1 | """Class Domain - |
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2 | 1D interval domains for finite-volume computations of |
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3 | the shallow water wave equation. |
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4 | |
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5 | This module contains a specialisation of class Domain from module domain.py |
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6 | consisting of methods specific to the Shallow Water Wave Equation |
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7 | |
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8 | |
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9 | U_t + E_x = S |
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10 | |
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11 | where |
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12 | |
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13 | U = [w, uh] |
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14 | E = [uh, u^2h + gh^2/2] |
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15 | S represents source terms forcing the system |
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16 | (e.g. gravity, friction, wind stress, ...) |
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17 | |
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18 | and _t, _x, _y denote the derivative with respect to t, x and y respectiely. |
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19 | |
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20 | The quantities are |
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21 | |
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22 | symbol variable name explanation |
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23 | x x horizontal distance from origin [m] |
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24 | z elevation elevation of bed on which flow is modelled [m] |
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25 | h height water height above z [m] |
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26 | w stage absolute water level, w = z+h [m] |
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27 | u speed in the x direction [m/s] |
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28 | uh xmomentum momentum in the x direction [m^2/s] |
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29 | |
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30 | eta mannings friction coefficient [to appear] |
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31 | nu wind stress coefficient [to appear] |
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32 | |
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33 | The conserved quantities are w, uh |
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34 | |
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35 | For details see e.g. |
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36 | Christopher Zoppou and Stephen Roberts, |
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37 | Catastrophic Collapse of Water Supply Reservoirs in Urban Areas, |
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38 | Journal of Hydraulic Engineering, vol. 127, No. 7 July 1999 |
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39 | |
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40 | |
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41 | John Jakeman, Ole Nielsen, Stephen Roberts, Duncan Gray, Christopher Zoppou |
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42 | Geoscience Australia, 2006 |
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43 | """ |
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44 | |
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45 | #from domain import * |
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46 | from domain_adjust import * |
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47 | Generic_Domain = Domain #Rename |
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48 | |
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49 | #Shallow water domain |
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50 | class Domain(Generic_Domain): |
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51 | |
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52 | def __init__(self, coordinates, boundary = None, tagged_elements = None, |
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53 | geo_reference = None): |
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54 | |
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55 | conserved_quantities = ['stage', 'xmomentum','height'] |
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56 | other_quantities = ['elevation', 'friction']#, 'height'] |
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57 | Generic_Domain.__init__(self, coordinates, boundary, |
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58 | conserved_quantities, other_quantities, |
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59 | tagged_elements, geo_reference) |
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60 | |
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61 | from config import minimum_allowed_height, g |
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62 | self.minimum_allowed_height = minimum_allowed_height |
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63 | self.g = g |
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64 | |
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65 | #forcing terms not included in 1d domain ?WHy? |
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66 | self.forcing_terms.append(gravity) |
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67 | #self.forcing_terms.append(manning_friction) |
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68 | #print "\nI have Removed forcing terms line 64 1dsw" |
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69 | |
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70 | #Realtime visualisation |
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71 | self.visualiser = None |
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72 | self.visualise = False |
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73 | self.visualise_color_stage = False |
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74 | self.visualise_stage_range = 1.0 |
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75 | self.visualise_timer = True |
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76 | self.visualise_range_z = None |
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77 | |
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78 | #Stored output |
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79 | self.store = True |
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80 | self.format = 'sww' |
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81 | self.smooth = True |
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82 | |
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83 | #Evolve parametrs |
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84 | self.cfl = 1.0 |
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85 | |
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86 | #Reduction operation for get_vertex_values |
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87 | from util import mean |
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88 | self.reduction = mean |
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89 | #self.reduction = min #Looks better near steep slopes |
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90 | |
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91 | self.quantities_to_be_stored = ['stage','xmomentum'] |
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92 | |
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93 | |
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94 | def set_quantities_to_be_stored(self, q): |
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95 | """Specify which quantities will be stored in the sww file. |
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96 | |
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97 | q must be either: |
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98 | - the name of a quantity |
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99 | - a list of quantity names |
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100 | - None |
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101 | |
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102 | In the two first cases, the named quantities will be stored at each |
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103 | yieldstep |
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104 | (This is in addition to the quantities elevation and friction) |
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105 | If q is None, storage will be switched off altogether. |
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106 | """ |
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107 | |
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108 | |
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109 | if q is None: |
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110 | self.quantities_to_be_stored = [] |
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111 | self.store = False |
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112 | return |
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113 | |
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114 | if isinstance(q, basestring): |
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115 | q = [q] # Turn argument into a list |
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116 | |
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117 | #Check correcness |
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118 | for quantity_name in q: |
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119 | msg = 'Quantity %s is not a valid conserved quantity' %quantity_name |
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120 | assert quantity_name in self.conserved_quantities, msg |
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121 | |
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122 | self.quantities_to_be_stored = q |
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123 | |
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124 | |
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125 | def initialise_visualiser(self,scale_z=1.0,rect=None): |
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126 | #Realtime visualisation |
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127 | if self.visualiser is None: |
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128 | from realtime_visualisation_new import Visualiser |
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129 | self.visualiser = Visualiser(self,scale_z,rect) |
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130 | self.visualiser.setup['elevation']=True |
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131 | self.visualiser.updating['stage']=True |
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132 | self.visualise = True |
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133 | if self.visualise_color_stage == True: |
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134 | self.visualiser.coloring['stage'] = True |
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135 | self.visualiser.qcolor['stage'] = (0.0, 0.0, 0.8) |
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136 | print 'initialise visualiser' |
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137 | print self.visualiser.setup |
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138 | print self.visualiser.updating |
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139 | |
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140 | def check_integrity(self): |
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141 | Generic_Domain.check_integrity(self) |
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142 | #Check that we are solving the shallow water wave equation |
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143 | |
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144 | msg = 'First conserved quantity must be "stage"' |
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145 | assert self.conserved_quantities[0] == 'stage', msg |
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146 | msg = 'Second conserved quantity must be "xmomentum"' |
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147 | assert self.conserved_quantities[1] == 'xmomentum', msg |
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148 | |
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149 | def extrapolate_second_order_sw(self): |
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150 | #Call correct module function |
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151 | #(either from this module or C-extension) |
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152 | extrapolate_second_order_sw(self) |
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153 | |
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154 | def compute_fluxes(self): |
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155 | #Call correct module function |
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156 | #(either from this module or C-extension) |
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157 | compute_fluxes(self) |
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158 | |
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159 | def compute_timestep(self): |
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160 | #Call correct module function |
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161 | compute_timestep(self) |
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162 | |
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163 | def distribute_to_vertices_and_edges(self): |
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164 | #Call correct module function |
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165 | #(either from this module or C-extension) |
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166 | distribute_to_vertices_and_edges(self) |
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167 | |
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168 | |
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169 | def distribute_stage_to_height(self): |
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170 | #Call correct module function |
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171 | #(either from this module or C-extension) |
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172 | distribute_stage_to_height(self) |
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173 | |
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174 | |
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175 | def classify_wet_dry_cells(self): |
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176 | #Call correct module function |
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177 | classify_wet_dry_cells(self) |
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178 | |
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179 | def set_initial_conserved_quanitites(self): |
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180 | #Call correct module function |
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181 | set_initial_conserved_quanitites(self) |
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182 | |
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183 | |
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184 | def adjust_partially_submerged_cells(self): |
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185 | #Call correct module function |
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186 | adjust_partially_submerged_cells(self) |
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187 | |
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188 | def pre_update(self): |
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189 | #Call correct module function |
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190 | pre_update(self) |
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191 | |
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192 | def post_update(self): |
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193 | #Call correct module function |
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194 | post_update(self) |
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195 | |
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196 | def evolve(self, yieldstep = None, finaltime = None, |
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197 | skip_initial_step = False): |
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198 | """Specialisation of basic evolve method from parent class |
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199 | """ |
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200 | |
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201 | #Call check integrity here rather than from user scripts |
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202 | #self.check_integrity() |
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203 | |
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204 | #msg = 'Parameter beta_h must be in the interval [0, 1)' |
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205 | #assert 0 <= self.beta_h < 1.0, msg |
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206 | #msg = 'Parameter beta_w must be in the interval [0, 1)' |
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207 | #assert 0 <= self.beta_w < 1.0, msg |
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208 | |
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209 | |
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210 | #Initial update of vertex and edge values before any storage |
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211 | #and or visualisation |
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212 | |
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213 | print "will not work if stage not set at vertices" |
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214 | self.set_initial_conserved_quanitites() |
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215 | |
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216 | self.distribute_to_vertices_and_edges() |
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217 | |
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218 | self.distribute_stage_to_height() |
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219 | |
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220 | #Initialise real time viz if requested |
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221 | #if self.visualise is True and self.time == 0.0: |
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222 | # if self.visualiser is None: |
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223 | # self.initialise_visualiser() |
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224 | # |
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225 | # self.visualiser.update_timer() |
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226 | # self.visualiser.setup_all() |
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227 | |
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228 | #Store model data, e.g. for visualisation |
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229 | #if self.store is True and self.time == 0.0: |
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230 | # self.initialise_storage() |
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231 | # #print 'Storing results in ' + self.writer.filename |
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232 | #else: |
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233 | # pass |
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234 | # #print 'Results will not be stored.' |
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235 | # #print 'To store results set domain.store = True' |
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236 | # #FIXME: Diagnostic output should be controlled by |
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237 | # # a 'verbose' flag living in domain (or in a parent class) |
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238 | |
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239 | #Call basic machinery from parent class |
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240 | for t in Generic_Domain.evolve(self, yieldstep, finaltime, |
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241 | skip_initial_step): |
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242 | #Real time viz |
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243 | # if self.visualise is True: |
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244 | # self.visualiser.update_all() |
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245 | # self.visualiser.update_timer() |
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246 | |
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247 | |
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248 | #Store model data, e.g. for subsequent visualisation |
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249 | # if self.store is True: |
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250 | # self.store_timestep(self.quantities_to_be_stored) |
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251 | |
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252 | #FIXME: Could maybe be taken from specified list |
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253 | #of 'store every step' quantities |
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254 | |
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255 | #Pass control on to outer loop for more specific actions |
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256 | yield(t) |
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257 | |
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258 | def initialise_storage(self): |
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259 | """Create and initialise self.writer object for storing data. |
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260 | Also, save x and bed elevation |
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261 | """ |
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262 | |
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263 | import data_manager |
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264 | |
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265 | #Initialise writer |
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266 | self.writer = data_manager.get_dataobject(self, mode = 'w') |
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267 | |
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268 | #Store vertices and connectivity |
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269 | self.writer.store_connectivity() |
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270 | |
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271 | |
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272 | def store_timestep(self, name): |
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273 | """Store named quantity and time. |
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274 | |
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275 | Precondition: |
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276 | self.write has been initialised |
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277 | """ |
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278 | self.writer.store_timestep(name) |
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279 | |
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280 | |
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281 | #=============== End of Shallow Water Domain =============================== |
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282 | |
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283 | #Rotation of momentum vector |
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284 | def rotate(q, normal, direction = 1): |
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285 | """Rotate the momentum component q (q[1], q[2]) |
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286 | from x,y coordinates to coordinates based on normal vector. |
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287 | |
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288 | If direction is negative the rotation is inverted. |
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289 | |
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290 | Input vector is preserved |
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291 | |
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292 | This function is specific to the shallow water wave equation |
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293 | """ |
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294 | |
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295 | from Numeric import zeros, Float |
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296 | |
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297 | assert len(q) == 3,\ |
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298 | 'Vector of conserved quantities must have length 3'\ |
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299 | 'for 2D shallow water equation' |
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300 | |
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301 | try: |
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302 | l = len(normal) |
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303 | except: |
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304 | raise 'Normal vector must be an Numeric array' |
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305 | |
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306 | assert l == 2, 'Normal vector must have 2 components' |
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307 | |
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308 | |
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309 | n1 = normal[0] |
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310 | n2 = normal[1] |
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311 | |
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312 | r = zeros(len(q), Float) #Rotated quantities |
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313 | r[0] = q[0] #First quantity, height, is not rotated |
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314 | |
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315 | if direction == -1: |
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316 | n2 = -n2 |
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317 | |
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318 | |
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319 | r[1] = n1*q[1] + n2*q[2] |
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320 | r[2] = -n2*q[1] + n1*q[2] |
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321 | |
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322 | return r |
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323 | |
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324 | def flux_function(normal, ql, qr, zl, zr): |
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325 | """Compute fluxes between volumes for the shallow water wave equation |
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326 | cast in terms of w = h+z using the 'central scheme' as described in |
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327 | |
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328 | Kurganov, Noelle, Petrova. 'Semidiscrete Central-Upwind Schemes For |
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329 | Hyperbolic Conservation Laws and Hamilton-Jacobi Equations'. |
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330 | Siam J. Sci. Comput. Vol. 23, No. 3, pp. 707-740. |
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331 | |
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332 | The implemented formula is given in equation (3.15) on page 714 |
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333 | |
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334 | Conserved quantities w, uh, are stored as elements 0 and 1 |
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335 | in the numerical vectors ql an qr. |
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336 | |
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337 | Bed elevations zl and zr. |
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338 | """ |
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339 | |
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340 | from config import g, epsilon |
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341 | from math import sqrt |
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342 | from Numeric import array |
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343 | |
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344 | #print 'ql',ql |
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345 | #print 'qr', qr |
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346 | |
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347 | #Align momentums with x-axis |
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348 | #q_left = rotate(ql, normal, direction = 1) |
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349 | #q_right = rotate(qr, normal, direction = 1) |
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350 | q_left = ql |
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351 | q_left[1] = q_left[1]*normal |
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352 | q_right = qr |
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353 | q_right[1] = q_right[1]*normal |
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354 | |
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355 | #z = (zl+zr)/2 #Take average of field values |
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356 | z = 0.5*(zl+zr) #Take average of field values |
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357 | |
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358 | h_left = q_left[0] #w=h+z |
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359 | w_left = h_left+z |
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360 | uh_left = q_left[1] |
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361 | |
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362 | if h_left < epsilon: |
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363 | u_left = 0.0 #Could have been negative |
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364 | h_left = 0.0 |
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365 | else: |
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366 | u_left = uh_left/h_left |
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367 | |
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368 | |
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369 | h_right = q_right[0] #w=h+z |
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370 | w_right = h_right+z |
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371 | uh_right = q_right[1] |
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372 | |
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373 | |
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374 | if h_right < epsilon: |
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375 | u_right = 0.0 #Could have been negative |
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376 | h_right = 0.0 |
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377 | else: |
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378 | u_right = uh_right/h_right |
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379 | |
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380 | #vh_left = q_left[2] |
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381 | #vh_right = q_right[2] |
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382 | |
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383 | #print "uright %f ulef %f"%(u_right,u_left) |
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384 | |
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385 | soundspeed_left = sqrt(g*h_left) |
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386 | soundspeed_right = sqrt(g*h_right) |
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387 | |
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388 | #Maximal wave speed |
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389 | s_max = max(u_left+soundspeed_left, u_right+soundspeed_right, 0) |
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390 | |
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391 | #Minimal wave speed |
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392 | s_min = min(u_left-soundspeed_left, u_right-soundspeed_right, 0) |
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393 | |
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394 | #Flux computation |
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395 | |
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396 | #flux_left = array([u_left*h_left, |
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397 | # u_left*uh_left + 0.5*g*h_left**2]) |
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398 | #flux_right = array([u_right*h_right, |
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399 | # u_right*uh_right + 0.5*g*h_right**2]) |
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400 | flux_left = array([u_left*h_left, |
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401 | u_left*uh_left + 0.5*g*h_left*h_left]) |
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402 | flux_right = array([u_right*h_right, |
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403 | u_right*uh_right + 0.5*g*h_right*h_right]) |
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404 | |
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405 | denom = s_max-s_min |
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406 | if denom == 0.0: |
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407 | edgeflux = array([0.0, 0.0]) |
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408 | max_speed = 0.0 |
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409 | else: |
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410 | edgeflux = (s_max*flux_left - s_min*flux_right)/denom |
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411 | edgeflux += s_max*s_min*(q_right-q_left)/denom |
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412 | |
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413 | edgeflux[1] = edgeflux[1]*normal |
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414 | |
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415 | max_speed = max(abs(s_max), abs(s_min)) |
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416 | |
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417 | return edgeflux, max_speed |
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418 | |
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419 | |
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420 | def flux_function_split(normal, ql, qr, zl, zr): |
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421 | from config import g, epsilon |
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422 | from math import sqrt |
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423 | from Numeric import array |
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424 | |
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425 | #print 'ql',ql |
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426 | |
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427 | #Align momentums with x-axis |
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428 | #q_left = rotate(ql, normal, direction = 1) |
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429 | #q_right = rotate(qr, normal, direction = 1) |
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430 | q_left = ql |
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431 | q_left[1] = q_left[1]*normal |
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432 | q_right = qr |
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433 | q_right[1] = q_right[1]*normal |
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434 | |
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435 | #z = (zl+zr)/2 #Take average of field values |
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436 | z = 0.5*(zl+zr) #Take average of field values |
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437 | |
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438 | w_left = q_left[0] #w=h+z |
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439 | h_left = w_left-z |
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440 | uh_left = q_left[1] |
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441 | |
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442 | if h_left < epsilon: |
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443 | u_left = 0.0 #Could have been negative |
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444 | h_left = 0.0 |
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445 | else: |
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446 | u_left = uh_left/h_left |
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447 | |
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448 | |
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449 | w_right = q_right[0] #w=h+z |
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450 | h_right = w_right-z |
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451 | uh_right = q_right[1] |
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452 | |
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453 | |
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454 | if h_right < epsilon: |
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455 | u_right = 0.0 #Could have been negative |
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456 | h_right = 0.0 |
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457 | else: |
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458 | u_right = uh_right/h_right |
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459 | |
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460 | #vh_left = q_left[2] |
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461 | #vh_right = q_right[2] |
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462 | |
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463 | #soundspeed_left = sqrt(g*h_left) |
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464 | #soundspeed_right = sqrt(g*h_right) |
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465 | |
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466 | #Maximal wave speed |
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467 | #s_max = max(u_left+soundspeed_left, u_right+soundspeed_right, 0) |
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468 | s_max = max(u_left, u_right, 0) |
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469 | |
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470 | #Minimal wave speed |
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471 | #s_min = min(u_left-soundspeed_left, u_right-soundspeed_right, 0) |
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472 | s_min = min(u_left, u_right, 0) |
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473 | |
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474 | #Flux computation |
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475 | |
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476 | #flux_left = array([u_left*h_left, |
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477 | # u_left*uh_left + 0.5*g*h_left*h_left]) |
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478 | #flux_right = array([u_right*h_right, |
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479 | # u_right*uh_right + 0.5*g*h_right*h_right]) |
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480 | flux_left = array([u_left*h_left, |
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481 | u_left*uh_left])# + 0.5*g*h_left*h_left]) |
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482 | flux_right = array([u_right*h_right, |
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483 | u_right*uh_right])# + 0.5*g*h_right*h_right]) |
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484 | |
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485 | denom = s_max-s_min |
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486 | if denom == 0.0: |
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487 | edgeflux = array([0.0, 0.0]) |
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488 | max_speed = 0.0 |
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489 | else: |
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490 | edgeflux = (s_max*flux_left - s_min*flux_right)/denom |
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491 | edgeflux += s_max*s_min*(q_right-q_left)/denom |
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492 | |
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493 | edgeflux[1] = edgeflux[1]*normal |
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494 | |
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495 | max_speed = max(abs(s_max), abs(s_min)) |
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496 | |
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497 | return edgeflux, max_speed |
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498 | |
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499 | def compute_timestep(domain): |
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500 | import sys |
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501 | from Numeric import zeros, Float |
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502 | |
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503 | N = domain.number_of_elements |
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504 | |
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505 | #Shortcuts |
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506 | Stage = domain.quantities['stage'] |
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507 | Xmom = domain.quantities['xmomentum'] |
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508 | Bed = domain.quantities['elevation'] |
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509 | |
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510 | stage = Stage.vertex_values |
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511 | xmom = Xmom.vertex_values |
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512 | bed = Bed.vertex_values |
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513 | |
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514 | stage_bdry = Stage.boundary_values |
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515 | xmom_bdry = Xmom.boundary_values |
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516 | |
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517 | flux = zeros(2, Float) #Work array for summing up fluxes |
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518 | ql = zeros(2, Float) |
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519 | qr = zeros(2, Float) |
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520 | |
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521 | #Loop |
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522 | timestep = float(sys.maxint) |
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523 | enter = True |
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524 | for k in range(N): |
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525 | |
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526 | flux[:] = 0. #Reset work array |
---|
527 | for i in range(2): |
---|
528 | #Quantities inside volume facing neighbour i |
---|
529 | ql = [stage[k, i], xmom[k, i]] |
---|
530 | zl = bed[k, i] |
---|
531 | |
---|
532 | #Quantities at neighbour on nearest face |
---|
533 | n = domain.neighbours[k,i] |
---|
534 | if n < 0: |
---|
535 | m = -n-1 #Convert negative flag to index |
---|
536 | qr[0] = stage_bdry[m] |
---|
537 | qr[1] = xmom_bdry[m] |
---|
538 | zr = zl #Extend bed elevation to boundary |
---|
539 | else: |
---|
540 | #m = domain.neighbour_edges[k,i] |
---|
541 | m = domain.neighbour_vertices[k,i] |
---|
542 | qr[0] = stage[n, m] |
---|
543 | qr[1] = xmom[n, m] |
---|
544 | zr = bed[n, m] |
---|
545 | |
---|
546 | |
---|
547 | #Outward pointing normal vector |
---|
548 | normal = domain.normals[k, i] |
---|
549 | |
---|
550 | if domain.split == False: |
---|
551 | edgeflux, max_speed = flux_function(normal, ql, qr, zl, zr) |
---|
552 | elif domain.split == True: |
---|
553 | edgeflux, max_speed = flux_function_split(normal, ql, qr, zl, zr) |
---|
554 | #Update optimal_timestep |
---|
555 | try: |
---|
556 | timestep = min(timestep, domain.cfl*0.5*domain.areas[k]/max_speed) |
---|
557 | except ZeroDivisionError: |
---|
558 | pass |
---|
559 | |
---|
560 | domain.timestep = timestep |
---|
561 | |
---|
562 | def compute_fluxes(domain): |
---|
563 | """Compute all fluxes and the timestep suitable for all volumes |
---|
564 | in domain. |
---|
565 | |
---|
566 | Compute total flux for each conserved quantity using "flux_function" |
---|
567 | |
---|
568 | Fluxes across each edge are scaled by edgelengths and summed up |
---|
569 | Resulting flux is then scaled by area and stored in |
---|
570 | explicit_update for each of the three conserved quantities |
---|
571 | stage, xmomentum and ymomentum |
---|
572 | |
---|
573 | The maximal allowable speed computed by the flux_function for each volume |
---|
574 | is converted to a timestep that must not be exceeded. The minimum of |
---|
575 | those is computed as the next overall timestep. |
---|
576 | |
---|
577 | Post conditions: |
---|
578 | domain.explicit_update is reset to computed flux values |
---|
579 | domain.timestep is set to the largest step satisfying all volumes. |
---|
580 | """ |
---|
581 | |
---|
582 | #print "in compute_fluxes" |
---|
583 | |
---|
584 | import sys |
---|
585 | from Numeric import zeros, Float |
---|
586 | |
---|
587 | N = domain.number_of_elements |
---|
588 | |
---|
589 | #Shortcuts |
---|
590 | #Stage = domain.quantities['stage'] |
---|
591 | Height = domain.quantities['height'] |
---|
592 | Xmom = domain.quantities['xmomentum'] |
---|
593 | # Ymom = domain.quantities['ymomentum'] |
---|
594 | Bed = domain.quantities['elevation'] |
---|
595 | |
---|
596 | #Arrays |
---|
597 | #stage = Stage.edge_values |
---|
598 | #xmom = Xmom.edge_values |
---|
599 | # ymom = Ymom.edge_values |
---|
600 | #bed = Bed.edge_values |
---|
601 | |
---|
602 | #stage = Stage.vertex_values |
---|
603 | height = Height.vertex_values |
---|
604 | xmom = Xmom.vertex_values |
---|
605 | bed = Bed.vertex_values |
---|
606 | |
---|
607 | #print 'stage edge values', stage |
---|
608 | #print 'xmom edge values', xmom |
---|
609 | #print 'bed values', bed |
---|
610 | |
---|
611 | #stage_bdry = Stage.boundary_values |
---|
612 | height_bdry = Height.boundary_values |
---|
613 | xmom_bdry = Xmom.boundary_values |
---|
614 | #print 'stage_bdry',stage_bdry |
---|
615 | #print 'xmom_bdry', xmom_bdry |
---|
616 | # ymom_bdry = Ymom.boundary_values |
---|
617 | |
---|
618 | # flux = zeros(3, Float) #Work array for summing up fluxes |
---|
619 | flux = zeros(2, Float) #Work array for summing up fluxes |
---|
620 | ql = zeros(2, Float) |
---|
621 | qr = zeros(2, Float) |
---|
622 | |
---|
623 | #Loop |
---|
624 | timestep = float(sys.maxint) |
---|
625 | enter = True |
---|
626 | for k in range(N): |
---|
627 | |
---|
628 | flux[:] = 0. #Reset work array |
---|
629 | #for i in range(3): |
---|
630 | for i in range(2): |
---|
631 | #Quantities inside volume facing neighbour i |
---|
632 | #ql = [stage[k, i], xmom[k, i]] |
---|
633 | ql = [height[k, i], xmom[k, i]] |
---|
634 | zl = bed[k, i] |
---|
635 | #print "cell",k,"left state",ql[0] |
---|
636 | |
---|
637 | #Quantities at neighbour on nearest face |
---|
638 | n = domain.neighbours[k,i] |
---|
639 | if n < 0: |
---|
640 | m = -n-1 #Convert negative flag to index |
---|
641 | #qr[0] = stage_bdry[m] |
---|
642 | qr[0] = height_bdry[m] |
---|
643 | qr[1] = xmom_bdry[m] |
---|
644 | zr = zl #Extend bed elevation to boundary |
---|
645 | else: |
---|
646 | #m = domain.neighbour_edges[k,i] |
---|
647 | m = domain.neighbour_vertices[k,i] |
---|
648 | #qr = [stage[n, m], xmom[n, m], ymom[n, m]] |
---|
649 | #qr[0] = stage[n, m] |
---|
650 | qr[0] = height[n, m] |
---|
651 | qr[1] = xmom[n, m] |
---|
652 | zr = bed[n, m] |
---|
653 | #print "cell",k,"right state",qr[0] |
---|
654 | |
---|
655 | |
---|
656 | #Outward pointing normal vector |
---|
657 | normal = domain.normals[k, i] |
---|
658 | |
---|
659 | #Flux computation using provided function |
---|
660 | #edgeflux, max_speed = flux_function(normal, ql, qr, zl, zr) |
---|
661 | #print 'ql',ql |
---|
662 | #print 'qr',qr |
---|
663 | |
---|
664 | |
---|
665 | if domain.split == False: |
---|
666 | edgeflux, max_speed = flux_function(normal, ql, qr, zl, zr) |
---|
667 | #print edgeflux |
---|
668 | elif domain.split == True: |
---|
669 | edgeflux, max_speed = flux_function_split(normal, ql, qr, zl, zr) |
---|
670 | #print 'edgeflux', edgeflux |
---|
671 | |
---|
672 | # THIS IS THE LINE TO DEAL WITH LEFT AND RIGHT FLUXES |
---|
673 | # flux = edgefluxleft - edgefluxright |
---|
674 | flux -= edgeflux #* domain.edgelengths[k,i] |
---|
675 | |
---|
676 | #Update optimal_timestep |
---|
677 | try: |
---|
678 | #timestep = min(timestep, 0.5*domain.radii[k]/max_speed) |
---|
679 | timestep = min(timestep, domain.cfl*0.5*domain.areas[k]/max_speed) |
---|
680 | #print "cell %d wet length %f"%(k,domain.areas[k]) |
---|
681 | #print "timestep %f max speed %f hl %f uhl %f hr %f uhr %f" %(timestep,max_speed,ql[0],ql[1],qr[0],qr[1]) |
---|
682 | except ZeroDivisionError: |
---|
683 | pass |
---|
684 | |
---|
685 | #Normalise by area and store for when all conserved |
---|
686 | #quantities get updated |
---|
687 | flux /= domain.areas[k] |
---|
688 | |
---|
689 | #try: |
---|
690 | # #if flux[0] > 1.0e-6: unecessary because only min is taken |
---|
691 | # if Height.centroid_values[k] > 1.0e-3: |
---|
692 | # timestep = min(timestep, domain.cfl*0.5*Height.centroid_values[k]*domain.areas[k]/abs(flux[0])) |
---|
693 | #except ZeroDivisionError: |
---|
694 | # pass |
---|
695 | |
---|
696 | |
---|
697 | |
---|
698 | #Stage.explicit_update[k] = flux[0] |
---|
699 | Height.explicit_update[k] = flux[0] |
---|
700 | Xmom.explicit_update[k] = flux[1] |
---|
701 | #Ymom.explicit_update[k] = flux[2] |
---|
702 | |
---|
703 | |
---|
704 | domain.timestep = timestep |
---|
705 | #print "flux" |
---|
706 | #print Height.explicit_update |
---|
707 | |
---|
708 | #print "integral %f"%domain.quantities['height'].get_integral() |
---|
709 | |
---|
710 | #################################### |
---|
711 | |
---|
712 | # Module functions for gradient limiting (distribute_to_vertices_and_edges) |
---|
713 | |
---|
714 | def distribute_to_vertices_and_edges(domain): |
---|
715 | """Distribution from centroids to vertices specific to the |
---|
716 | shallow water wave |
---|
717 | equation. |
---|
718 | |
---|
719 | It will ensure that h (w-z) is always non-negative even in the |
---|
720 | presence of steep bed-slopes by taking a weighted average between shallow |
---|
721 | and deep cases. |
---|
722 | |
---|
723 | In addition, all conserved quantities get distributed as per either a |
---|
724 | constant (order==1) or a piecewise linear function (order==2). |
---|
725 | |
---|
726 | FIXME: more explanation about removal of artificial variability etc |
---|
727 | |
---|
728 | Precondition: |
---|
729 | All quantities defined at centroids and bed elevation defined at |
---|
730 | vertices. |
---|
731 | |
---|
732 | Postcondition |
---|
733 | Conserved quantities defined at vertices |
---|
734 | |
---|
735 | """ |
---|
736 | |
---|
737 | #print "in distribute to vertices and edges" |
---|
738 | #print "integral %f"%domain.quantities['height'].get_integral() |
---|
739 | |
---|
740 | #from config import optimised_gradient_limiter |
---|
741 | |
---|
742 | #Remove very thin layers of water |
---|
743 | #protect_against_infinitesimal_and_negative_heights(domain) |
---|
744 | |
---|
745 | #classify_wet_dry_cells(domain) |
---|
746 | #import copy |
---|
747 | #print domain.wet_nodes |
---|
748 | #StageQ = copy.copy(domain.quantities['stage'].centroid_values) |
---|
749 | #adjust_partially_submerged_cells(domain) |
---|
750 | #StageQ2 = domain.quantities['stage'].centroid_values |
---|
751 | #print StageQ-StageQ2 |
---|
752 | |
---|
753 | #Extrapolate all conserved quantities |
---|
754 | #if optimised_gradient_limiter: |
---|
755 | # #MH090605 if second order, |
---|
756 | # #perform the extrapolation and limiting on |
---|
757 | # #all of the conserved quantities |
---|
758 | |
---|
759 | # if (domain.order == 1): |
---|
760 | # for name in domain.conserved_quantities: |
---|
761 | # Q = domain.quantities[name] |
---|
762 | # Q.extrapolate_first_order() |
---|
763 | # elif domain.order == 2: |
---|
764 | # domain.extrapolate_second_order_sw() |
---|
765 | # else: |
---|
766 | # raise 'Unknown order' |
---|
767 | #else: |
---|
768 | #old code: |
---|
769 | |
---|
770 | for name in domain.conserved_quantities: |
---|
771 | Q = domain.quantities[name] |
---|
772 | if domain.order == 1: |
---|
773 | Q.extrapolate_first_order() |
---|
774 | elif domain.order == 2: |
---|
775 | #print "add extrapolate second order to shallow water" |
---|
776 | if (name != 'height'):#& (name != "xmomentum"): |
---|
777 | Q.extrapolate_second_order() |
---|
778 | #Q.limit() |
---|
779 | else: |
---|
780 | raise 'Unknown order' |
---|
781 | |
---|
782 | #Take bed elevation into account when water heights are small |
---|
783 | #balance_deep_and_shallow(domain) |
---|
784 | protect_dry_beds(domain) |
---|
785 | |
---|
786 | #Compute edge values by interpolation |
---|
787 | #for name in domain.conserved_quantities: |
---|
788 | # Q = domain.quantities[name] |
---|
789 | # Q.interpolate_from_vertices_to_edges() |
---|
790 | |
---|
791 | #print domain.quantities['stage'].centroid_values |
---|
792 | |
---|
793 | def protect_dry_beds(domain): |
---|
794 | #print "in protect dry beds" |
---|
795 | #print "integral %f"%domain.quantities['height'].get_integral() |
---|
796 | |
---|
797 | N = domain.number_of_elements |
---|
798 | wc = domain.quantities['stage'].centroid_values |
---|
799 | zc = domain.quantities['elevation'].centroid_values |
---|
800 | hc = domain.quantities['height'].centroid_values |
---|
801 | wv = domain.quantities['stage'].vertex_values |
---|
802 | zv = domain.quantities['elevation'].vertex_values |
---|
803 | xmomv = domain.quantities['xmomentum'].vertex_values |
---|
804 | xmomc = domain.quantities['xmomentum'].centroid_values |
---|
805 | min_centroid_height = 1e-3 |
---|
806 | |
---|
807 | for k in range(N): |
---|
808 | if hc[k] < domain.minimum_allowed_height: |
---|
809 | if hc[k] < domain.epsilon: |
---|
810 | wc[k] = zc[k] |
---|
811 | wv[k,0] = zv[k,0] |
---|
812 | wv[k,1] = zv[k,1] |
---|
813 | xmomc[k] = 0.0 |
---|
814 | xmomv[k,:] = 0.0 |
---|
815 | |
---|
816 | |
---|
817 | def set_initial_conserved_quanitites(domain): |
---|
818 | from util import calculate_new_wet_area, calculate_wetted_area |
---|
819 | from Numeric import allclose |
---|
820 | |
---|
821 | N = domain.number_of_elements |
---|
822 | wv = domain.quantities['stage'].vertex_values |
---|
823 | zv = domain.quantities['elevation'].vertex_values |
---|
824 | xv = domain.vertices |
---|
825 | zc = domain.quantities['elevation'].centroid_values |
---|
826 | wc = domain.quantities['stage'].centroid_values |
---|
827 | hc = domain.quantities['height'].centroid_values |
---|
828 | xmomc = domain.quantities['xmomentum'].centroid_values |
---|
829 | |
---|
830 | #A1 = domain.quantities['stage'].get_integral() |
---|
831 | for k in range(N): |
---|
832 | if hc[k] < 0.0: |
---|
833 | print "ERROR!!!!!!!!!!!!!!!!!!" |
---|
834 | #if (domain.wet_nodes[k,0] == 0) | (domain.wet_nodes[k,1] == 0): |
---|
835 | if (wv[k,0] < zv[k,0]) | (wv[k,1] < zv[k,1]): |
---|
836 | # cell is dry or wetted |
---|
837 | #print "cell %d is wetted or dry"%k |
---|
838 | w1 = wv[k,0] |
---|
839 | w2 = wv[k,1] |
---|
840 | z1 = zv[k,0] |
---|
841 | z2 = zv[k,1] |
---|
842 | x1 = xv[k,0] |
---|
843 | x2 = xv[k,1] |
---|
844 | #print w1,w2 |
---|
845 | A = calculate_wetted_area(x1,x2,z1,z2,w1,w2) |
---|
846 | L = x2-x1 |
---|
847 | w_centroid, wet_len = calculate_new_wet_area(x1,x2,z1,z2,A) |
---|
848 | #print "cell",k,"stage",w1,w2 |
---|
849 | #print A |
---|
850 | if A > 0.0: |
---|
851 | wc[k] = w_centroid # surface is flat in wetted bed |
---|
852 | #wv[k,0] = w1 |
---|
853 | #wv[k,1] = w2 |
---|
854 | domain.wet_nodes[k,0] = 2 # stops limiter from limiting these cells |
---|
855 | domain.wet_nodes[k,1] = 2 |
---|
856 | hc[k] = A/L |
---|
857 | # print "hc %f" %hc[k] |
---|
858 | #xmomc[k] = 0.0 |
---|
859 | #print "cell",k,"stage",wc[k],hc[k],wet_len |
---|
860 | #if wet_len > 0.0: |
---|
861 | #domain.areas[k] = wet_len |
---|
862 | else: |
---|
863 | #print "cell %d is not wetted but dry"%k |
---|
864 | wc[k] = 0.5*(w1+w2) # bed is completely dry |
---|
865 | wv[k,0] = zv[k,0] |
---|
866 | wv[k,1] = zv[k,1] |
---|
867 | domain.wet_nodes[k,0] = 0 |
---|
868 | domain.wet_nodes[k,1] = 0 |
---|
869 | hc[k] = 0.0 |
---|
870 | else: |
---|
871 | #print "cell",k,"is wet" |
---|
872 | hc[k] = wc[k]-zc[k] |
---|
873 | |
---|
874 | #A2 = domain.quantities['stage'].get_integral() |
---|
875 | #assert allclose(A1,A2) |
---|
876 | print "Must set initial conditions for momentum as well in set_initial_conserved_quanitites and adjust" |
---|
877 | #print hc |
---|
878 | |
---|
879 | |
---|
880 | def adjust_partially_submerged_cells(domain): |
---|
881 | #normal# |
---|
882 | #print "in adjust wetted_cells" |
---|
883 | #print "integral %f"%domain.quantities['height'].get_integral() |
---|
884 | |
---|
885 | from util import calculate_new_wet_area, analytic_cannal |
---|
886 | min_centroid_height = 1.0e-3 |
---|
887 | N = domain.number_of_elements |
---|
888 | wv = domain.quantities['stage'].vertex_values |
---|
889 | zv = domain.quantities['elevation'].vertex_values |
---|
890 | xv = domain.vertices |
---|
891 | xc = domain.centroids |
---|
892 | zc = domain.quantities['elevation'].centroid_values |
---|
893 | wc = domain.quantities['stage'].centroid_values |
---|
894 | hc = domain.quantities['height'].centroid_values |
---|
895 | xmomc = domain.quantities['xmomentum'].centroid_values |
---|
896 | xmomv = domain.quantities['xmomentum'].vertex_values |
---|
897 | |
---|
898 | domain.wet_nodes[:,:] = 0.0 |
---|
899 | |
---|
900 | #print hc |
---|
901 | |
---|
902 | for k in range(N): |
---|
903 | domain.areas[k] = xv[k,1]-xv[k,0] |
---|
904 | |
---|
905 | if hc[k] <= domain.epsilon: |
---|
906 | if hc[k] < 0.0: |
---|
907 | if hc[k+1] > domain.epsilon: |
---|
908 | hc[k+1] += hc[k] |
---|
909 | else: #hc[k-1] > domain.epsilon: |
---|
910 | hc[k-1] += hc[k] |
---|
911 | |
---|
912 | hc[k] = 0.0 # if this not here get negative heights means timesteping wrong |
---|
913 | wc[k] = zc[k] |
---|
914 | xmomc[k] = 0.0 |
---|
915 | xmomv[k,0] = 0.0 |
---|
916 | xmomv[k,1] = 0.0 |
---|
917 | else: #hc[k] > domain.epsilon: #min_centroid_height: |
---|
918 | z1 = zv[k,0] |
---|
919 | z2 = zv[k,1] |
---|
920 | x1 = xv[k,0] |
---|
921 | x2 = xv[k,1] |
---|
922 | L = x2-x1 |
---|
923 | A = hc[k]*L |
---|
924 | if A > 0.0: |
---|
925 | w_centroid, wet_len = calculate_new_wet_area(x1,x2,z1,z2,A) |
---|
926 | if (w_centroid > max(z1,z2)): |
---|
927 | wc[k] = w_centroid |
---|
928 | #xmomc[k] = 0.5*(uh1+uh2) |
---|
929 | #xmomv[k,0] = uh1 |
---|
930 | #xmomv[k,1] = uh2 # sets xmom to be analytic everwhere |
---|
931 | |
---|
932 | elif (w_centroid > min(z1,z2)): |
---|
933 | wc[k] = w_centroid # surface is flat in wetted bed |
---|
934 | #wv[k,0] = w1 |
---|
935 | #wv[k,1] = w2 # this is done by slope limiter |
---|
936 | domain.wet_nodes[k,0] = 2 # stops limiter from limiting these cells |
---|
937 | domain.wet_nodes[k,1] = 2 |
---|
938 | #print "cell",k, hc[k], A,L, w1,w2 |
---|
939 | wcrap,uhc = analytic_cannal(xc[k],domain.time+domain.timestep) |
---|
940 | w1,uh1 = analytic_cannal(x1,domain.time+domain.timestep) |
---|
941 | w2,uh2 = analytic_cannal(x2,domain.time+domain.timestep) |
---|
942 | |
---|
943 | if (w_centroid > z1): |
---|
944 | #w1,uh1 = analytic_cannal(xc[k-1],domain.time+domain.timestep) |
---|
945 | #xmomv[k,0] = uh1 |
---|
946 | xmomv[k,0] = 0.0 |
---|
947 | xmomv[k,1] = 0.0 |
---|
948 | #xmomc[k] = uh1 |
---|
949 | xmomc[k] = 0.0 |
---|
950 | |
---|
951 | else: |
---|
952 | #w2,uh2 = analytic_cannal(xc[k+1],domain.time+domain.timestep) |
---|
953 | xmomv[k,0] = 0.0 |
---|
954 | xmomv[k,1] = 0.0 |
---|
955 | #xmomv[k,1] = uh2 |
---|
956 | #xmomc[k] = uh2 |
---|
957 | xmomc[k] = 0.0 |
---|
958 | else: |
---|
959 | wc[k] = zc[k] # bed is completely dry |
---|
960 | domain.wet_nodes[k,0] = 0 |
---|
961 | domain.wet_nodes[k,1] = 0 |
---|
962 | hc[k] = 0.0 |
---|
963 | xmomc[k] = 0.0 |
---|
964 | xmomv[k,0] = 0.0 |
---|
965 | xmomv[k,1] = 0.0 |
---|
966 | #if wet_len > 0.0: |
---|
967 | #domain.areas[k] = wet_len |
---|
968 | # if wet_len is 0 then bed is flat and area = x2-x1 (as default) |
---|
969 | else: |
---|
970 | wc[k] = zc[k] # bed is completely dry |
---|
971 | domain.wet_nodes[k,0] = 0 |
---|
972 | domain.wet_nodes[k,1] = 0 |
---|
973 | hc[k] = 0.0 |
---|
974 | xmomc[k] = 0.0 |
---|
975 | xmomv[k,0] = 0.0 |
---|
976 | xmomv[k,1] = 0.0 |
---|
977 | |
---|
978 | #for k in range(N): |
---|
979 | # |
---|
980 | # wcrap,uhc = analytic_cannal(xc[int(N/2)],domain.time+domain.timestep) |
---|
981 | # if (k > 1) & (k<N-2): |
---|
982 | # if (wc[k-2] < max(zv[k-2,0],zv[k-2,1])) & (wc[k-2] > min(zv[k-2,0],zv[k-2,1])) & (hc[k+1] < domain.epsilon): |
---|
983 | # #print "TRUE" |
---|
984 | # xmomc[k] = uhc |
---|
985 | # if (wc[k+2] < max(zv[k+2,0],zv[k+2,1])) & (wc[k+2] > min(zv[k+2,0],zv[k+2,1])) & (hc[k-1] < domain.epsilon): |
---|
986 | # #print "FALSE" |
---|
987 | # xmomc[k] = uhc |
---|
988 | |
---|
989 | |
---|
990 | #print "integral %f"%domain.quantities['height'].get_integral() |
---|
991 | #print domain.quantities['height'].centroid_values |
---|
992 | |
---|
993 | def adjust_partially_submerged_cells_analytic(domain): |
---|
994 | #analytic# |
---|
995 | |
---|
996 | #print "in adjust wetted_cells" |
---|
997 | from util import calculate_new_wet_area_analytic |
---|
998 | min_centroid_height = 1.0e-3 |
---|
999 | N = domain.number_of_elements |
---|
1000 | wv = domain.quantities['stage'].vertex_values |
---|
1001 | zv = domain.quantities['elevation'].vertex_values |
---|
1002 | xv = domain.vertices |
---|
1003 | zc = domain.quantities['elevation'].centroid_values |
---|
1004 | wc = domain.quantities['stage'].centroid_values |
---|
1005 | hc = domain.quantities['height'].centroid_values |
---|
1006 | xmomc = domain.quantities['xmomentum'].centroid_values |
---|
1007 | xmomv = domain.quantities['xmomentum'].vertex_values |
---|
1008 | |
---|
1009 | domain.wet_nodes[:,:] = 0.0 |
---|
1010 | |
---|
1011 | #print hc |
---|
1012 | |
---|
1013 | for k in range(N): |
---|
1014 | domain.areas[k] = xv[k,1]-xv[k,0] |
---|
1015 | if hc[k] > domain.epsilon:#min_centroid_height: |
---|
1016 | z1 = zv[k,0] |
---|
1017 | z2 = zv[k,1] |
---|
1018 | x1 = xv[k,0] |
---|
1019 | x2 = xv[k,1] |
---|
1020 | L = x2-x1 |
---|
1021 | A = hc[k]*L |
---|
1022 | if A > 0.0: |
---|
1023 | #print "cell %d is wetted" %k |
---|
1024 | #print "time: %f -- is 1 sec behind real time in adjust. i.e. time has not been updated"%domain.time |
---|
1025 | w1,w2, wet_len,uh1,uh2 = calculate_new_wet_area_analytic(x1,x2,z1,z2,A,domain.time+1.0) |
---|
1026 | xmomc[k] = 0.5*(uh1+uh2) |
---|
1027 | xmomv[k,0] = uh1 |
---|
1028 | xmomv[k,1] = uh2 |
---|
1029 | if (w1 > z1) & (w2 > z2): |
---|
1030 | #wc[k] = (w1+w2)*0.5 |
---|
1031 | #wv[k,0] = w1 |
---|
1032 | #wv[k,1] = w2 |
---|
1033 | wc[k] = zc[k]+hc[k] |
---|
1034 | xmomv[k,0] = uh1 |
---|
1035 | xmomv[k,1] = uh2 |
---|
1036 | xmomc[k] = 0.5*(uh1+uh2) |
---|
1037 | #print w1,w2 |
---|
1038 | elif (w1 > min(z1,z2)) | (w2 > min(z1,z2)): |
---|
1039 | wc[k] = 0.5*(w1+w2) |
---|
1040 | wv[k,0] = w1 |
---|
1041 | wv[k,1] = w2 |
---|
1042 | #print "cell %d w1 %f w2 %f" %(k,w1,w2) |
---|
1043 | # stops limiter from limiting these cells |
---|
1044 | domain.wet_nodes[k,0] = 2 |
---|
1045 | domain.wet_nodes[k,1] = 2 |
---|
1046 | if (w1 > z1): |
---|
1047 | xmomv[k,0] = uh1 |
---|
1048 | xmomv[k,1] = 0.0 |
---|
1049 | else: |
---|
1050 | xmomv[k,0] = 0.0 |
---|
1051 | xmomv[k,1] = uh2 |
---|
1052 | else: |
---|
1053 | wc[k] = zc[k] # bed is completely dry |
---|
1054 | domain.wet_nodes[k,0] = 0 |
---|
1055 | domain.wet_nodes[k,1] = 0 |
---|
1056 | hc[k] = 0.0 |
---|
1057 | xmomc[k] = 0.0 |
---|
1058 | if wet_len > 0.0: |
---|
1059 | domain.areas[k] = wet_len |
---|
1060 | #print w1,w2 |
---|
1061 | #print "cell %d wet length %f"%(k,wet_len) |
---|
1062 | # if wet_len is 0 then bed is flat and area = x2-x1 (as default) |
---|
1063 | else: |
---|
1064 | wc[k] = zc[k] # bed is completely dry |
---|
1065 | domain.wet_nodes[k,0] = 0 |
---|
1066 | domain.wet_nodes[k,1] = 0 |
---|
1067 | hc[k] = 0.0 |
---|
1068 | #xmomc[k] = 0.0 |
---|
1069 | else: |
---|
1070 | wc[k] = zc[k] |
---|
1071 | xmomc[k] = 0.0 |
---|
1072 | |
---|
1073 | |
---|
1074 | def distribute_stage_to_height(domain): |
---|
1075 | |
---|
1076 | #print "in distribute stage to height" |
---|
1077 | #print "integral %f"%domain.quantities['height'].get_integral() |
---|
1078 | |
---|
1079 | #print "hv1",domain.quantities['height'].vertex_values |
---|
1080 | #print "hc1",domain.quantities['height'].centroid_values |
---|
1081 | |
---|
1082 | min_centroid_height = 1.0e-3 |
---|
1083 | N = domain.number_of_elements |
---|
1084 | wv = domain.quantities['stage'].vertex_values |
---|
1085 | zv = domain.quantities['elevation'].vertex_values |
---|
1086 | hv = domain.quantities['height'].vertex_values |
---|
1087 | hc = domain.quantities['height'].centroid_values |
---|
1088 | for k in range(N): |
---|
1089 | for i in range(2): |
---|
1090 | if hc[k] > domain.epsilon: |
---|
1091 | hv[k,i] = wv[k,i]-zv[k,i] |
---|
1092 | elif hc[k] < 0: |
---|
1093 | print "ERROR" |
---|
1094 | else: |
---|
1095 | hv[k,i] = 0.0 |
---|
1096 | |
---|
1097 | #print "hv2",domain.quantities['height'].vertex_values |
---|
1098 | #print "hc2",domain.quantities['height'].centroid_values |
---|
1099 | #print "integral %f"%domain.quantities['height'].get_integral() |
---|
1100 | |
---|
1101 | def protect_against_infinitesimal_and_negative_heights(domain): |
---|
1102 | """Protect against infinitesimal heights and associated high velocities |
---|
1103 | """ |
---|
1104 | |
---|
1105 | #Shortcuts |
---|
1106 | wc = domain.quantities['stage'].centroid_values |
---|
1107 | zc = domain.quantities['elevation'].centroid_values |
---|
1108 | xmomc = domain.quantities['xmomentum'].centroid_values |
---|
1109 | # ymomc = domain.quantities['ymomentum'].centroid_values |
---|
1110 | hc = wc - zc #Water depths at centroids |
---|
1111 | |
---|
1112 | zv = domain.quantities['elevation'].vertex_values |
---|
1113 | wv = domain.quantities['stage'].vertex_values |
---|
1114 | #remove the above two lines and corresponding code below |
---|
1115 | |
---|
1116 | #Update |
---|
1117 | for k in range(domain.number_of_elements): |
---|
1118 | |
---|
1119 | if hc[k] < domain.minimum_allowed_height: |
---|
1120 | #Control stage |
---|
1121 | if hc[k] < domain.epsilon: |
---|
1122 | wc[k] = zc[k] # Contain 'lost mass' error |
---|
1123 | wv[k,0] = zv[k,0] |
---|
1124 | wv[k,1] = zv[k,1] |
---|
1125 | |
---|
1126 | #Control momentum |
---|
1127 | #xmomc[k] = ymomc[k] = 0.0 |
---|
1128 | xmomc[k] = 0.0 |
---|
1129 | |
---|
1130 | def h_limiter(domain): |
---|
1131 | """Limit slopes for each volume to eliminate artificial variance |
---|
1132 | introduced by e.g. second order extrapolator |
---|
1133 | |
---|
1134 | limit on h = w-z |
---|
1135 | |
---|
1136 | This limiter depends on two quantities (w,z) so it resides within |
---|
1137 | this module rather than within quantity.py |
---|
1138 | """ |
---|
1139 | |
---|
1140 | from Numeric import zeros, Float |
---|
1141 | |
---|
1142 | N = domain.number_of_elements |
---|
1143 | beta_h = domain.beta_h |
---|
1144 | |
---|
1145 | #Shortcuts |
---|
1146 | wc = domain.quantities['stage'].centroid_values |
---|
1147 | zc = domain.quantities['elevation'].centroid_values |
---|
1148 | hc = wc - zc |
---|
1149 | |
---|
1150 | wv = domain.quantities['stage'].vertex_values |
---|
1151 | zv = domain.quantities['elevation'].vertex_values |
---|
1152 | hv = wv-zv |
---|
1153 | |
---|
1154 | hvbar = zeros(hv.shape, Float) #h-limited values |
---|
1155 | |
---|
1156 | #Find min and max of this and neighbour's centroid values |
---|
1157 | hmax = zeros(hc.shape, Float) |
---|
1158 | hmin = zeros(hc.shape, Float) |
---|
1159 | |
---|
1160 | for k in range(N): |
---|
1161 | hmax[k] = hmin[k] = hc[k] |
---|
1162 | #for i in range(3): |
---|
1163 | for i in range(2): |
---|
1164 | n = domain.neighbours[k,i] |
---|
1165 | if n >= 0: |
---|
1166 | hn = hc[n] #Neighbour's centroid value |
---|
1167 | |
---|
1168 | hmin[k] = min(hmin[k], hn) |
---|
1169 | hmax[k] = max(hmax[k], hn) |
---|
1170 | |
---|
1171 | |
---|
1172 | #Diffences between centroids and maxima/minima |
---|
1173 | dhmax = hmax - hc |
---|
1174 | dhmin = hmin - hc |
---|
1175 | |
---|
1176 | #Deltas between vertex and centroid values |
---|
1177 | dh = zeros(hv.shape, Float) |
---|
1178 | #for i in range(3): |
---|
1179 | for i in range(2): |
---|
1180 | dh[:,i] = hv[:,i] - hc |
---|
1181 | |
---|
1182 | #Phi limiter |
---|
1183 | for k in range(N): |
---|
1184 | |
---|
1185 | #Find the gradient limiter (phi) across vertices |
---|
1186 | phi = 1.0 |
---|
1187 | #for i in range(3): |
---|
1188 | for i in range(2): |
---|
1189 | r = 1.0 |
---|
1190 | if (dh[k,i] > 0): r = dhmax[k]/dh[k,i] |
---|
1191 | if (dh[k,i] < 0): r = dhmin[k]/dh[k,i] |
---|
1192 | |
---|
1193 | phi = min( min(r*beta_h, 1), phi ) |
---|
1194 | |
---|
1195 | #Then update using phi limiter |
---|
1196 | #for i in range(3): |
---|
1197 | for i in range(2): |
---|
1198 | hvbar[k,i] = hc[k] + phi*dh[k,i] |
---|
1199 | |
---|
1200 | return hvbar |
---|
1201 | |
---|
1202 | def balance_deep_and_shallow(domain): |
---|
1203 | """Compute linear combination between stage as computed by |
---|
1204 | gradient-limiters limiting using w, and stage computed by |
---|
1205 | gradient-limiters limiting using h (h-limiter). |
---|
1206 | The former takes precedence when heights are large compared to the |
---|
1207 | bed slope while the latter takes precedence when heights are |
---|
1208 | relatively small. Anything in between is computed as a balanced |
---|
1209 | linear combination in order to avoid numerical disturbances which |
---|
1210 | would otherwise appear as a result of hard switching between |
---|
1211 | modes. |
---|
1212 | |
---|
1213 | The h-limiter is always applied irrespective of the order. |
---|
1214 | """ |
---|
1215 | |
---|
1216 | #Shortcuts |
---|
1217 | wc = domain.quantities['stage'].centroid_values |
---|
1218 | zc = domain.quantities['elevation'].centroid_values |
---|
1219 | hc = wc - zc |
---|
1220 | |
---|
1221 | wv = domain.quantities['stage'].vertex_values |
---|
1222 | zv = domain.quantities['elevation'].vertex_values |
---|
1223 | hv = wv-zv |
---|
1224 | |
---|
1225 | #Limit h |
---|
1226 | hvbar = h_limiter(domain) |
---|
1227 | |
---|
1228 | for k in range(domain.number_of_elements): |
---|
1229 | #Compute maximal variation in bed elevation |
---|
1230 | # This quantitiy is |
---|
1231 | # dz = max_i abs(z_i - z_c) |
---|
1232 | # and it is independent of dimension |
---|
1233 | # In the 1d case zc = (z0+z1)/2 |
---|
1234 | # In the 2d case zc = (z0+z1+z2)/3 |
---|
1235 | |
---|
1236 | dz = max(abs(zv[k,0]-zc[k]), |
---|
1237 | abs(zv[k,1]-zc[k]))#, |
---|
1238 | # abs(zv[k,2]-zc[k])) |
---|
1239 | |
---|
1240 | |
---|
1241 | hmin = min( hv[k,:] ) |
---|
1242 | |
---|
1243 | #Create alpha in [0,1], where alpha==0 means using the h-limited |
---|
1244 | #stage and alpha==1 means using the w-limited stage as |
---|
1245 | #computed by the gradient limiter (both 1st or 2nd order) |
---|
1246 | |
---|
1247 | #If hmin > dz/2 then alpha = 1 and the bed will have no effect |
---|
1248 | #If hmin < 0 then alpha = 0 reverting to constant height above bed. |
---|
1249 | |
---|
1250 | if dz > 0.0: |
---|
1251 | alpha = max( min( 2*hmin/dz, 1.0), 0.0 ) |
---|
1252 | else: |
---|
1253 | #Flat bed |
---|
1254 | alpha = 1.0 |
---|
1255 | |
---|
1256 | alpha = 0.0 |
---|
1257 | #Let |
---|
1258 | # |
---|
1259 | # wvi be the w-limited stage (wvi = zvi + hvi) |
---|
1260 | # wvi- be the h-limited state (wvi- = zvi + hvi-) |
---|
1261 | # |
---|
1262 | # |
---|
1263 | #where i=0,1,2 denotes the vertex ids |
---|
1264 | # |
---|
1265 | #Weighted balance between w-limited and h-limited stage is |
---|
1266 | # |
---|
1267 | # wvi := (1-alpha)*(zvi+hvi-) + alpha*(zvi+hvi) |
---|
1268 | # |
---|
1269 | #It follows that the updated wvi is |
---|
1270 | # wvi := zvi + (1-alpha)*hvi- + alpha*hvi |
---|
1271 | # |
---|
1272 | # Momentum is balanced between constant and limited |
---|
1273 | |
---|
1274 | |
---|
1275 | #for i in range(3): |
---|
1276 | # wv[k,i] = zv[k,i] + hvbar[k,i] |
---|
1277 | |
---|
1278 | #return |
---|
1279 | |
---|
1280 | if alpha < 1: |
---|
1281 | |
---|
1282 | #for i in range(3): |
---|
1283 | for i in range(2): |
---|
1284 | wv[k,i] = zv[k,i] + (1.0-alpha)*hvbar[k,i] + alpha*hv[k,i] |
---|
1285 | |
---|
1286 | #Momentums at centroids |
---|
1287 | xmomc = domain.quantities['xmomentum'].centroid_values |
---|
1288 | # ymomc = domain.quantities['ymomentum'].centroid_values |
---|
1289 | |
---|
1290 | #Momentums at vertices |
---|
1291 | xmomv = domain.quantities['xmomentum'].vertex_values |
---|
1292 | # ymomv = domain.quantities['ymomentum'].vertex_values |
---|
1293 | |
---|
1294 | # Update momentum as a linear combination of |
---|
1295 | # xmomc and ymomc (shallow) and momentum |
---|
1296 | # from extrapolator xmomv and ymomv (deep). |
---|
1297 | xmomv[k,:] = (1.0-alpha)*xmomc[k] + alpha*xmomv[k,:] |
---|
1298 | # ymomv[k,:] = (1-alpha)*ymomc[k] + alpha*ymomv[k,:] |
---|
1299 | |
---|
1300 | |
---|
1301 | ############################################### |
---|
1302 | #Boundaries - specific to the shallow water wave equation |
---|
1303 | class Reflective_boundary(Boundary): |
---|
1304 | """Reflective boundary returns same conserved quantities as |
---|
1305 | those present in its neighbour volume but reflected. |
---|
1306 | |
---|
1307 | This class is specific to the shallow water equation as it |
---|
1308 | works with the momentum quantities assumed to be the second |
---|
1309 | and third conserved quantities. |
---|
1310 | """ |
---|
1311 | |
---|
1312 | def __init__(self, domain = None): |
---|
1313 | Boundary.__init__(self) |
---|
1314 | |
---|
1315 | if domain is None: |
---|
1316 | msg = 'Domain must be specified for reflective boundary' |
---|
1317 | raise msg |
---|
1318 | |
---|
1319 | #Handy shorthands |
---|
1320 | #self.stage = domain.quantities['stage'].edge_values |
---|
1321 | #self.xmom = domain.quantities['xmomentum'].edge_values |
---|
1322 | #self.ymom = domain.quantities['ymomentum'].edge_values |
---|
1323 | #self.normals = domain.normals |
---|
1324 | self.stage = domain.quantities['stage'].vertex_values |
---|
1325 | self.xmom = domain.quantities['xmomentum'].vertex_values |
---|
1326 | self.height = domain.quantities['height'].vertex_values |
---|
1327 | |
---|
1328 | from Numeric import zeros, Float |
---|
1329 | self.conserved_quantities = zeros(3, Float) |
---|
1330 | #self.conserved_quantities = zeros(2, Float) |
---|
1331 | |
---|
1332 | def __repr__(self): |
---|
1333 | return 'Reflective_boundary' |
---|
1334 | |
---|
1335 | |
---|
1336 | def evaluate(self, vol_id, edge_id): |
---|
1337 | """Reflective boundaries reverses the outward momentum |
---|
1338 | of the volume they serve. |
---|
1339 | """ |
---|
1340 | |
---|
1341 | q = self.conserved_quantities |
---|
1342 | q[0] = self.stage[vol_id, edge_id] |
---|
1343 | q[1] = self.xmom[vol_id, edge_id] |
---|
1344 | #q[2] = self.ymom[vol_id, edge_id] |
---|
1345 | q[2] = self.height[vol_id,edge_id] |
---|
1346 | #normal = self.normals[vol_id, 2*edge_id:2*edge_id+2] |
---|
1347 | #normal = self.normals[vol_id, 2*edge_id:2*edge_id+1] |
---|
1348 | |
---|
1349 | |
---|
1350 | #r = rotate(q, normal, direction = 1) |
---|
1351 | #r[1] = -r[1] |
---|
1352 | #q = rotate(r, normal, direction = -1) |
---|
1353 | r = q |
---|
1354 | r[1] = -q[1] |
---|
1355 | q = r |
---|
1356 | #For start interval there is no outward momentum so do not need to |
---|
1357 | #reverse direction in this case |
---|
1358 | |
---|
1359 | return q |
---|
1360 | |
---|
1361 | class Dirichlet_boundary(Boundary): |
---|
1362 | """Dirichlet boundary returns constant values for the |
---|
1363 | conserved quantities |
---|
1364 | """ |
---|
1365 | |
---|
1366 | |
---|
1367 | def __init__(self, conserved_quantities=None): |
---|
1368 | Boundary.__init__(self) |
---|
1369 | |
---|
1370 | if conserved_quantities is None: |
---|
1371 | msg = 'Must specify one value for each conserved quantity' |
---|
1372 | raise msg |
---|
1373 | |
---|
1374 | from Numeric import array, Float |
---|
1375 | self.conserved_quantities=array(conserved_quantities).astype(Float) |
---|
1376 | |
---|
1377 | def __repr__(self): |
---|
1378 | return 'Dirichlet boundary (%s)' %self.conserved_quantities |
---|
1379 | |
---|
1380 | def evaluate(self, vol_id=None, edge_id=None): |
---|
1381 | return self.conserved_quantities |
---|
1382 | |
---|
1383 | |
---|
1384 | ######################### |
---|
1385 | #Standard forcing terms: |
---|
1386 | # |
---|
1387 | def gravity(domain): |
---|
1388 | """Apply gravitational pull in the presence of bed slope |
---|
1389 | """ |
---|
1390 | #print "in gravity" |
---|
1391 | #print "integral %f"%domain.quantities['height'].get_integral() |
---|
1392 | from util import gradient |
---|
1393 | from Numeric import zeros, Float, array, sum |
---|
1394 | |
---|
1395 | xmom = domain.quantities['xmomentum'].explicit_update |
---|
1396 | stage = domain.quantities['stage'].explicit_update |
---|
1397 | # ymom = domain.quantities['ymomentum'].explicit_update |
---|
1398 | |
---|
1399 | Stage = domain.quantities['stage'] |
---|
1400 | Elevation = domain.quantities['elevation'] |
---|
1401 | Height = domain.quantities['height'] |
---|
1402 | #h = Stage.edge_values - Elevation.edge_values |
---|
1403 | h = Stage.vertex_values - Elevation.vertex_values |
---|
1404 | hc = Height.centroid_values |
---|
1405 | h = Height.vertex_values |
---|
1406 | b = Elevation.vertex_values |
---|
1407 | w = Stage.vertex_values |
---|
1408 | |
---|
1409 | x = domain.get_vertex_coordinates() |
---|
1410 | g = domain.g |
---|
1411 | |
---|
1412 | for k in range(domain.number_of_elements): |
---|
1413 | # avg_h = sum( h[k,:] )/3 |
---|
1414 | #avg_h = sum( h[k,:] )/2 |
---|
1415 | avg_h = hc[k] |
---|
1416 | |
---|
1417 | #Compute bed slope |
---|
1418 | #x0, y0, x1, y1, x2, y2 = x[k,:] |
---|
1419 | x0, x1 = x[k,:] |
---|
1420 | #z0, z1, z2 = v[k,:] |
---|
1421 | b0, b1 = b[k,:] |
---|
1422 | |
---|
1423 | w0, w1 = w[k,:] |
---|
1424 | wx = gradient(x0, x1, w0, w1) |
---|
1425 | |
---|
1426 | #zx, zy = gradient(x0, y0, x1, y1, x2, y2, z0, z1, z2) |
---|
1427 | bx = gradient(x0, x1, b0, b1) |
---|
1428 | |
---|
1429 | #Update momentum (explicit update is reset to source values) |
---|
1430 | if domain.split == False: |
---|
1431 | xmom[k] += -g*bx*avg_h |
---|
1432 | #xmom[k] = -g*bx*avg_h |
---|
1433 | #stage[k] = 0.0 |
---|
1434 | elif domain.split == True: |
---|
1435 | xmom[k] += -g*wx*avg_h |
---|
1436 | #xmom[k] = -g*wx*avg_h |
---|
1437 | #ymom[k] += -g*zy*avg_h |
---|
1438 | |
---|
1439 | def manning_friction(domain): |
---|
1440 | """Apply (Manning) friction to water momentum |
---|
1441 | """ |
---|
1442 | |
---|
1443 | from math import sqrt |
---|
1444 | |
---|
1445 | w = domain.quantities['stage'].centroid_values |
---|
1446 | z = domain.quantities['elevation'].centroid_values |
---|
1447 | h = w-z |
---|
1448 | |
---|
1449 | uh = domain.quantities['xmomentum'].centroid_values |
---|
1450 | #vh = domain.quantities['ymomentum'].centroid_values |
---|
1451 | eta = domain.quantities['friction'].centroid_values |
---|
1452 | |
---|
1453 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
---|
1454 | #ymom_update = domain.quantities['ymomentum'].semi_implicit_update |
---|
1455 | |
---|
1456 | N = domain.number_of_elements |
---|
1457 | eps = domain.minimum_allowed_height |
---|
1458 | g = domain.g |
---|
1459 | |
---|
1460 | for k in range(N): |
---|
1461 | if eta[k] >= eps: |
---|
1462 | if h[k] >= eps: |
---|
1463 | #S = -g * eta[k]**2 * sqrt((uh[k]**2 + vh[k]**2)) |
---|
1464 | S = -g * eta[k]**2 * uh[k] |
---|
1465 | S /= h[k]**(7.0/3) |
---|
1466 | |
---|
1467 | #Update momentum |
---|
1468 | xmom_update[k] += S*uh[k] |
---|
1469 | #ymom_update[k] += S*vh[k] |
---|
1470 | |
---|
1471 | def linear_friction(domain): |
---|
1472 | """Apply linear friction to water momentum |
---|
1473 | |
---|
1474 | Assumes quantity: 'linear_friction' to be present |
---|
1475 | """ |
---|
1476 | |
---|
1477 | from math import sqrt |
---|
1478 | |
---|
1479 | w = domain.quantities['stage'].centroid_values |
---|
1480 | z = domain.quantities['elevation'].centroid_values |
---|
1481 | h = w-z |
---|
1482 | |
---|
1483 | uh = domain.quantities['xmomentum'].centroid_values |
---|
1484 | # vh = domain.quantities['ymomentum'].centroid_values |
---|
1485 | tau = domain.quantities['linear_friction'].centroid_values |
---|
1486 | |
---|
1487 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
---|
1488 | # ymom_update = domain.quantities['ymomentum'].semi_implicit_update |
---|
1489 | |
---|
1490 | N = domain.number_of_elements |
---|
1491 | eps = domain.minimum_allowed_height |
---|
1492 | g = domain.g #Not necessary? Why was this added? |
---|
1493 | |
---|
1494 | for k in range(N): |
---|
1495 | if tau[k] >= eps: |
---|
1496 | if h[k] >= eps: |
---|
1497 | S = -tau[k]/h[k] |
---|
1498 | |
---|
1499 | #Update momentum |
---|
1500 | xmom_update[k] += S*uh[k] |
---|
1501 | # ymom_update[k] += S*vh[k] |
---|
1502 | |
---|
1503 | |
---|
1504 | |
---|
1505 | def check_forcefield(f): |
---|
1506 | """Check that f is either |
---|
1507 | 1: a callable object f(t,x,y), where x and y are vectors |
---|
1508 | and that it returns an array or a list of same length |
---|
1509 | as x and y |
---|
1510 | 2: a scalar |
---|
1511 | """ |
---|
1512 | |
---|
1513 | from Numeric import ones, Float, array |
---|
1514 | |
---|
1515 | |
---|
1516 | if callable(f): |
---|
1517 | #N = 3 |
---|
1518 | N = 2 |
---|
1519 | #x = ones(3, Float) |
---|
1520 | #y = ones(3, Float) |
---|
1521 | x = ones(2, Float) |
---|
1522 | #y = ones(2, Float) |
---|
1523 | |
---|
1524 | try: |
---|
1525 | #q = f(1.0, x=x, y=y) |
---|
1526 | q = f(1.0, x=x) |
---|
1527 | except Exception, e: |
---|
1528 | msg = 'Function %s could not be executed:\n%s' %(f, e) |
---|
1529 | #FIXME: Reconsider this semantics |
---|
1530 | raise msg |
---|
1531 | |
---|
1532 | try: |
---|
1533 | q = array(q).astype(Float) |
---|
1534 | except: |
---|
1535 | msg = 'Return value from vector function %s could ' %f |
---|
1536 | msg += 'not be converted into a Numeric array of floats.\n' |
---|
1537 | msg += 'Specified function should return either list or array.' |
---|
1538 | raise msg |
---|
1539 | |
---|
1540 | #Is this really what we want? |
---|
1541 | msg = 'Return vector from function %s ' %f |
---|
1542 | msg += 'must have same lenght as input vectors' |
---|
1543 | assert len(q) == N, msg |
---|
1544 | |
---|
1545 | else: |
---|
1546 | try: |
---|
1547 | f = float(f) |
---|
1548 | except: |
---|
1549 | msg = 'Force field %s must be either a scalar' %f |
---|
1550 | msg += ' or a vector function' |
---|
1551 | raise msg |
---|
1552 | return f |
---|
1553 | |
---|
1554 | class Wind_stress: |
---|
1555 | """Apply wind stress to water momentum in terms of |
---|
1556 | wind speed [m/s] and wind direction [degrees] |
---|
1557 | """ |
---|
1558 | |
---|
1559 | def __init__(self, *args, **kwargs): |
---|
1560 | """Initialise windfield from wind speed s [m/s] |
---|
1561 | and wind direction phi [degrees] |
---|
1562 | |
---|
1563 | Inputs v and phi can be either scalars or Python functions, e.g. |
---|
1564 | |
---|
1565 | W = Wind_stress(10, 178) |
---|
1566 | |
---|
1567 | #FIXME - 'normal' degrees are assumed for now, i.e. the |
---|
1568 | vector (1,0) has zero degrees. |
---|
1569 | We may need to convert from 'compass' degrees later on and also |
---|
1570 | map from True north to grid north. |
---|
1571 | |
---|
1572 | Arguments can also be Python functions of t,x,y as in |
---|
1573 | |
---|
1574 | def speed(t,x,y): |
---|
1575 | ... |
---|
1576 | return s |
---|
1577 | |
---|
1578 | def angle(t,x,y): |
---|
1579 | ... |
---|
1580 | return phi |
---|
1581 | |
---|
1582 | where x and y are vectors. |
---|
1583 | |
---|
1584 | and then pass the functions in |
---|
1585 | |
---|
1586 | W = Wind_stress(speed, angle) |
---|
1587 | |
---|
1588 | The instantiated object W can be appended to the list of |
---|
1589 | forcing_terms as in |
---|
1590 | |
---|
1591 | Alternatively, one vector valued function for (speed, angle) |
---|
1592 | can be applied, providing both quantities simultaneously. |
---|
1593 | As in |
---|
1594 | W = Wind_stress(F), where returns (speed, angle) for each t. |
---|
1595 | |
---|
1596 | domain.forcing_terms.append(W) |
---|
1597 | """ |
---|
1598 | |
---|
1599 | from config import rho_a, rho_w, eta_w |
---|
1600 | from Numeric import array, Float |
---|
1601 | |
---|
1602 | if len(args) == 2: |
---|
1603 | s = args[0] |
---|
1604 | phi = args[1] |
---|
1605 | elif len(args) == 1: |
---|
1606 | #Assume vector function returning (s, phi)(t,x,y) |
---|
1607 | vector_function = args[0] |
---|
1608 | #s = lambda t,x,y: vector_function(t,x=x,y=y)[0] |
---|
1609 | #phi = lambda t,x,y: vector_function(t,x=x,y=y)[1] |
---|
1610 | s = lambda t,x: vector_function(t,x=x)[0] |
---|
1611 | phi = lambda t,x: vector_function(t,x=x)[1] |
---|
1612 | else: |
---|
1613 | #Assume info is in 2 keyword arguments |
---|
1614 | |
---|
1615 | if len(kwargs) == 2: |
---|
1616 | s = kwargs['s'] |
---|
1617 | phi = kwargs['phi'] |
---|
1618 | else: |
---|
1619 | raise 'Assumes two keyword arguments: s=..., phi=....' |
---|
1620 | |
---|
1621 | print 'phi', phi |
---|
1622 | self.speed = check_forcefield(s) |
---|
1623 | self.phi = check_forcefield(phi) |
---|
1624 | |
---|
1625 | self.const = eta_w*rho_a/rho_w |
---|
1626 | |
---|
1627 | |
---|
1628 | def __call__(self, domain): |
---|
1629 | """Evaluate windfield based on values found in domain |
---|
1630 | """ |
---|
1631 | |
---|
1632 | from math import pi, cos, sin, sqrt |
---|
1633 | from Numeric import Float, ones, ArrayType |
---|
1634 | |
---|
1635 | xmom_update = domain.quantities['xmomentum'].explicit_update |
---|
1636 | #ymom_update = domain.quantities['ymomentum'].explicit_update |
---|
1637 | |
---|
1638 | N = domain.number_of_elements |
---|
1639 | t = domain.time |
---|
1640 | |
---|
1641 | if callable(self.speed): |
---|
1642 | xc = domain.get_centroid_coordinates() |
---|
1643 | #s_vec = self.speed(t, xc[:,0], xc[:,1]) |
---|
1644 | s_vec = self.speed(t, xc) |
---|
1645 | else: |
---|
1646 | #Assume s is a scalar |
---|
1647 | |
---|
1648 | try: |
---|
1649 | s_vec = self.speed * ones(N, Float) |
---|
1650 | except: |
---|
1651 | msg = 'Speed must be either callable or a scalar: %s' %self.s |
---|
1652 | raise msg |
---|
1653 | |
---|
1654 | |
---|
1655 | if callable(self.phi): |
---|
1656 | xc = domain.get_centroid_coordinates() |
---|
1657 | #phi_vec = self.phi(t, xc[:,0], xc[:,1]) |
---|
1658 | phi_vec = self.phi(t, xc) |
---|
1659 | else: |
---|
1660 | #Assume phi is a scalar |
---|
1661 | |
---|
1662 | try: |
---|
1663 | phi_vec = self.phi * ones(N, Float) |
---|
1664 | except: |
---|
1665 | msg = 'Angle must be either callable or a scalar: %s' %self.phi |
---|
1666 | raise msg |
---|
1667 | |
---|
1668 | #assign_windfield_values(xmom_update, ymom_update, |
---|
1669 | # s_vec, phi_vec, self.const) |
---|
1670 | assign_windfield_values(xmom_update, s_vec, phi_vec, self.const) |
---|
1671 | |
---|
1672 | |
---|
1673 | #def assign_windfield_values(xmom_update, ymom_update, |
---|
1674 | # s_vec, phi_vec, const): |
---|
1675 | def assign_windfield_values(xmom_update, s_vec, phi_vec, const): |
---|
1676 | """Python version of assigning wind field to update vectors. |
---|
1677 | A c version also exists (for speed) |
---|
1678 | """ |
---|
1679 | from math import pi, cos, sin, sqrt |
---|
1680 | |
---|
1681 | N = len(s_vec) |
---|
1682 | for k in range(N): |
---|
1683 | s = s_vec[k] |
---|
1684 | phi = phi_vec[k] |
---|
1685 | |
---|
1686 | #Convert to radians |
---|
1687 | phi = phi*pi/180 |
---|
1688 | |
---|
1689 | #Compute velocity vector (u, v) |
---|
1690 | u = s*cos(phi) |
---|
1691 | v = s*sin(phi) |
---|
1692 | |
---|
1693 | #Compute wind stress |
---|
1694 | #S = const * sqrt(u**2 + v**2) |
---|
1695 | S = const * u |
---|
1696 | xmom_update[k] += S*u |
---|
1697 | #ymom_update[k] += S*v |
---|