based on normal vector. |
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482 | |
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483 | If direction is negative the rotation is inverted. |
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484 | |
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485 | Input vector is preserved |
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486 | |
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487 | This function is specific to the shallow water wave equation |
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488 | """ |
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489 | |
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490 | assert len(q) == 3,\ |
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491 | 'Vector of conserved quantities must have length 3'\ |
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492 | 'for 2D shallow water equation' |
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493 | |
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494 | try: |
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495 | l = len(normal) |
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496 | except: |
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497 | raise 'Normal vector must be an Numeric array' |
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498 | |
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499 | assert l == 2, 'Normal vector must have 2 components' |
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500 | |
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501 | |
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502 | n1 = normal[0] |
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503 | n2 = normal[1] |
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504 | |
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505 | r = zeros(len(q), Float) #Rotated quantities |
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506 | r[0] = q[0] #First quantity, height, is not rotated |
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507 | |
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508 | if direction == -1: |
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509 | n2 = -n2 |
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510 | |
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511 | |
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512 | r[1] = n1*q[1] + n2*q[2] |
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513 | r[2] = -n2*q[1] + n1*q[2] |
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514 | |
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515 | return r |
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516 | |
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517 | |
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518 | |
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519 | #################################### |
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520 | # Flux computation |
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521 | def flux_function_central(normal, ql, qr, zl, zr): |
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522 | """Compute fluxes between volumes for the shallow water wave equation |
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523 | cast in terms of w = h+z using the 'central scheme' as described in |
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524 | |
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525 | Kurganov, Noelle, Petrova. 'Semidiscrete Central-Upwind Schemes For |
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526 | Hyperbolic Conservation Laws and Hamilton-Jacobi Equations'. |
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527 | Siam J. Sci. Comput. Vol. 23, No. 3, pp. 707-740. |
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528 | |
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529 | The implemented formula is given in equation (3.15) on page 714 |
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530 | |
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531 | Conserved quantities w, uh, vh are stored as elements 0, 1 and 2 |
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532 | in the numerical vectors ql and qr. |
---|
533 | |
---|
534 | Bed elevations zl and zr. |
---|
535 | """ |
---|
536 | |
---|
537 | from anuga.config import g, epsilon |
---|
538 | from math import sqrt |
---|
539 | |
---|
540 | #Align momentums with x-axis |
---|
541 | q_left = rotate(ql, normal, direction = 1) |
---|
542 | q_right = rotate(qr, normal, direction = 1) |
---|
543 | |
---|
544 | z = (zl+zr)/2 #Take average of field values |
---|
545 | |
---|
546 | w_left = q_left[0] #w=h+z |
---|
547 | h_left = w_left-z |
---|
548 | uh_left = q_left[1] |
---|
549 | |
---|
550 | if h_left < epsilon: |
---|
551 | u_left = 0.0 #Could have been negative |
---|
552 | h_left = 0.0 |
---|
553 | else: |
---|
554 | u_left = uh_left/h_left |
---|
555 | |
---|
556 | |
---|
557 | w_right = q_right[0] #w=h+z |
---|
558 | h_right = w_right-z |
---|
559 | uh_right = q_right[1] |
---|
560 | |
---|
561 | |
---|
562 | if h_right < epsilon: |
---|
563 | u_right = 0.0 #Could have been negative |
---|
564 | h_right = 0.0 |
---|
565 | else: |
---|
566 | u_right = uh_right/h_right |
---|
567 | |
---|
568 | vh_left = q_left[2] |
---|
569 | vh_right = q_right[2] |
---|
570 | |
---|
571 | soundspeed_left = sqrt(g*h_left) |
---|
572 | soundspeed_right = sqrt(g*h_right) |
---|
573 | |
---|
574 | #Maximal wave speed |
---|
575 | s_max = max(u_left+soundspeed_left, u_right+soundspeed_right, 0) |
---|
576 | |
---|
577 | #Minimal wave speed |
---|
578 | s_min = min(u_left-soundspeed_left, u_right-soundspeed_right, 0) |
---|
579 | |
---|
580 | #Flux computation |
---|
581 | |
---|
582 | #FIXME(Ole): Why is it again that we don't |
---|
583 | #use uh_left and uh_right directly in the first entries? |
---|
584 | flux_left = array([u_left*h_left, |
---|
585 | u_left*uh_left + 0.5*g*h_left**2, |
---|
586 | u_left*vh_left]) |
---|
587 | flux_right = array([u_right*h_right, |
---|
588 | u_right*uh_right + 0.5*g*h_right**2, |
---|
589 | u_right*vh_right]) |
---|
590 | |
---|
591 | denom = s_max-s_min |
---|
592 | if denom == 0.0: |
---|
593 | edgeflux = array([0.0, 0.0, 0.0]) |
---|
594 | max_speed = 0.0 |
---|
595 | else: |
---|
596 | edgeflux = (s_max*flux_left - s_min*flux_right)/denom |
---|
597 | edgeflux += s_max*s_min*(q_right-q_left)/denom |
---|
598 | |
---|
599 | edgeflux = rotate(edgeflux, normal, direction=-1) |
---|
600 | max_speed = max(abs(s_max), abs(s_min)) |
---|
601 | |
---|
602 | return edgeflux, max_speed |
---|
603 | |
---|
604 | def erfcc(x): |
---|
605 | |
---|
606 | from math import fabs, exp |
---|
607 | |
---|
608 | z=fabs(x) |
---|
609 | t=1.0/(1.0+0.5*z) |
---|
610 | result=t*exp(-z*z-1.26551223+t*(1.00002368+t*(.37409196+ |
---|
611 | t*(.09678418+t*(-.18628806+t*(.27886807+t*(-1.13520398+ |
---|
612 | t*(1.48851587+t*(-.82215223+t*.17087277))))))))) |
---|
613 | if x < 0.0: |
---|
614 | result = 2.0-result |
---|
615 | |
---|
616 | return result |
---|
617 | |
---|
618 | def flux_function_kinetic(normal, ql, qr, zl, zr): |
---|
619 | """Compute fluxes between volumes for the shallow water wave equation |
---|
620 | cast in terms of w = h+z using the 'central scheme' as described in |
---|
621 | |
---|
622 | Zhang et. al., Advances in Water Resources, 26(6), 2003, 635-647. |
---|
623 | |
---|
624 | |
---|
625 | Conserved quantities w, uh, vh are stored as elements 0, 1 and 2 |
---|
626 | in the numerical vectors ql an qr. |
---|
627 | |
---|
628 | Bed elevations zl and zr. |
---|
629 | """ |
---|
630 | |
---|
631 | from anuga.config import g, epsilon |
---|
632 | from math import sqrt |
---|
633 | from Numeric import array |
---|
634 | |
---|
635 | #Align momentums with x-axis |
---|
636 | q_left = rotate(ql, normal, direction = 1) |
---|
637 | q_right = rotate(qr, normal, direction = 1) |
---|
638 | |
---|
639 | z = (zl+zr)/2 #Take average of field values |
---|
640 | |
---|
641 | w_left = q_left[0] #w=h+z |
---|
642 | h_left = w_left-z |
---|
643 | uh_left = q_left[1] |
---|
644 | |
---|
645 | if h_left < epsilon: |
---|
646 | u_left = 0.0 #Could have been negative |
---|
647 | h_left = 0.0 |
---|
648 | else: |
---|
649 | u_left = uh_left/h_left |
---|
650 | |
---|
651 | |
---|
652 | w_right = q_right[0] #w=h+z |
---|
653 | h_right = w_right-z |
---|
654 | uh_right = q_right[1] |
---|
655 | |
---|
656 | |
---|
657 | if h_right < epsilon: |
---|
658 | u_right = 0.0 #Could have been negative |
---|
659 | h_right = 0.0 |
---|
660 | else: |
---|
661 | u_right = uh_right/h_right |
---|
662 | |
---|
663 | vh_left = q_left[2] |
---|
664 | vh_right = q_right[2] |
---|
665 | |
---|
666 | soundspeed_left = sqrt(g*h_left) |
---|
667 | soundspeed_right = sqrt(g*h_right) |
---|
668 | |
---|
669 | #Maximal wave speed |
---|
670 | s_max = max(u_left+soundspeed_left, u_right+soundspeed_right, 0) |
---|
671 | |
---|
672 | #Minimal wave speed |
---|
673 | s_min = min(u_left-soundspeed_left, u_right-soundspeed_right, 0) |
---|
674 | |
---|
675 | #Flux computation |
---|
676 | |
---|
677 | F_left = 0.0 |
---|
678 | F_right = 0.0 |
---|
679 | from math import sqrt, pi, exp |
---|
680 | if h_left > 0.0: |
---|
681 | F_left = u_left/sqrt(g*h_left) |
---|
682 | if h_right > 0.0: |
---|
683 | F_right = u_right/sqrt(g*h_right) |
---|
684 | |
---|
685 | edgeflux = array([0.0, 0.0, 0.0]) |
---|
686 | |
---|
687 | edgeflux[0] = h_left*u_left/2.0*erfcc(-F_left) + \ |
---|
688 | h_left*sqrt(g*h_left)/2.0/sqrt(pi)*exp(-(F_left**2)) + \ |
---|
689 | h_right*u_right/2.0*erfcc(F_right) - \ |
---|
690 | h_right*sqrt(g*h_right)/2.0/sqrt(pi)*exp(-(F_right**2)) |
---|
691 | |
---|
692 | edgeflux[1] = (h_left*u_left**2 + g/2.0*h_left**2)/2.0*erfcc(-F_left) + \ |
---|
693 | u_left*h_left*sqrt(g*h_left)/2.0/sqrt(pi)*exp(-(F_left**2)) + \ |
---|
694 | (h_right*u_right**2 + g/2.0*h_right**2)/2.0*erfcc(F_right) - \ |
---|
695 | u_right*h_right*sqrt(g*h_right)/2.0/sqrt(pi)*exp(-(F_right**2)) |
---|
696 | |
---|
697 | edgeflux[2] = vh_left*u_left/2.0*erfcc(-F_left) + \ |
---|
698 | vh_left*sqrt(g*h_left)/2.0/sqrt(pi)*exp(-(F_left**2)) + \ |
---|
699 | vh_right*u_right/2.0*erfcc(F_right) - \ |
---|
700 | vh_right*sqrt(g*h_right)/2.0/sqrt(pi)*exp(-(F_right**2)) |
---|
701 | |
---|
702 | |
---|
703 | edgeflux = rotate(edgeflux, normal, direction=-1) |
---|
704 | max_speed = max(abs(s_max), abs(s_min)) |
---|
705 | |
---|
706 | return edgeflux, max_speed |
---|
707 | |
---|
708 | |
---|
709 | |
---|
710 | def compute_fluxes(domain): |
---|
711 | """Compute all fluxes and the timestep suitable for all volumes |
---|
712 | in domain. |
---|
713 | |
---|
714 | Compute total flux for each conserved quantity using "flux_function" |
---|
715 | |
---|
716 | Fluxes across each edge are scaled by edgelengths and summed up |
---|
717 | Resulting flux is then scaled by area and stored in |
---|
718 | explicit_update for each of the three conserved quantities |
---|
719 | stage, xmomentum and ymomentum |
---|
720 | |
---|
721 | The maximal allowable speed computed by the flux_function for each volume |
---|
722 | is converted to a timestep that must not be exceeded. The minimum of |
---|
723 | those is computed as the next overall timestep. |
---|
724 | |
---|
725 | Post conditions: |
---|
726 | domain.explicit_update is reset to computed flux values |
---|
727 | domain.timestep is set to the largest step satisfying all volumes. |
---|
728 | """ |
---|
729 | |
---|
730 | import sys |
---|
731 | |
---|
732 | N = len(domain) # number_of_triangles |
---|
733 | |
---|
734 | #Shortcuts |
---|
735 | Stage = domain.quantities['stage'] |
---|
736 | Xmom = domain.quantities['xmomentum'] |
---|
737 | Ymom = domain.quantities['ymomentum'] |
---|
738 | Bed = domain.quantities['elevation'] |
---|
739 | |
---|
740 | #Arrays |
---|
741 | stage = Stage.edge_values |
---|
742 | xmom = Xmom.edge_values |
---|
743 | ymom = Ymom.edge_values |
---|
744 | bed = Bed.edge_values |
---|
745 | |
---|
746 | stage_bdry = Stage.boundary_values |
---|
747 | xmom_bdry = Xmom.boundary_values |
---|
748 | ymom_bdry = Ymom.boundary_values |
---|
749 | |
---|
750 | flux = zeros(3, Float) #Work array for summing up fluxes |
---|
751 | |
---|
752 | |
---|
753 | #Loop |
---|
754 | timestep = float(sys.maxint) |
---|
755 | for k in range(N): |
---|
756 | |
---|
757 | flux[:] = 0. #Reset work array |
---|
758 | for i in range(3): |
---|
759 | #Quantities inside volume facing neighbour i |
---|
760 | ql = [stage[k, i], xmom[k, i], ymom[k, i]] |
---|
761 | zl = bed[k, i] |
---|
762 | |
---|
763 | #Quantities at neighbour on nearest face |
---|
764 | n = domain.neighbours[k,i] |
---|
765 | if n < 0: |
---|
766 | m = -n-1 #Convert negative flag to index |
---|
767 | qr = [stage_bdry[m], xmom_bdry[m], ymom_bdry[m]] |
---|
768 | zr = zl #Extend bed elevation to boundary |
---|
769 | else: |
---|
770 | m = domain.neighbour_edges[k,i] |
---|
771 | qr = [stage[n, m], xmom[n, m], ymom[n, m]] |
---|
772 | zr = bed[n, m] |
---|
773 | |
---|
774 | |
---|
775 | #Outward pointing normal vector |
---|
776 | normal = domain.normals[k, 2*i:2*i+2] |
---|
777 | |
---|
778 | #Flux computation using provided function |
---|
779 | edgeflux, max_speed = domain.flux_function(normal, ql, qr, zl, zr) |
---|
780 | flux -= edgeflux * domain.edgelengths[k,i] |
---|
781 | |
---|
782 | #Update optimal_timestep on full cells |
---|
783 | if domain.tri_full_flag[k] == 1: |
---|
784 | try: |
---|
785 | timestep = min(timestep, 0.5*domain.radii[k]/max_speed) |
---|
786 | except ZeroDivisionError: |
---|
787 | pass |
---|
788 | |
---|
789 | #Normalise by area and store for when all conserved |
---|
790 | #quantities get updated |
---|
791 | flux /= domain.areas[k] |
---|
792 | Stage.explicit_update[k] = flux[0] |
---|
793 | Xmom.explicit_update[k] = flux[1] |
---|
794 | Ymom.explicit_update[k] = flux[2] |
---|
795 | domain.max_speed[k] = max_speed |
---|
796 | |
---|
797 | |
---|
798 | domain.timestep = timestep |
---|
799 | |
---|
800 | #MH090605 The following method belongs to the shallow_water domain class |
---|
801 | #see comments in the corresponding method in shallow_water_ext.c |
---|
802 | def extrapolate_second_order_sw_c(domain): |
---|
803 | """Wrapper calling C version of extrapolate_second_order_sw |
---|
804 | """ |
---|
805 | import sys |
---|
806 | |
---|
807 | N = len(domain) # number_of_triangles |
---|
808 | |
---|
809 | #Shortcuts |
---|
810 | Stage = domain.quantities['stage'] |
---|
811 | Xmom = domain.quantities['xmomentum'] |
---|
812 | Ymom = domain.quantities['ymomentum'] |
---|
813 | Elevation = domain.quantities['elevation'] |
---|
814 | from shallow_water_ext import extrapolate_second_order_sw |
---|
815 | extrapolate_second_order_sw(domain, |
---|
816 | domain.surrogate_neighbours, |
---|
817 | domain.number_of_boundaries, |
---|
818 | domain.centroid_coordinates, |
---|
819 | Stage.centroid_values, |
---|
820 | Xmom.centroid_values, |
---|
821 | Ymom.centroid_values, |
---|
822 | Elevation.centroid_values, |
---|
823 | domain.vertex_coordinates, |
---|
824 | Stage.vertex_values, |
---|
825 | Xmom.vertex_values, |
---|
826 | Ymom.vertex_values, |
---|
827 | Elevation.vertex_values) |
---|
828 | |
---|
829 | def compute_fluxes_c(domain): |
---|
830 | """Wrapper calling C version of compute fluxes |
---|
831 | """ |
---|
832 | |
---|
833 | import sys |
---|
834 | |
---|
835 | N = len(domain) # number_of_triangles |
---|
836 | |
---|
837 | #Shortcuts |
---|
838 | Stage = domain.quantities['stage'] |
---|
839 | Xmom = domain.quantities['xmomentum'] |
---|
840 | Ymom = domain.quantities['ymomentum'] |
---|
841 | Bed = domain.quantities['elevation'] |
---|
842 | |
---|
843 | timestep = float(sys.maxint) |
---|
844 | from shallow_water_ext import\ |
---|
845 | compute_fluxes_ext_central as compute_fluxes_ext |
---|
846 | |
---|
847 | |
---|
848 | domain.timestep = compute_fluxes_ext(timestep, domain.epsilon, |
---|
849 | domain.H0, |
---|
850 | domain.g, |
---|
851 | domain.neighbours, |
---|
852 | domain.neighbour_edges, |
---|
853 | domain.normals, |
---|
854 | domain.edgelengths, |
---|
855 | domain.radii, |
---|
856 | domain.areas, |
---|
857 | domain.tri_full_flag, |
---|
858 | Stage.edge_values, |
---|
859 | Xmom.edge_values, |
---|
860 | Ymom.edge_values, |
---|
861 | Bed.edge_values, |
---|
862 | Stage.boundary_values, |
---|
863 | Xmom.boundary_values, |
---|
864 | Ymom.boundary_values, |
---|
865 | Stage.explicit_update, |
---|
866 | Xmom.explicit_update, |
---|
867 | Ymom.explicit_update, |
---|
868 | domain.already_computed_flux, |
---|
869 | domain.max_speed) |
---|
870 | |
---|
871 | |
---|
872 | #################################### |
---|
873 | # Module functions for gradient limiting (distribute_to_vertices_and_edges) |
---|
874 | |
---|
875 | def distribute_to_vertices_and_edges(domain): |
---|
876 | """Distribution from centroids to vertices specific to the |
---|
877 | shallow water wave |
---|
878 | equation. |
---|
879 | |
---|
880 | It will ensure that h (w-z) is always non-negative even in the |
---|
881 | presence of steep bed-slopes by taking a weighted average between shallow |
---|
882 | and deep cases. |
---|
883 | |
---|
884 | In addition, all conserved quantities get distributed as per either a |
---|
885 | constant (order==1) or a piecewise linear function (order==2). |
---|
886 | |
---|
887 | FIXME: more explanation about removal of artificial variability etc |
---|
888 | |
---|
889 | Precondition: |
---|
890 | All quantities defined at centroids and bed elevation defined at |
---|
891 | vertices. |
---|
892 | |
---|
893 | Postcondition |
---|
894 | Conserved quantities defined at vertices |
---|
895 | |
---|
896 | """ |
---|
897 | |
---|
898 | from anuga.config import optimised_gradient_limiter |
---|
899 | |
---|
900 | #Remove very thin layers of water |
---|
901 | protect_against_infinitesimal_and_negative_heights(domain) |
---|
902 | |
---|
903 | #Extrapolate all conserved quantities |
---|
904 | if optimised_gradient_limiter: |
---|
905 | #MH090605 if second order, |
---|
906 | #perform the extrapolation and limiting on |
---|
907 | #all of the conserved quantitie |
---|
908 | |
---|
909 | if (domain._order_ == 1): |
---|
910 | for name in domain.conserved_quantities: |
---|
911 | Q = domain.quantities[name] |
---|
912 | Q.extrapolate_first_order() |
---|
913 | elif domain._order_ == 2: |
---|
914 | domain.extrapolate_second_order_sw() |
---|
915 | else: |
---|
916 | raise 'Unknown order' |
---|
917 | else: |
---|
918 | #old code: |
---|
919 | for name in domain.conserved_quantities: |
---|
920 | Q = domain.quantities[name] |
---|
921 | if domain._order_ == 1: |
---|
922 | Q.extrapolate_first_order() |
---|
923 | elif domain._order_ == 2: |
---|
924 | Q.extrapolate_second_order() |
---|
925 | Q.limit() |
---|
926 | else: |
---|
927 | raise 'Unknown order' |
---|
928 | |
---|
929 | |
---|
930 | #Take bed elevation into account when water heights are small |
---|
931 | balance_deep_and_shallow(domain) |
---|
932 | |
---|
933 | #Compute edge values by interpolation |
---|
934 | for name in domain.conserved_quantities: |
---|
935 | Q = domain.quantities[name] |
---|
936 | Q.interpolate_from_vertices_to_edges() |
---|
937 | |
---|
938 | |
---|
939 | def protect_against_infinitesimal_and_negative_heights(domain): |
---|
940 | """Protect against infinitesimal heights and associated high velocities |
---|
941 | """ |
---|
942 | |
---|
943 | #Shortcuts |
---|
944 | wc = domain.quantities['stage'].centroid_values |
---|
945 | zc = domain.quantities['elevation'].centroid_values |
---|
946 | xmomc = domain.quantities['xmomentum'].centroid_values |
---|
947 | ymomc = domain.quantities['ymomentum'].centroid_values |
---|
948 | hc = wc - zc #Water depths at centroids |
---|
949 | |
---|
950 | #Update |
---|
951 | #FIXME: Modify according to c-version - or discard altogether. |
---|
952 | for k in range(len(domain)): |
---|
953 | |
---|
954 | if hc[k] < domain.minimum_allowed_height: |
---|
955 | #Control stage |
---|
956 | if hc[k] < domain.epsilon: |
---|
957 | wc[k] = zc[k] # Contain 'lost mass' error |
---|
958 | |
---|
959 | #Control momentum |
---|
960 | xmomc[k] = ymomc[k] = 0.0 |
---|
961 | |
---|
962 | |
---|
963 | def protect_against_infinitesimal_and_negative_heights_c(domain): |
---|
964 | """Protect against infinitesimal heights and associated high velocities |
---|
965 | """ |
---|
966 | |
---|
967 | #Shortcuts |
---|
968 | wc = domain.quantities['stage'].centroid_values |
---|
969 | zc = domain.quantities['elevation'].centroid_values |
---|
970 | xmomc = domain.quantities['xmomentum'].centroid_values |
---|
971 | ymomc = domain.quantities['ymomentum'].centroid_values |
---|
972 | |
---|
973 | from shallow_water_ext import protect |
---|
974 | |
---|
975 | protect(domain.minimum_allowed_height, domain.maximum_allowed_speed, |
---|
976 | domain.epsilon, wc, zc, xmomc, ymomc) |
---|
977 | |
---|
978 | |
---|
979 | |
---|
980 | def h_limiter(domain): |
---|
981 | """Limit slopes for each volume to eliminate artificial variance |
---|
982 | introduced by e.g. second order extrapolator |
---|
983 | |
---|
984 | limit on h = w-z |
---|
985 | |
---|
986 | This limiter depends on two quantities (w,z) so it resides within |
---|
987 | this module rather than within quantity.py |
---|
988 | """ |
---|
989 | |
---|
990 | N = len(domain) |
---|
991 | beta_h = domain.beta_h |
---|
992 | |
---|
993 | #Shortcuts |
---|
994 | wc = domain.quantities['stage'].centroid_values |
---|
995 | zc = domain.quantities['elevation'].centroid_values |
---|
996 | hc = wc - zc |
---|
997 | |
---|
998 | wv = domain.quantities['stage'].vertex_values |
---|
999 | zv = domain.quantities['elevation'].vertex_values |
---|
1000 | hv = wv-zv |
---|
1001 | |
---|
1002 | hvbar = zeros(hv.shape, Float) #h-limited values |
---|
1003 | |
---|
1004 | #Find min and max of this and neighbour's centroid values |
---|
1005 | hmax = zeros(hc.shape, Float) |
---|
1006 | hmin = zeros(hc.shape, Float) |
---|
1007 | |
---|
1008 | for k in range(N): |
---|
1009 | hmax[k] = hmin[k] = hc[k] |
---|
1010 | for i in range(3): |
---|
1011 | n = domain.neighbours[k,i] |
---|
1012 | if n >= 0: |
---|
1013 | hn = hc[n] #Neighbour's centroid value |
---|
1014 | |
---|
1015 | hmin[k] = min(hmin[k], hn) |
---|
1016 | hmax[k] = max(hmax[k], hn) |
---|
1017 | |
---|
1018 | |
---|
1019 | #Diffences between centroids and maxima/minima |
---|
1020 | dhmax = hmax - hc |
---|
1021 | dhmin = hmin - hc |
---|
1022 | |
---|
1023 | #Deltas between vertex and centroid values |
---|
1024 | dh = zeros(hv.shape, Float) |
---|
1025 | for i in range(3): |
---|
1026 | dh[:,i] = hv[:,i] - hc |
---|
1027 | |
---|
1028 | #Phi limiter |
---|
1029 | for k in range(N): |
---|
1030 | |
---|
1031 | #Find the gradient limiter (phi) across vertices |
---|
1032 | phi = 1.0 |
---|
1033 | for i in range(3): |
---|
1034 | r = 1.0 |
---|
1035 | if (dh[k,i] > 0): r = dhmax[k]/dh[k,i] |
---|
1036 | if (dh[k,i] < 0): r = dhmin[k]/dh[k,i] |
---|
1037 | |
---|
1038 | phi = min( min(r*beta_h, 1), phi ) |
---|
1039 | |
---|
1040 | #Then update using phi limiter |
---|
1041 | for i in range(3): |
---|
1042 | hvbar[k,i] = hc[k] + phi*dh[k,i] |
---|
1043 | |
---|
1044 | return hvbar |
---|
1045 | |
---|
1046 | |
---|
1047 | |
---|
1048 | def h_limiter_c(domain): |
---|
1049 | """Limit slopes for each volume to eliminate artificial variance |
---|
1050 | introduced by e.g. second order extrapolator |
---|
1051 | |
---|
1052 | limit on h = w-z |
---|
1053 | |
---|
1054 | This limiter depends on two quantities (w,z) so it resides within |
---|
1055 | this module rather than within quantity.py |
---|
1056 | |
---|
1057 | Wrapper for c-extension |
---|
1058 | """ |
---|
1059 | |
---|
1060 | N = len(domain) # number_of_triangles |
---|
1061 | beta_h = domain.beta_h |
---|
1062 | |
---|
1063 | #Shortcuts |
---|
1064 | wc = domain.quantities['stage'].centroid_values |
---|
1065 | zc = domain.quantities['elevation'].centroid_values |
---|
1066 | hc = wc - zc |
---|
1067 | |
---|
1068 | wv = domain.quantities['stage'].vertex_values |
---|
1069 | zv = domain.quantities['elevation'].vertex_values |
---|
1070 | hv = wv - zv |
---|
1071 | |
---|
1072 | #Call C-extension |
---|
1073 | from shallow_water_ext import h_limiter_sw as h_limiter |
---|
1074 | hvbar = h_limiter(domain, hc, hv) |
---|
1075 | |
---|
1076 | return hvbar |
---|
1077 | |
---|
1078 | |
---|
1079 | def balance_deep_and_shallow(domain): |
---|
1080 | """Compute linear combination between stage as computed by |
---|
1081 | gradient-limiters limiting using w, and stage computed by |
---|
1082 | gradient-limiters limiting using h (h-limiter). |
---|
1083 | The former takes precedence when heights are large compared to the |
---|
1084 | bed slope while the latter takes precedence when heights are |
---|
1085 | relatively small. Anything in between is computed as a balanced |
---|
1086 | linear combination in order to avoid numerical disturbances which |
---|
1087 | would otherwise appear as a result of hard switching between |
---|
1088 | modes. |
---|
1089 | |
---|
1090 | The h-limiter is always applied irrespective of the order. |
---|
1091 | """ |
---|
1092 | |
---|
1093 | #Shortcuts |
---|
1094 | wc = domain.quantities['stage'].centroid_values |
---|
1095 | zc = domain.quantities['elevation'].centroid_values |
---|
1096 | hc = wc - zc |
---|
1097 | |
---|
1098 | wv = domain.quantities['stage'].vertex_values |
---|
1099 | zv = domain.quantities['elevation'].vertex_values |
---|
1100 | hv = wv-zv |
---|
1101 | |
---|
1102 | #Limit h |
---|
1103 | hvbar = h_limiter(domain) |
---|
1104 | |
---|
1105 | for k in range(len(domain)): |
---|
1106 | #Compute maximal variation in bed elevation |
---|
1107 | # This quantitiy is |
---|
1108 | # dz = max_i abs(z_i - z_c) |
---|
1109 | # and it is independent of dimension |
---|
1110 | # In the 1d case zc = (z0+z1)/2 |
---|
1111 | # In the 2d case zc = (z0+z1+z2)/3 |
---|
1112 | |
---|
1113 | dz = max(abs(zv[k,0]-zc[k]), |
---|
1114 | abs(zv[k,1]-zc[k]), |
---|
1115 | abs(zv[k,2]-zc[k])) |
---|
1116 | |
---|
1117 | |
---|
1118 | hmin = min( hv[k,:] ) |
---|
1119 | |
---|
1120 | #Create alpha in [0,1], where alpha==0 means using the h-limited |
---|
1121 | #stage and alpha==1 means using the w-limited stage as |
---|
1122 | #computed by the gradient limiter (both 1st or 2nd order) |
---|
1123 | |
---|
1124 | #If hmin > dz/2 then alpha = 1 and the bed will have no effect |
---|
1125 | #If hmin < 0 then alpha = 0 reverting to constant height above bed. |
---|
1126 | |
---|
1127 | if dz > 0.0: |
---|
1128 | alpha = max( min( 2*hmin/dz, 1.0), 0.0 ) |
---|
1129 | else: |
---|
1130 | #Flat bed |
---|
1131 | alpha = 1.0 |
---|
1132 | |
---|
1133 | #Let |
---|
1134 | # |
---|
1135 | # wvi be the w-limited stage (wvi = zvi + hvi) |
---|
1136 | # wvi- be the h-limited state (wvi- = zvi + hvi-) |
---|
1137 | # |
---|
1138 | # |
---|
1139 | #where i=0,1,2 denotes the vertex ids |
---|
1140 | # |
---|
1141 | #Weighted balance between w-limited and h-limited stage is |
---|
1142 | # |
---|
1143 | # wvi := (1-alpha)*(zvi+hvi-) + alpha*(zvi+hvi) |
---|
1144 | # |
---|
1145 | #It follows that the updated wvi is |
---|
1146 | # wvi := zvi + (1-alpha)*hvi- + alpha*hvi |
---|
1147 | # |
---|
1148 | # Momentum is balanced between constant and limited |
---|
1149 | |
---|
1150 | |
---|
1151 | #for i in range(3): |
---|
1152 | # wv[k,i] = zv[k,i] + hvbar[k,i] |
---|
1153 | |
---|
1154 | #return |
---|
1155 | |
---|
1156 | if alpha < 1: |
---|
1157 | |
---|
1158 | for i in range(3): |
---|
1159 | wv[k,i] = zv[k,i] + (1-alpha)*hvbar[k,i] + alpha*hv[k,i] |
---|
1160 | |
---|
1161 | #Momentums at centroids |
---|
1162 | xmomc = domain.quantities['xmomentum'].centroid_values |
---|
1163 | ymomc = domain.quantities['ymomentum'].centroid_values |
---|
1164 | |
---|
1165 | #Momentums at vertices |
---|
1166 | xmomv = domain.quantities['xmomentum'].vertex_values |
---|
1167 | ymomv = domain.quantities['ymomentum'].vertex_values |
---|
1168 | |
---|
1169 | # Update momentum as a linear combination of |
---|
1170 | # xmomc and ymomc (shallow) and momentum |
---|
1171 | # from extrapolator xmomv and ymomv (deep). |
---|
1172 | xmomv[k,:] = (1-alpha)*xmomc[k] + alpha*xmomv[k,:] |
---|
1173 | ymomv[k,:] = (1-alpha)*ymomc[k] + alpha*ymomv[k,:] |
---|
1174 | |
---|
1175 | |
---|
1176 | def balance_deep_and_shallow_c(domain): |
---|
1177 | """Wrapper for C implementation |
---|
1178 | """ |
---|
1179 | |
---|
1180 | #Shortcuts |
---|
1181 | wc = domain.quantities['stage'].centroid_values |
---|
1182 | zc = domain.quantities['elevation'].centroid_values |
---|
1183 | hc = wc - zc |
---|
1184 | |
---|
1185 | wv = domain.quantities['stage'].vertex_values |
---|
1186 | zv = domain.quantities['elevation'].vertex_values |
---|
1187 | hv = wv - zv |
---|
1188 | |
---|
1189 | #Momentums at centroids |
---|
1190 | xmomc = domain.quantities['xmomentum'].centroid_values |
---|
1191 | ymomc = domain.quantities['ymomentum'].centroid_values |
---|
1192 | |
---|
1193 | #Momentums at vertices |
---|
1194 | xmomv = domain.quantities['xmomentum'].vertex_values |
---|
1195 | ymomv = domain.quantities['ymomentum'].vertex_values |
---|
1196 | |
---|
1197 | #Limit h |
---|
1198 | if domain.beta_h > 0: |
---|
1199 | hvbar = h_limiter(domain) |
---|
1200 | else: |
---|
1201 | # print 'Using first order h-limiter' |
---|
1202 | |
---|
1203 | |
---|
1204 | #This is how one would make a first order h_limited value |
---|
1205 | #as in the old balancer (pre 17 Feb 2005): |
---|
1206 | # If we wish to hard wire this, one should modify the C-code |
---|
1207 | from Numeric import zeros, Float |
---|
1208 | hvbar = zeros( (len(hc), 3), Float) |
---|
1209 | for i in range(3): |
---|
1210 | hvbar[:,i] = hc[:] |
---|
1211 | |
---|
1212 | from shallow_water_ext import balance_deep_and_shallow |
---|
1213 | balance_deep_and_shallow(domain, wc, zc, hc, wv, zv, hv, hvbar, |
---|
1214 | xmomc, ymomc, xmomv, ymomv) |
---|
1215 | |
---|
1216 | |
---|
1217 | |
---|
1218 | |
---|
1219 | ############################################### |
---|
1220 | #Boundaries - specific to the shallow water wave equation |
---|
1221 | class Reflective_boundary(Boundary): |
---|
1222 | """Reflective boundary returns same conserved quantities as |
---|
1223 | those present in its neighbour volume but reflected. |
---|
1224 | |
---|
1225 | This class is specific to the shallow water equation as it |
---|
1226 | works with the momentum quantities assumed to be the second |
---|
1227 | and third conserved quantities. |
---|
1228 | """ |
---|
1229 | |
---|
1230 | def __init__(self, domain = None): |
---|
1231 | Boundary.__init__(self) |
---|
1232 | |
---|
1233 | if domain is None: |
---|
1234 | msg = 'Domain must be specified for reflective boundary' |
---|
1235 | raise msg |
---|
1236 | |
---|
1237 | #Handy shorthands |
---|
1238 | self.stage = domain.quantities['stage'].edge_values |
---|
1239 | self.xmom = domain.quantities['xmomentum'].edge_values |
---|
1240 | self.ymom = domain.quantities['ymomentum'].edge_values |
---|
1241 | self.normals = domain.normals |
---|
1242 | |
---|
1243 | self.conserved_quantities = zeros(3, Float) |
---|
1244 | |
---|
1245 | def __repr__(self): |
---|
1246 | return 'Reflective_boundary' |
---|
1247 | |
---|
1248 | |
---|
1249 | def evaluate(self, vol_id, edge_id): |
---|
1250 | """Reflective boundaries reverses the outward momentum |
---|
1251 | of the volume they serve. |
---|
1252 | """ |
---|
1253 | |
---|
1254 | q = self.conserved_quantities |
---|
1255 | q[0] = self.stage[vol_id, edge_id] |
---|
1256 | q[1] = self.xmom[vol_id, edge_id] |
---|
1257 | q[2] = self.ymom[vol_id, edge_id] |
---|
1258 | |
---|
1259 | normal = self.normals[vol_id, 2*edge_id:2*edge_id+2] |
---|
1260 | |
---|
1261 | |
---|
1262 | r = rotate(q, normal, direction = 1) |
---|
1263 | r[1] = -r[1] |
---|
1264 | q = rotate(r, normal, direction = -1) |
---|
1265 | |
---|
1266 | return q |
---|
1267 | |
---|
1268 | |
---|
1269 | |
---|
1270 | class Transmissive_Momentum_Set_Stage_boundary(Boundary): |
---|
1271 | """Returns same momentum conserved quantities as |
---|
1272 | those present in its neighbour volume. |
---|
1273 | Sets stage by specifying a function f of time which may either be a |
---|
1274 | vector function or a scalar function |
---|
1275 | |
---|
1276 | Example: |
---|
1277 | |
---|
1278 | def waveform(t): |
---|
1279 | return sea_level + normalized_amplitude/cosh(t-25)**2 |
---|
1280 | |
---|
1281 | Bts = Transmissive_Momentum_Set_Stage_boundary(domain, waveform) |
---|
1282 | |
---|
1283 | |
---|
1284 | Underlying domain must be specified when boundary is instantiated |
---|
1285 | """ |
---|
1286 | |
---|
1287 | def __init__(self, domain = None, function=None): |
---|
1288 | Boundary.__init__(self) |
---|
1289 | |
---|
1290 | if domain is None: |
---|
1291 | msg = 'Domain must be specified for this type boundary' |
---|
1292 | raise msg |
---|
1293 | |
---|
1294 | if function is None: |
---|
1295 | msg = 'Function must be specified for this type boundary' |
---|
1296 | raise msg |
---|
1297 | |
---|
1298 | self.domain = domain |
---|
1299 | self.function = function |
---|
1300 | |
---|
1301 | def __repr__(self): |
---|
1302 | return 'Transmissive_Momentum_Set_Stage_boundary(%s)' %self.domain |
---|
1303 | |
---|
1304 | def evaluate(self, vol_id, edge_id): |
---|
1305 | """Transmissive Momentum Set Stage boundaries return the edge momentum |
---|
1306 | values of the volume they serve. |
---|
1307 | """ |
---|
1308 | |
---|
1309 | q = self.domain.get_conserved_quantities(vol_id, edge = edge_id) |
---|
1310 | value = self.function(self.domain.time) |
---|
1311 | |
---|
1312 | try: |
---|
1313 | x = float(value) |
---|
1314 | except: |
---|
1315 | x = float(value[0]) |
---|
1316 | |
---|
1317 | q[0] = x |
---|
1318 | return q |
---|
1319 | |
---|
1320 | |
---|
1321 | #FIXME: Consider this (taken from File_boundary) to allow |
---|
1322 | #spatial variation |
---|
1323 | #if vol_id is not None and edge_id is not None: |
---|
1324 | # i = self.boundary_indices[ vol_id, edge_id ] |
---|
1325 | # return self.F(t, point_id = i) |
---|
1326 | #else: |
---|
1327 | # return self.F(t) |
---|
1328 | |
---|
1329 | |
---|
1330 | |
---|
1331 | class Dirichlet_Discharge_boundary(Boundary): |
---|
1332 | """ |
---|
1333 | Sets stage (stage0) |
---|
1334 | Sets momentum (wh0) in the inward normal direction. |
---|
1335 | |
---|
1336 | Underlying domain must be specified when boundary is instantiated |
---|
1337 | """ |
---|
1338 | |
---|
1339 | def __init__(self, domain = None, stage0=None, wh0=None): |
---|
1340 | Boundary.__init__(self) |
---|
1341 | |
---|
1342 | if domain is None: |
---|
1343 | msg = 'Domain must be specified for this type boundary' |
---|
1344 | raise msg |
---|
1345 | |
---|
1346 | if stage0 is None: |
---|
1347 | raise 'set stage' |
---|
1348 | |
---|
1349 | if wh0 is None: |
---|
1350 | wh0 = 0.0 |
---|
1351 | |
---|
1352 | self.domain = domain |
---|
1353 | self.stage0 = stage0 |
---|
1354 | self.wh0 = wh0 |
---|
1355 | |
---|
1356 | def __repr__(self): |
---|
1357 | return 'Dirichlet_Discharge_boundary(%s)' %self.domain |
---|
1358 | |
---|
1359 | def evaluate(self, vol_id, edge_id): |
---|
1360 | """Set discharge in the (inward) normal direction |
---|
1361 | """ |
---|
1362 | |
---|
1363 | normal = self.domain.get_normal(vol_id,edge_id) |
---|
1364 | q = [self.stage0, -self.wh0*normal[0], -self.wh0*normal[1]] |
---|
1365 | return q |
---|
1366 | |
---|
1367 | |
---|
1368 | #FIXME: Consider this (taken from File_boundary) to allow |
---|
1369 | #spatial variation |
---|
1370 | #if vol_id is not None and edge_id is not None: |
---|
1371 | # i = self.boundary_indices[ vol_id, edge_id ] |
---|
1372 | # return self.F(t, point_id = i) |
---|
1373 | #else: |
---|
1374 | # return self.F(t) |
---|
1375 | |
---|
1376 | |
---|
1377 | |
---|
1378 | |
---|
1379 | |
---|
1380 | ######################### |
---|
1381 | #Standard forcing terms: |
---|
1382 | # |
---|
1383 | def gravity(domain): |
---|
1384 | """Apply gravitational pull in the presence of bed slope |
---|
1385 | """ |
---|
1386 | |
---|
1387 | xmom = domain.quantities['xmomentum'].explicit_update |
---|
1388 | ymom = domain.quantities['ymomentum'].explicit_update |
---|
1389 | |
---|
1390 | Stage = domain.quantities['stage'] |
---|
1391 | Elevation = domain.quantities['elevation'] |
---|
1392 | h = Stage.edge_values - Elevation.edge_values |
---|
1393 | v = Elevation.vertex_values |
---|
1394 | |
---|
1395 | x = domain.get_vertex_coordinates() |
---|
1396 | g = domain.g |
---|
1397 | |
---|
1398 | for k in range(len(domain)): |
---|
1399 | avg_h = sum( h[k,:] )/3 |
---|
1400 | |
---|
1401 | #Compute bed slope |
---|
1402 | x0, y0, x1, y1, x2, y2 = x[k,:] |
---|
1403 | z0, z1, z2 = v[k,:] |
---|
1404 | |
---|
1405 | zx, zy = gradient(x0, y0, x1, y1, x2, y2, z0, z1, z2) |
---|
1406 | |
---|
1407 | #Update momentum |
---|
1408 | xmom[k] += -g*zx*avg_h |
---|
1409 | ymom[k] += -g*zy*avg_h |
---|
1410 | |
---|
1411 | |
---|
1412 | def gravity_c(domain): |
---|
1413 | """Wrapper calling C version |
---|
1414 | """ |
---|
1415 | |
---|
1416 | xmom = domain.quantities['xmomentum'].explicit_update |
---|
1417 | ymom = domain.quantities['ymomentum'].explicit_update |
---|
1418 | |
---|
1419 | Stage = domain.quantities['stage'] |
---|
1420 | Elevation = domain.quantities['elevation'] |
---|
1421 | h = Stage.edge_values - Elevation.edge_values |
---|
1422 | v = Elevation.vertex_values |
---|
1423 | |
---|
1424 | x = domain.get_vertex_coordinates() |
---|
1425 | g = domain.g |
---|
1426 | |
---|
1427 | |
---|
1428 | from shallow_water_ext import gravity |
---|
1429 | gravity(g, h, v, x, xmom, ymom) |
---|
1430 | |
---|
1431 | |
---|
1432 | def manning_friction(domain): |
---|
1433 | """Apply (Manning) friction to water momentum |
---|
1434 | (Python version) |
---|
1435 | """ |
---|
1436 | |
---|
1437 | from math import sqrt |
---|
1438 | |
---|
1439 | w = domain.quantities['stage'].centroid_values |
---|
1440 | z = domain.quantities['elevation'].centroid_values |
---|
1441 | h = w-z |
---|
1442 | |
---|
1443 | uh = domain.quantities['xmomentum'].centroid_values |
---|
1444 | vh = domain.quantities['ymomentum'].centroid_values |
---|
1445 | eta = domain.quantities['friction'].centroid_values |
---|
1446 | |
---|
1447 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
---|
1448 | ymom_update = domain.quantities['ymomentum'].semi_implicit_update |
---|
1449 | |
---|
1450 | N = len(domain) |
---|
1451 | eps = domain.minimum_allowed_height |
---|
1452 | g = domain.g |
---|
1453 | |
---|
1454 | for k in range(N): |
---|
1455 | if eta[k] >= eps: |
---|
1456 | if h[k] >= eps: |
---|
1457 | S = -g * eta[k]**2 * sqrt((uh[k]**2 + vh[k]**2)) |
---|
1458 | S /= h[k]**(7.0/3) |
---|
1459 | |
---|
1460 | #Update momentum |
---|
1461 | xmom_update[k] += S*uh[k] |
---|
1462 | ymom_update[k] += S*vh[k] |
---|
1463 | |
---|
1464 | |
---|
1465 | def manning_friction_implicit_c(domain): |
---|
1466 | """Wrapper for c version |
---|
1467 | """ |
---|
1468 | |
---|
1469 | |
---|
1470 | #print 'Implicit friction' |
---|
1471 | |
---|
1472 | xmom = domain.quantities['xmomentum'] |
---|
1473 | ymom = domain.quantities['ymomentum'] |
---|
1474 | |
---|
1475 | w = domain.quantities['stage'].centroid_values |
---|
1476 | z = domain.quantities['elevation'].centroid_values |
---|
1477 | |
---|
1478 | uh = xmom.centroid_values |
---|
1479 | vh = ymom.centroid_values |
---|
1480 | eta = domain.quantities['friction'].centroid_values |
---|
1481 | |
---|
1482 | xmom_update = xmom.semi_implicit_update |
---|
1483 | ymom_update = ymom.semi_implicit_update |
---|
1484 | |
---|
1485 | N = len(domain) |
---|
1486 | eps = domain.minimum_allowed_height |
---|
1487 | g = domain.g |
---|
1488 | |
---|
1489 | from shallow_water_ext import manning_friction |
---|
1490 | manning_friction(g, eps, w, z, uh, vh, eta, xmom_update, ymom_update) |
---|
1491 | |
---|
1492 | |
---|
1493 | def manning_friction_explicit_c(domain): |
---|
1494 | """Wrapper for c version |
---|
1495 | """ |
---|
1496 | |
---|
1497 | #print 'Explicit friction' |
---|
1498 | |
---|
1499 | xmom = domain.quantities['xmomentum'] |
---|
1500 | ymom = domain.quantities['ymomentum'] |
---|
1501 | |
---|
1502 | w = domain.quantities['stage'].centroid_values |
---|
1503 | z = domain.quantities['elevation'].centroid_values |
---|
1504 | |
---|
1505 | uh = xmom.centroid_values |
---|
1506 | vh = ymom.centroid_values |
---|
1507 | eta = domain.quantities['friction'].centroid_values |
---|
1508 | |
---|
1509 | xmom_update = xmom.explicit_update |
---|
1510 | ymom_update = ymom.explicit_update |
---|
1511 | |
---|
1512 | N = len(domain) |
---|
1513 | eps = domain.minimum_allowed_height |
---|
1514 | g = domain.g |
---|
1515 | |
---|
1516 | from shallow_water_ext import manning_friction |
---|
1517 | manning_friction(g, eps, w, z, uh, vh, eta, xmom_update, ymom_update) |
---|
1518 | |
---|
1519 | |
---|
1520 | def linear_friction(domain): |
---|
1521 | """Apply linear friction to water momentum |
---|
1522 | |
---|
1523 | Assumes quantity: 'linear_friction' to be present |
---|
1524 | """ |
---|
1525 | |
---|
1526 | from math import sqrt |
---|
1527 | |
---|
1528 | w = domain.quantities['stage'].centroid_values |
---|
1529 | z = domain.quantities['elevation'].centroid_values |
---|
1530 | h = w-z |
---|
1531 | |
---|
1532 | uh = domain.quantities['xmomentum'].centroid_values |
---|
1533 | vh = domain.quantities['ymomentum'].centroid_values |
---|
1534 | tau = domain.quantities['linear_friction'].centroid_values |
---|
1535 | |
---|
1536 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
---|
1537 | ymom_update = domain.quantities['ymomentum'].semi_implicit_update |
---|
1538 | |
---|
1539 | N = len(domain) # number_of_triangles |
---|
1540 | eps = domain.minimum_allowed_height |
---|
1541 | g = domain.g #Not necessary? Why was this added? |
---|
1542 | |
---|
1543 | for k in range(N): |
---|
1544 | if tau[k] >= eps: |
---|
1545 | if h[k] >= eps: |
---|
1546 | S = -tau[k]/h[k] |
---|
1547 | |
---|
1548 | #Update momentum |
---|
1549 | xmom_update[k] += S*uh[k] |
---|
1550 | ymom_update[k] += S*vh[k] |
---|
1551 | |
---|
1552 | |
---|
1553 | |
---|
1554 | def check_forcefield(f): |
---|
1555 | """Check that f is either |
---|
1556 | 1: a callable object f(t,x,y), where x and y are vectors |
---|
1557 | and that it returns an array or a list of same length |
---|
1558 | as x and y |
---|
1559 | 2: a scalar |
---|
1560 | """ |
---|
1561 | |
---|
1562 | if callable(f): |
---|
1563 | N = 3 |
---|
1564 | x = ones(3, Float) |
---|
1565 | y = ones(3, Float) |
---|
1566 | try: |
---|
1567 | q = f(1.0, x=x, y=y) |
---|
1568 | except Exception, e: |
---|
1569 | msg = 'Function %s could not be executed:\n%s' %(f, e) |
---|
1570 | #FIXME: Reconsider this semantics |
---|
1571 | raise msg |
---|
1572 | |
---|
1573 | try: |
---|
1574 | q = array(q).astype(Float) |
---|
1575 | except: |
---|
1576 | msg = 'Return value from vector function %s could ' %f |
---|
1577 | msg += 'not be converted into a Numeric array of floats.\n' |
---|
1578 | msg += 'Specified function should return either list or array.' |
---|
1579 | raise msg |
---|
1580 | |
---|
1581 | #Is this really what we want? |
---|
1582 | msg = 'Return vector from function %s ' %f |
---|
1583 | msg += 'must have same lenght as input vectors' |
---|
1584 | assert len(q) == N, msg |
---|
1585 | |
---|
1586 | else: |
---|
1587 | try: |
---|
1588 | f = float(f) |
---|
1589 | except: |
---|
1590 | msg = 'Force field %s must be either a scalar' %f |
---|
1591 | msg += ' or a vector function' |
---|
1592 | raise Exception(msg) |
---|
1593 | return f |
---|
1594 | |
---|
1595 | |
---|
1596 | class Wind_stress: |
---|
1597 | """Apply wind stress to water momentum in terms of |
---|
1598 | wind speed [m/s] and wind direction [degrees] |
---|
1599 | """ |
---|
1600 | |
---|
1601 | def __init__(self, *args, **kwargs): |
---|
1602 | """Initialise windfield from wind speed s [m/s] |
---|
1603 | and wind direction phi [degrees] |
---|
1604 | |
---|
1605 | Inputs v and phi can be either scalars or Python functions, e.g. |
---|
1606 | |
---|
1607 | W = Wind_stress(10, 178) |
---|
1608 | |
---|
1609 | #FIXME - 'normal' degrees are assumed for now, i.e. the |
---|
1610 | vector (1,0) has zero degrees. |
---|
1611 | We may need to convert from 'compass' degrees later on and also |
---|
1612 | map from True north to grid north. |
---|
1613 | |
---|
1614 | Arguments can also be Python functions of t,x,y as in |
---|
1615 | |
---|
1616 | def speed(t,x,y): |
---|
1617 | ... |
---|
1618 | return s |
---|
1619 | |
---|
1620 | def angle(t,x,y): |
---|
1621 | ... |
---|
1622 | return phi |
---|
1623 | |
---|
1624 | where x and y are vectors. |
---|
1625 | |
---|
1626 | and then pass the functions in |
---|
1627 | |
---|
1628 | W = Wind_stress(speed, angle) |
---|
1629 | |
---|
1630 | The instantiated object W can be appended to the list of |
---|
1631 | forcing_terms as in |
---|
1632 | |
---|
1633 | Alternatively, one vector valued function for (speed, angle) |
---|
1634 | can be applied, providing both quantities simultaneously. |
---|
1635 | As in |
---|
1636 | W = Wind_stress(F), where returns (speed, angle) for each t. |
---|
1637 | |
---|
1638 | domain.forcing_terms.append(W) |
---|
1639 | """ |
---|
1640 | |
---|
1641 | from anuga.config import rho_a, rho_w, eta_w |
---|
1642 | from Numeric import array, Float |
---|
1643 | |
---|
1644 | if len(args) == 2: |
---|
1645 | s = args[0] |
---|
1646 | phi = args[1] |
---|
1647 | elif len(args) == 1: |
---|
1648 | #Assume vector function returning (s, phi)(t,x,y) |
---|
1649 | vector_function = args[0] |
---|
1650 | s = lambda t,x,y: vector_function(t,x=x,y=y)[0] |
---|
1651 | phi = lambda t,x,y: vector_function(t,x=x,y=y)[1] |
---|
1652 | else: |
---|
1653 | #Assume info is in 2 keyword arguments |
---|
1654 | |
---|
1655 | if len(kwargs) == 2: |
---|
1656 | s = kwargs['s'] |
---|
1657 | phi = kwargs['phi'] |
---|
1658 | else: |
---|
1659 | raise 'Assumes two keyword arguments: s=..., phi=....' |
---|
1660 | |
---|
1661 | self.speed = check_forcefield(s) |
---|
1662 | self.phi = check_forcefield(phi) |
---|
1663 | |
---|
1664 | self.const = eta_w*rho_a/rho_w |
---|
1665 | |
---|
1666 | |
---|
1667 | def __call__(self, domain): |
---|
1668 | """Evaluate windfield based on values found in domain |
---|
1669 | """ |
---|
1670 | |
---|
1671 | from math import pi, cos, sin, sqrt |
---|
1672 | from Numeric import Float, ones, ArrayType |
---|
1673 | |
---|
1674 | xmom_update = domain.quantities['xmomentum'].explicit_update |
---|
1675 | ymom_update = domain.quantities['ymomentum'].explicit_update |
---|
1676 | |
---|
1677 | N = len(domain) # number_of_triangles |
---|
1678 | t = domain.time |
---|
1679 | |
---|
1680 | if callable(self.speed): |
---|
1681 | xc = domain.get_centroid_coordinates() |
---|
1682 | s_vec = self.speed(t, xc[:,0], xc[:,1]) |
---|
1683 | else: |
---|
1684 | #Assume s is a scalar |
---|
1685 | |
---|
1686 | try: |
---|
1687 | s_vec = self.speed * ones(N, Float) |
---|
1688 | except: |
---|
1689 | msg = 'Speed must be either callable or a scalar: %s' %self.s |
---|
1690 | raise msg |
---|
1691 | |
---|
1692 | |
---|
1693 | if callable(self.phi): |
---|
1694 | xc = domain.get_centroid_coordinates() |
---|
1695 | phi_vec = self.phi(t, xc[:,0], xc[:,1]) |
---|
1696 | else: |
---|
1697 | #Assume phi is a scalar |
---|
1698 | |
---|
1699 | try: |
---|
1700 | phi_vec = self.phi * ones(N, Float) |
---|
1701 | except: |
---|
1702 | msg = 'Angle must be either callable or a scalar: %s' %self.phi |
---|
1703 | raise msg |
---|
1704 | |
---|
1705 | assign_windfield_values(xmom_update, ymom_update, |
---|
1706 | s_vec, phi_vec, self.const) |
---|
1707 | |
---|
1708 | |
---|
1709 | def assign_windfield_values(xmom_update, ymom_update, |
---|
1710 | s_vec, phi_vec, const): |
---|
1711 | """Python version of assigning wind field to update vectors. |
---|
1712 | A c version also exists (for speed) |
---|
1713 | """ |
---|
1714 | from math import pi, cos, sin, sqrt |
---|
1715 | |
---|
1716 | N = len(s_vec) |
---|
1717 | for k in range(N): |
---|
1718 | s = s_vec[k] |
---|
1719 | phi = phi_vec[k] |
---|
1720 | |
---|
1721 | #Convert to radians |
---|
1722 | phi = phi*pi/180 |
---|
1723 | |
---|
1724 | #Compute velocity vector (u, v) |
---|
1725 | u = s*cos(phi) |
---|
1726 | v = s*sin(phi) |
---|
1727 | |
---|
1728 | #Compute wind stress |
---|
1729 | S = const * sqrt(u**2 + v**2) |
---|
1730 | xmom_update[k] += S*u |
---|
1731 | ymom_update[k] += S*v |
---|
1732 | |
---|
1733 | |
---|
1734 | |
---|
1735 | ############################## |
---|
1736 | #OBSOLETE STUFF |
---|
1737 | |
---|
1738 | def balance_deep_and_shallow_old(domain): |
---|
1739 | """Compute linear combination between stage as computed by |
---|
1740 | gradient-limiters and stage computed as constant height above bed. |
---|
1741 | The former takes precedence when heights are large compared to the |
---|
1742 | bed slope while the latter takes precedence when heights are |
---|
1743 | relatively small. Anything in between is computed as a balanced |
---|
1744 | linear combination in order to avoid numerical disturbances which |
---|
1745 | would otherwise appear as a result of hard switching between |
---|
1746 | modes. |
---|
1747 | """ |
---|
1748 | |
---|
1749 | #OBSOLETE |
---|
1750 | |
---|
1751 | #Shortcuts |
---|
1752 | wc = domain.quantities['stage'].centroid_values |
---|
1753 | zc = domain.quantities['elevation'].centroid_values |
---|
1754 | hc = wc - zc |
---|
1755 | |
---|
1756 | wv = domain.quantities['stage'].vertex_values |
---|
1757 | zv = domain.quantities['elevation'].vertex_values |
---|
1758 | hv = wv-zv |
---|
1759 | |
---|
1760 | |
---|
1761 | #Computed linear combination between constant stages and and |
---|
1762 | #stages parallel to the bed elevation. |
---|
1763 | for k in range(len(domain)): |
---|
1764 | #Compute maximal variation in bed elevation |
---|
1765 | # This quantitiy is |
---|
1766 | # dz = max_i abs(z_i - z_c) |
---|
1767 | # and it is independent of dimension |
---|
1768 | # In the 1d case zc = (z0+z1)/2 |
---|
1769 | # In the 2d case zc = (z0+z1+z2)/3 |
---|
1770 | |
---|
1771 | dz = max(abs(zv[k,0]-zc[k]), |
---|
1772 | abs(zv[k,1]-zc[k]), |
---|
1773 | abs(zv[k,2]-zc[k])) |
---|
1774 | |
---|
1775 | |
---|
1776 | hmin = min( hv[k,:] ) |
---|
1777 | |
---|
1778 | #Create alpha in [0,1], where alpha==0 means using shallow |
---|
1779 | #first order scheme and alpha==1 means using the stage w as |
---|
1780 | #computed by the gradient limiter (1st or 2nd order) |
---|
1781 | # |
---|
1782 | #If hmin > dz/2 then alpha = 1 and the bed will have no effect |
---|
1783 | #If hmin < 0 then alpha = 0 reverting to constant height above bed. |
---|
1784 | |
---|
1785 | if dz > 0.0: |
---|
1786 | alpha = max( min( 2*hmin/dz, 1.0), 0.0 ) |
---|
1787 | else: |
---|
1788 | #Flat bed |
---|
1789 | alpha = 1.0 |
---|
1790 | |
---|
1791 | #Weighted balance between stage parallel to bed elevation |
---|
1792 | #(wvi = zvi + hc) and stage as computed by 1st or 2nd |
---|
1793 | #order gradient limiter |
---|
1794 | #(wvi = zvi + hvi) where i=0,1,2 denotes the vertex ids |
---|
1795 | # |
---|
1796 | #It follows that the updated wvi is |
---|
1797 | # wvi := (1-alpha)*(zvi+hc) + alpha*(zvi+hvi) = |
---|
1798 | # zvi + hc + alpha*(hvi - hc) |
---|
1799 | # |
---|
1800 | #Note that hvi = zc+hc-zvi in the first order case (constant). |
---|
1801 | |
---|
1802 | if alpha < 1: |
---|
1803 | for i in range(3): |
---|
1804 | wv[k,i] = zv[k,i] + hc[k] + alpha*(hv[k,i]-hc[k]) |
---|
1805 | |
---|
1806 | |
---|
1807 | #Momentums at centroids |
---|
1808 | xmomc = domain.quantities['xmomentum'].centroid_values |
---|
1809 | ymomc = domain.quantities['ymomentum'].centroid_values |
---|
1810 | |
---|
1811 | #Momentums at vertices |
---|
1812 | xmomv = domain.quantities['xmomentum'].vertex_values |
---|
1813 | ymomv = domain.quantities['ymomentum'].vertex_values |
---|
1814 | |
---|
1815 | # Update momentum as a linear combination of |
---|
1816 | # xmomc and ymomc (shallow) and momentum |
---|
1817 | # from extrapolator xmomv and ymomv (deep). |
---|
1818 | xmomv[k,:] = (1-alpha)*xmomc[k] + alpha*xmomv[k,:] |
---|
1819 | ymomv[k,:] = (1-alpha)*ymomc[k] + alpha*ymomv[k,:] |
---|
1820 | |
---|
1821 | |
---|
1822 | |
---|
1823 | |
---|
1824 | |
---|
1825 | ########################### |
---|
1826 | ########################### |
---|
1827 | #Geometries |
---|
1828 | |
---|
1829 | |
---|
1830 | #FIXME: Rethink this way of creating values. |
---|
1831 | |
---|
1832 | |
---|
1833 | class Weir: |
---|
1834 | """Set a bathymetry for weir with a hole and a downstream gutter |
---|
1835 | x,y are assumed to be in the unit square |
---|
1836 | """ |
---|
1837 | |
---|
1838 | def __init__(self, stage): |
---|
1839 | self.inflow_stage = stage |
---|
1840 | |
---|
1841 | def __call__(self, x, y): |
---|
1842 | from Numeric import zeros, Float |
---|
1843 | from math import sqrt |
---|
1844 | |
---|
1845 | N = len(x) |
---|
1846 | assert N == len(y) |
---|
1847 | |
---|
1848 | z = zeros(N, Float) |
---|
1849 | for i in range(N): |
---|
1850 | z[i] = -x[i]/2 #General slope |
---|
1851 | |
---|
1852 | #Flattish bit to the left |
---|
1853 | if x[i] < 0.3: |
---|
1854 | z[i] = -x[i]/10 |
---|
1855 | |
---|
1856 | #Weir |
---|
1857 | if x[i] >= 0.3 and x[i] < 0.4: |
---|
1858 | z[i] = -x[i]+0.9 |
---|
1859 | |
---|
1860 | #Dip |
---|
1861 | x0 = 0.6 |
---|
1862 | #depth = -1.3 |
---|
1863 | depth = -1.0 |
---|
1864 | #plateaux = -0.9 |
---|
1865 | plateaux = -0.6 |
---|
1866 | if y[i] < 0.7: |
---|
1867 | if x[i] > x0 and x[i] < 0.9: |
---|
1868 | z[i] = depth |
---|
1869 | |
---|
1870 | #RHS plateaux |
---|
1871 | if x[i] >= 0.9: |
---|
1872 | z[i] = plateaux |
---|
1873 | |
---|
1874 | |
---|
1875 | elif y[i] >= 0.7 and y[i] < 1.5: |
---|
1876 | #Restrict and deepen |
---|
1877 | if x[i] >= x0 and x[i] < 0.8: |
---|
1878 | z[i] = depth-(y[i]/3-0.3) |
---|
1879 | #z[i] = depth-y[i]/5 |
---|
1880 | #z[i] = depth |
---|
1881 | elif x[i] >= 0.8: |
---|
1882 | #RHS plateaux |
---|
1883 | z[i] = plateaux |
---|
1884 | |
---|
1885 | elif y[i] >= 1.5: |
---|
1886 | if x[i] >= x0 and x[i] < 0.8 + (y[i]-1.5)/1.2: |
---|
1887 | #Widen up and stay at constant depth |
---|
1888 | z[i] = depth-1.5/5 |
---|
1889 | elif x[i] >= 0.8 + (y[i]-1.5)/1.2: |
---|
1890 | #RHS plateaux |
---|
1891 | z[i] = plateaux |
---|
1892 | |
---|
1893 | |
---|
1894 | #Hole in weir (slightly higher than inflow condition) |
---|
1895 | if x[i] >= 0.3 and x[i] < 0.4 and y[i] > 0.2 and y[i] < 0.4: |
---|
1896 | z[i] = -x[i]+self.inflow_stage + 0.02 |
---|
1897 | |
---|
1898 | #Channel behind weir |
---|
1899 | x0 = 0.5 |
---|
1900 | if x[i] >= 0.4 and x[i] < x0 and y[i] > 0.2 and y[i] < 0.4: |
---|
1901 | z[i] = -x[i]+self.inflow_stage + 0.02 |
---|
1902 | |
---|
1903 | if x[i] >= x0 and x[i] < 0.6 and y[i] > 0.2 and y[i] < 0.4: |
---|
1904 | #Flatten it out towards the end |
---|
1905 | z[i] = -x0+self.inflow_stage + 0.02 + (x0-x[i])/5 |
---|
1906 | |
---|
1907 | #Hole to the east |
---|
1908 | x0 = 1.1; y0 = 0.35 |
---|
1909 | #if x[i] < -0.2 and y < 0.5: |
---|
1910 | if sqrt((2*(x[i]-x0))**2 + (2*(y[i]-y0))**2) < 0.2: |
---|
1911 | z[i] = sqrt(((x[i]-x0))**2 + ((y[i]-y0))**2)-1.0 |
---|
1912 | |
---|
1913 | #Tiny channel draining hole |
---|
1914 | if x[i] >= 1.14 and x[i] < 1.2 and y[i] >= 0.4 and y[i] < 0.6: |
---|
1915 | z[i] = -0.9 #North south |
---|
1916 | |
---|
1917 | if x[i] >= 0.9 and x[i] < 1.18 and y[i] >= 0.58 and y[i] < 0.65: |
---|
1918 | z[i] = -1.0 + (x[i]-0.9)/3 #East west |
---|
1919 | |
---|
1920 | |
---|
1921 | |
---|
1922 | #Stuff not in use |
---|
1923 | |
---|
1924 | #Upward slope at inlet to the north west |
---|
1925 | #if x[i] < 0.0: # and y[i] > 0.5: |
---|
1926 | # #z[i] = -y[i]+0.5 #-x[i]/2 |
---|
1927 | # z[i] = x[i]/4 - y[i]**2 + 0.5 |
---|
1928 | |
---|
1929 | #Hole to the west |
---|
1930 | #x0 = -0.4; y0 = 0.35 # center |
---|
1931 | #if sqrt((2*(x[i]-x0))**2 + (2*(y[i]-y0))**2) < 0.2: |
---|
1932 | # z[i] = sqrt(((x[i]-x0))**2 + ((y[i]-y0))**2)-0.2 |
---|
1933 | |
---|
1934 | |
---|
1935 | |
---|
1936 | |
---|
1937 | |
---|
1938 | return z/2 |
---|
1939 | |
---|
1940 | class Weir_simple: |
---|
1941 | """Set a bathymetry for weir with a hole and a downstream gutter |
---|
1942 | x,y are assumed to be in the unit square |
---|
1943 | """ |
---|
1944 | |
---|
1945 | def __init__(self, stage): |
---|
1946 | self.inflow_stage = stage |
---|
1947 | |
---|
1948 | def __call__(self, x, y): |
---|
1949 | from Numeric import zeros, Float |
---|
1950 | |
---|
1951 | N = len(x) |
---|
1952 | assert N == len(y) |
---|
1953 | |
---|
1954 | z = zeros(N, Float) |
---|
1955 | for i in range(N): |
---|
1956 | z[i] = -x[i] #General slope |
---|
1957 | |
---|
1958 | #Flat bit to the left |
---|
1959 | if x[i] < 0.3: |
---|
1960 | z[i] = -x[i]/10 #General slope |
---|
1961 | |
---|
1962 | #Weir |
---|
1963 | if x[i] > 0.3 and x[i] < 0.4: |
---|
1964 | z[i] = -x[i]+0.9 |
---|
1965 | |
---|
1966 | #Dip |
---|
1967 | if x[i] > 0.6 and x[i] < 0.9: |
---|
1968 | z[i] = -x[i]-0.5 #-y[i]/5 |
---|
1969 | |
---|
1970 | #Hole in weir (slightly higher than inflow condition) |
---|
1971 | if x[i] > 0.3 and x[i] < 0.4 and y[i] > 0.2 and y[i] < 0.4: |
---|
1972 | z[i] = -x[i]+self.inflow_stage + 0.05 |
---|
1973 | |
---|
1974 | |
---|
1975 | return z/2 |
---|
1976 | |
---|
1977 | |
---|
1978 | |
---|
1979 | class Constant_stage: |
---|
1980 | """Set an initial condition with constant stage |
---|
1981 | """ |
---|
1982 | def __init__(self, s): |
---|
1983 | self.s = s |
---|
1984 | |
---|
1985 | def __call__(self, x, y): |
---|
1986 | return self.s |
---|
1987 | |
---|
1988 | class Constant_height: |
---|
1989 | """Set an initial condition with constant water height, e.g |
---|
1990 | stage s = z+h |
---|
1991 | """ |
---|
1992 | |
---|
1993 | def __init__(self, W, h): |
---|
1994 | self.W = W |
---|
1995 | self.h = h |
---|
1996 | |
---|
1997 | def __call__(self, x, y): |
---|
1998 | if self.W is None: |
---|
1999 | from Numeric import ones, Float |
---|
2000 | return self.h*ones(len(x), Float) |
---|
2001 | else: |
---|
2002 | return self.W(x,y) + self.h |
---|
2003 | |
---|
2004 | |
---|
2005 | |
---|
2006 | |
---|
2007 | def compute_fluxes_python(domain): |
---|
2008 | """Compute all fluxes and the timestep suitable for all volumes |
---|
2009 | in domain. |
---|
2010 | |
---|
2011 | Compute total flux for each conserved quantity using "flux_function" |
---|
2012 | |
---|
2013 | Fluxes across each edge are scaled by edgelengths and summed up |
---|
2014 | Resulting flux is then scaled by area and stored in |
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2015 | explicit_update for each of the three conserved quantities |
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2016 | stage, xmomentum and ymomentum |
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2017 | |
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2018 | The maximal allowable speed computed by the flux_function for each volume |
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2019 | is converted to a timestep that must not be exceeded. The minimum of |
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2020 | those is computed as the next overall timestep. |
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2021 | |
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2022 | Post conditions: |
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2023 | domain.explicit_update is reset to computed flux values |
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2024 | domain.timestep is set to the largest step satisfying all volumes. |
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2025 | """ |
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2026 | |
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2027 | import sys |
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2028 | from Numeric import zeros, Float |
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2029 | |
---|
2030 | N = len(domain) # number_of_triangles |
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2031 | |
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2032 | #Shortcuts |
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2033 | Stage = domain.quantities['stage'] |
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2034 | Xmom = domain.quantities['xmomentum'] |
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2035 | Ymom = domain.quantities['ymomentum'] |
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2036 | Bed = domain.quantities['elevation'] |
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2037 | |
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2038 | #Arrays |
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2039 | stage = Stage.edge_values |
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2040 | xmom = Xmom.edge_values |
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2041 | ymom = Ymom.edge_values |
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2042 | bed = Bed.edge_values |
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2043 | |
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2044 | stage_bdry = Stage.boundary_values |
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2045 | xmom_bdry = Xmom.boundary_values |
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2046 | ymom_bdry = Ymom.boundary_values |
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2047 | |
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2048 | flux = zeros((N,3), Float) #Work array for summing up fluxes |
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2049 | |
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2050 | #Loop |
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2051 | timestep = float(sys.maxint) |
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2052 | for k in range(N): |
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2053 | |
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2054 | for i in range(3): |
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2055 | #Quantities inside volume facing neighbour i |
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2056 | ql = [stage[k, i], xmom[k, i], ymom[k, i]] |
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2057 | zl = bed[k, i] |
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2058 | |
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2059 | #Quantities at neighbour on nearest face |
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2060 | n = domain.neighbours[k,i] |
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2061 | if n < 0: |
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2062 | m = -n-1 #Convert negative flag to index |
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2063 | qr = [stage_bdry[m], xmom_bdry[m], ymom_bdry[m]] |
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2064 | zr = zl #Extend bed elevation to boundary |
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2065 | else: |
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2066 | m = domain.neighbour_edges[k,i] |
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2067 | qr = [stage[n, m], xmom[n, m], ymom[n, m]] |
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2068 | zr = bed[n, m] |
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2069 | |
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2070 | |
---|
2071 | #Outward pointing normal vector |
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2072 | normal = domain.normals[k, 2*i:2*i+2] |
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2073 | |
---|
2074 | #Flux computation using provided function |
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2075 | edgeflux, max_speed = flux_function(normal, ql, qr, zl, zr) |
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2076 | |
---|
2077 | flux[k,:] = edgeflux |
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2078 | |
---|
2079 | return flux |
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2080 | |
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2081 | |
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2082 | |
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2083 | |
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2084 | |
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2085 | |
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2086 | |
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2087 | ############################################## |
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2088 | #Initialise module |
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2089 | |
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2090 | |
---|
2091 | from anuga.utilities import compile |
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2092 | if compile.can_use_C_extension('shallow_water_ext.c'): |
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2093 | #Replace python version with c implementations |
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2094 | |
---|
2095 | from shallow_water_ext import rotate, assign_windfield_values |
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2096 | compute_fluxes = compute_fluxes_c |
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2097 | extrapolate_second_order_sw=extrapolate_second_order_sw_c |
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2098 | gravity = gravity_c |
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2099 | manning_friction = manning_friction_implicit_c |
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2100 | h_limiter = h_limiter_c |
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2101 | balance_deep_and_shallow = balance_deep_and_shallow_c |
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2102 | protect_against_infinitesimal_and_negative_heights =\ |
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2103 | protect_against_infinitesimal_and_negative_heights_c |
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2104 | |
---|
2105 | #distribute_to_vertices_and_edges =\ |
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2106 | # distribute_to_vertices_and_edges_c #(like MH's) |
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2107 | |
---|
2108 | |
---|
2109 | |
---|
2110 | #Optimisation with psyco |
---|
2111 | from anuga.config import use_psyco |
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2112 | if use_psyco: |
---|
2113 | try: |
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2114 | import psyco |
---|
2115 | except: |
---|
2116 | import os |
---|
2117 | if os.name == 'posix' and os.uname()[4] == 'x86_64': |
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2118 | pass |
---|
2119 | #Psyco isn't supported on 64 bit systems, but it doesn't matter |
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2120 | else: |
---|
2121 | msg = 'WARNING: psyco (speedup) could not import'+\ |
---|
2122 | ', you may want to consider installing it' |
---|
2123 | print msg |
---|
2124 | else: |
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2125 | psyco.bind(Domain.distribute_to_vertices_and_edges) |
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2126 | psyco.bind(Domain.compute_fluxes) |
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2127 | |
---|
2128 | if __name__ == "__main__": |
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2129 | pass |
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2130 | |
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2131 | # Profiling stuff |
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2132 | #import profile |
---|
2133 | #profiler = profile.Profile() |
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