1 | """Class Domain - |
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2 | 1D interval domains for finite-volume computations of |
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3 | the shallow water wave equation. |
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4 | |
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5 | This module contains a specialisation of class Domain from module domain.py |
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6 | consisting of methods specific to the Shallow Water Wave Equation |
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7 | |
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8 | |
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9 | U_t + E_x = S |
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10 | |
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11 | where |
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12 | |
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13 | U = [w, uh] |
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14 | E = [uh, u^2h + gh^2/2] |
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15 | S represents source terms forcing the system |
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16 | (e.g. gravity, friction, wind stress, ...) |
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17 | |
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18 | and _t, _x, _y denote the derivative with respect to t, x and y respectiely. |
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19 | |
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20 | The quantities are |
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21 | |
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22 | symbol variable name explanation |
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23 | x x horizontal distance from origin [m] |
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24 | z elevation elevation of bed on which flow is modelled [m] |
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25 | h height water height above z [m] |
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26 | w stage absolute water level, w = z+h [m] |
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27 | u speed in the x direction [m/s] |
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28 | uh xmomentum momentum in the x direction [m^2/s] |
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29 | |
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30 | eta mannings friction coefficient [to appear] |
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31 | nu wind stress coefficient [to appear] |
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32 | |
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33 | The conserved quantities are w, uh |
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34 | |
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35 | For details see e.g. |
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36 | Christopher Zoppou and Stephen Roberts, |
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37 | Catastrophic Collapse of Water Supply Reservoirs in Urban Areas, |
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38 | Journal of Hydraulic Engineering, vol. 127, No. 7 July 1999 |
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39 | |
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40 | |
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41 | John Jakeman, Ole Nielsen, Stephen Roberts, Duncan Gray, Christopher Zoppou |
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42 | Geoscience Australia, 2006 |
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43 | """ |
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44 | |
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45 | |
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46 | from domain import * |
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47 | Generic_Domain = Domain #Rename |
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48 | |
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49 | #Shallow water domain |
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50 | class Domain(Generic_Domain): |
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51 | |
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52 | def __init__(self, coordinates, boundary = None, tagged_elements = None): |
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53 | |
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54 | conserved_quantities = ['stage', 'xmomentum'] |
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55 | other_quantities = ['elevation', 'friction'] |
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56 | Generic_Domain.__init__(self, |
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57 | coordinates = coordinates, |
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58 | boundary = boundary, |
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59 | conserved_quantities = conserved_quantities, |
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60 | other_quantities = other_quantities, |
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61 | tagged_elements = tagged_elements) |
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62 | |
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63 | from config import minimum_allowed_height, g, h0 |
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64 | self.minimum_allowed_height = minimum_allowed_height |
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65 | self.g = g |
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66 | self.h0 = h0 |
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67 | |
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68 | #forcing terms not included in 1d domain ?WHy? |
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69 | self.forcing_terms.append(gravity) |
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70 | #self.forcing_terms.append(manning_friction) |
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71 | #print "\nI have Removed forcing terms line 64 1dsw" |
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72 | |
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73 | |
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74 | #Stored output |
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75 | self.store = True |
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76 | self.format = 'sww' |
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77 | self.smooth = True |
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78 | |
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79 | #Evolve parametrs |
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80 | self.set_CFL(1.0) |
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81 | |
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82 | #Reduction operation for get_vertex_values |
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83 | from util import mean |
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84 | self.reduction = mean |
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85 | #self.reduction = min #Looks better near steep slopes |
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86 | |
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87 | self.set_quantities_to_be_stored(['stage','xmomentum']) |
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88 | |
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89 | self.__doc__ = 'shallow_water_domain' |
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90 | |
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91 | self.check_integrity() |
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92 | |
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93 | def set_quantities_to_be_stored(self, q): |
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94 | """Specify which quantities will be stored in the sww file. |
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95 | |
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96 | q must be either: |
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97 | - the name of a quantity |
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98 | - a list of quantity names |
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99 | - None |
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100 | |
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101 | In the two first cases, the named quantities will be stored at each |
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102 | yieldstep |
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103 | (This is in addition to the quantities elevation and friction) |
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104 | If q is None, storage will be switched off altogether. |
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105 | """ |
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106 | |
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107 | |
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108 | if q is None: |
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109 | self.quantities_to_be_stored = [] |
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110 | self.store = False |
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111 | return |
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112 | |
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113 | if isinstance(q, basestring): |
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114 | q = [q] # Turn argument into a list |
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115 | |
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116 | #Check correcness |
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117 | for quantity_name in q: |
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118 | msg = 'Quantity %s is not a valid conserved quantity' %quantity_name |
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119 | assert quantity_name in self.conserved_quantities, msg |
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120 | |
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121 | self.quantities_to_be_stored = q |
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122 | |
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123 | |
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124 | def check_integrity(self): |
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125 | |
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126 | #Check that we are solving the shallow water wave equation |
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127 | |
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128 | msg = 'First conserved quantity must be "stage"' |
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129 | assert self.conserved_quantities[0] == 'stage', msg |
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130 | msg = 'Second conserved quantity must be "xmomentum"' |
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131 | assert self.conserved_quantities[1] == 'xmomentum', msg |
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132 | |
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133 | msg = 'First evolved quantity must be "stage"' |
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134 | assert self.evolved_quantities[0] == 'stage', msg |
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135 | msg = 'Second evolved quantity must be "xmomentum"' |
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136 | assert self.evolved_quantities[1] == 'xmomentum', msg |
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137 | |
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138 | Generic_Domain.check_integrity(self) |
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139 | |
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140 | def extrapolate_second_order_sw(self): |
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141 | #Call correct module function |
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142 | #(either from this module or C-extension) |
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143 | extrapolate_second_order_sw(self) |
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144 | |
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145 | def compute_fluxes(self): |
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146 | #Call correct module function |
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147 | #(either from this module or C-extension) |
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148 | compute_fluxes_C_short(self) |
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149 | |
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150 | def compute_timestep(self): |
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151 | #Call correct module function |
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152 | compute_timestep(self) |
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153 | |
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154 | def distribute_to_vertices_and_edges(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 | distribute_to_vertices_and_edges(self) |
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158 | |
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159 | def evolve(self, yieldstep = None, finaltime = None, duration = None, |
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160 | skip_initial_step = False): |
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161 | """Specialisation of basic evolve method from parent class |
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162 | """ |
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163 | |
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164 | #Call check integrity here rather than from user scripts |
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165 | #self.check_integrity() |
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166 | |
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167 | #msg = 'Parameter beta_h must be in the interval [0, 1)' |
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168 | #assert 0 <= self.beta_h < 1.0, msg |
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169 | #msg = 'Parameter beta_w must be in the interval [0, 1)' |
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170 | #assert 0 <= self.beta_w < 1.0, msg |
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171 | |
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172 | |
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173 | #Initial update of vertex and edge values before any storage |
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174 | #and or visualisation |
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175 | |
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176 | self.distribute_to_vertices_and_edges() |
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177 | |
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178 | #Initialise real time viz if requested |
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179 | #if self.visualise is True and self.time == 0.0: |
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180 | # if self.visualiser is None: |
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181 | # self.initialise_visualiser() |
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182 | # |
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183 | # self.visualiser.update_timer() |
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184 | # self.visualiser.setup_all() |
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185 | |
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186 | #Store model data, e.g. for visualisation |
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187 | #if self.store is True and self.time == 0.0: |
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188 | # self.initialise_storage() |
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189 | # #print 'Storing results in ' + self.writer.filename |
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190 | #else: |
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191 | # pass |
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192 | # #print 'Results will not be stored.' |
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193 | # #print 'To store results set domain.store = True' |
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194 | # #FIXME: Diagnostic output should be controlled by |
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195 | # # a 'verbose' flag living in domain (or in a parent class) |
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196 | |
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197 | #Call basic machinery from parent class |
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198 | for t in Generic_Domain.evolve(self, yieldstep, finaltime,duration, |
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199 | skip_initial_step): |
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200 | #Real time viz |
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201 | # if self.visualise is True: |
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202 | # self.visualiser.update_all() |
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203 | # self.visualiser.update_timer() |
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204 | |
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205 | |
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206 | #Store model data, e.g. for subsequent visualisation |
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207 | # if self.store is True: |
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208 | # self.store_timestep(self.quantities_to_be_stored) |
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209 | |
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210 | #FIXME: Could maybe be taken from specified list |
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211 | #of 'store every step' quantities |
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212 | |
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213 | #Pass control on to outer loop for more specific actions |
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214 | yield(t) |
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215 | |
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216 | def initialise_storage(self): |
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217 | """Create and initialise self.writer object for storing data. |
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218 | Also, save x and bed elevation |
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219 | """ |
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220 | |
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221 | import data_manager |
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222 | |
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223 | #Initialise writer |
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224 | self.writer = data_manager.get_dataobject(self, mode = 'w') |
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225 | |
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226 | #Store vertices and connectivity |
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227 | self.writer.store_connectivity() |
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228 | |
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229 | |
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230 | def store_timestep(self, name): |
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231 | """Store named quantity and time. |
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232 | |
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233 | Precondition: |
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234 | self.write has been initialised |
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235 | """ |
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236 | self.writer.store_timestep(name) |
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237 | |
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238 | |
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239 | #=============== End of Shallow Water Domain =============================== |
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240 | |
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241 | #Rotation of momentum vector |
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242 | def rotate(q, normal, direction = 1): |
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243 | """Rotate the momentum component q (q[1], q[2]) |
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244 | from x,y coordinates to coordinates based on normal vector. |
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245 | |
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246 | If direction is negative the rotation is inverted. |
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247 | |
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248 | Input vector is preserved |
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249 | |
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250 | This function is specific to the shallow water wave equation |
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251 | """ |
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252 | |
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253 | from Numeric import zeros, Float |
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254 | |
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255 | assert len(q) == 3,\ |
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256 | 'Vector of conserved quantities must have length 3'\ |
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257 | 'for 2D shallow water equation' |
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258 | |
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259 | try: |
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260 | l = len(normal) |
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261 | except: |
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262 | raise 'Normal vector must be an Numeric array' |
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263 | |
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264 | assert l == 2, 'Normal vector must have 2 components' |
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265 | |
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266 | |
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267 | n1 = normal[0] |
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268 | n2 = normal[1] |
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269 | |
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270 | r = zeros(len(q), Float) #Rotated quantities |
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271 | r[0] = q[0] #First quantity, height, is not rotated |
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272 | |
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273 | if direction == -1: |
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274 | n2 = -n2 |
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275 | |
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276 | |
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277 | r[1] = n1*q[1] + n2*q[2] |
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278 | r[2] = -n2*q[1] + n1*q[2] |
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279 | |
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280 | return r |
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281 | |
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282 | |
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283 | def flux_function(normal, ql, qr, zl, zr): |
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284 | """Compute fluxes between volumes for the shallow water wave equation |
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285 | cast in terms of w = h+z using the 'central scheme' as described in |
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286 | |
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287 | Kurganov, Noelle, Petrova. 'Semidiscrete Central-Upwind Schemes For |
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288 | Hyperbolic Conservation Laws and Hamilton-Jacobi Equations'. |
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289 | Siam J. Sci. Comput. Vol. 23, No. 3, pp. 707-740. |
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290 | |
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291 | The implemented formula is given in equation (3.15) on page 714 |
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292 | |
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293 | Conserved quantities w, uh, are stored as elements 0 and 1 |
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294 | in the numerical vectors ql an qr. |
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295 | |
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296 | Bed elevations zl and zr. |
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297 | """ |
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298 | |
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299 | from config import g, epsilon, h0 |
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300 | from math import sqrt |
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301 | from Numeric import array |
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302 | |
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303 | #print 'ql',ql |
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304 | |
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305 | #Align momentums with x-axis |
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306 | #q_left = rotate(ql, normal, direction = 1) |
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307 | #q_right = rotate(qr, normal, direction = 1) |
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308 | q_left = ql |
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309 | q_left[1] = q_left[1]*normal |
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310 | q_right = qr |
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311 | q_right[1] = q_right[1]*normal |
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312 | |
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313 | #z = (zl+zr)/2 #Take average of field values |
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314 | z = 0.5*(zl+zr) #Take average of field values |
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315 | |
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316 | w_left = q_left[0] #w=h+z |
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317 | h_left = w_left-z |
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318 | uh_left = q_left[1] |
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319 | |
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320 | if h_left < epsilon: |
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321 | u_left = 0.0 #Could have been negative |
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322 | h_left = 0.0 |
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323 | else: |
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324 | u_left = uh_left/(h_left + h0/h_left) |
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325 | |
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326 | |
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327 | uh_left = u_left*h_left |
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328 | |
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329 | |
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330 | w_right = q_right[0] #w=h+z |
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331 | h_right = w_right-z |
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332 | uh_right = q_right[1] |
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333 | |
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334 | if h_right < epsilon: |
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335 | u_right = 0.0 #Could have been negative |
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336 | h_right = 0.0 |
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337 | else: |
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338 | u_right = uh_right/(h_right + h0/h_right) |
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339 | |
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340 | uh_right = u_right*h_right |
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341 | |
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342 | #vh_left = q_left[2] |
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343 | #vh_right = q_right[2] |
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344 | |
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345 | #print h_right |
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346 | #print u_right |
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347 | #print h_left |
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348 | #print u_right |
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349 | |
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350 | soundspeed_left = sqrt(g*h_left) |
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351 | soundspeed_right = sqrt(g*h_right) |
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352 | |
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353 | #Maximal wave speed |
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354 | s_max = max(u_left+soundspeed_left, u_right+soundspeed_right, 0) |
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355 | |
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356 | #Minimal wave speed |
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357 | s_min = min(u_left-soundspeed_left, u_right-soundspeed_right, 0) |
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358 | |
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359 | #Flux computation |
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360 | |
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361 | #flux_left = array([u_left*h_left, |
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362 | # u_left*uh_left + 0.5*g*h_left**2]) |
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363 | #flux_right = array([u_right*h_right, |
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364 | # u_right*uh_right + 0.5*g*h_right**2]) |
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365 | flux_left = array([u_left*h_left, |
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366 | u_left*uh_left + 0.5*g*h_left*h_left]) |
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367 | flux_right = array([u_right*h_right, |
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368 | u_right*uh_right + 0.5*g*h_right*h_right]) |
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369 | |
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370 | denom = s_max-s_min |
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371 | if denom == 0.0: |
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372 | edgeflux = array([0.0, 0.0]) |
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373 | max_speed = 0.0 |
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374 | else: |
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375 | edgeflux = (s_max*flux_left - s_min*flux_right)/denom |
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376 | edgeflux += s_max*s_min*(q_right-q_left)/denom |
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377 | |
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378 | edgeflux[1] = edgeflux[1]*normal |
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379 | |
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380 | max_speed = max(abs(s_max), abs(s_min)) |
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381 | |
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382 | return edgeflux, max_speed |
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383 | |
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384 | |
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385 | |
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386 | |
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387 | def compute_timestep(domain): |
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388 | import sys |
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389 | from Numeric import zeros, Float |
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390 | |
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391 | N = domain.number_of_elements |
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392 | |
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393 | #Shortcuts |
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394 | Stage = domain.quantities['stage'] |
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395 | Xmom = domain.quantities['xmomentum'] |
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396 | Bed = domain.quantities['elevation'] |
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397 | |
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398 | stage = Stage.vertex_values |
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399 | xmom = Xmom.vertex_values |
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400 | bed = Bed.vertex_values |
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401 | |
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402 | stage_bdry = Stage.boundary_values |
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403 | xmom_bdry = Xmom.boundary_values |
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404 | |
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405 | flux = zeros(2, Float) #Work array for summing up fluxes |
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406 | ql = zeros(2, Float) |
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407 | qr = zeros(2, Float) |
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408 | |
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409 | #Loop |
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410 | timestep = float(sys.maxint) |
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411 | enter = True |
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412 | for k in range(N): |
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413 | |
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414 | flux[:] = 0. #Reset work array |
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415 | for i in range(2): |
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416 | #Quantities inside volume facing neighbour i |
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417 | ql = [stage[k, i], xmom[k, i]] |
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418 | zl = bed[k, i] |
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419 | |
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420 | #Quantities at neighbour on nearest face |
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421 | n = domain.neighbours[k,i] |
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422 | if n < 0: |
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423 | m = -n-1 #Convert negative flag to index |
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424 | qr[0] = stage_bdry[m] |
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425 | qr[1] = xmom_bdry[m] |
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426 | zr = zl #Extend bed elevation to boundary |
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427 | else: |
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428 | #m = domain.neighbour_edges[k,i] |
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429 | m = domain.neighbour_vertices[k,i] |
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430 | qr[0] = stage[n, m] |
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431 | qr[1] = xmom[n, m] |
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432 | zr = bed[n, m] |
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433 | |
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434 | |
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435 | #Outward pointing normal vector |
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436 | normal = domain.normals[k, i] |
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437 | |
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438 | edgeflux, max_speed = flux_function(normal, ql, qr, zl, zr) |
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439 | |
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440 | #Update optimal_timestep |
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441 | try: |
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442 | timestep = min(timestep, domain.cfl*0.5*domain.areas[k]/max_speed) |
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443 | except ZeroDivisionError: |
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444 | pass |
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445 | |
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446 | domain.timestep = timestep |
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447 | |
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448 | def compute_fluxes(domain): |
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449 | """Compute all fluxes and the timestep suitable for all volumes |
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450 | in domain. |
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451 | |
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452 | Compute total flux for each conserved quantity using "flux_function" |
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453 | |
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454 | Fluxes across each edge are scaled by edgelengths and summed up |
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455 | Resulting flux is then scaled by area and stored in |
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456 | explicit_update for each of the three conserved quantities |
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457 | stage, xmomentum and ymomentum |
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458 | |
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459 | The maximal allowable speed computed by the flux_function for each volume |
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460 | is converted to a timestep that must not be exceeded. The minimum of |
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461 | those is computed as the next overall timestep. |
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462 | |
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463 | Post conditions: |
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464 | domain.explicit_update is reset to computed flux values |
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465 | domain.timestep is set to the largest step satisfying all volumes. |
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466 | """ |
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467 | |
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468 | import sys |
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469 | from Numeric import zeros, Float |
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470 | |
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471 | N = domain.number_of_elements |
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472 | |
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473 | #Shortcuts |
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474 | Stage = domain.quantities['stage'] |
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475 | Xmom = domain.quantities['xmomentum'] |
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476 | # Ymom = domain.quantities['ymomentum'] |
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477 | Bed = domain.quantities['elevation'] |
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478 | |
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479 | #Arrays |
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480 | #stage = Stage.edge_values |
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481 | #xmom = Xmom.edge_values |
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482 | # ymom = Ymom.edge_values |
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483 | #bed = Bed.edge_values |
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484 | |
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485 | stage = Stage.vertex_values |
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486 | xmom = Xmom.vertex_values |
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487 | bed = Bed.vertex_values |
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488 | |
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489 | #print 'stage edge values', stage |
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490 | #print 'xmom edge values', xmom |
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491 | #print 'bed values', bed |
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492 | |
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493 | stage_bdry = Stage.boundary_values |
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494 | xmom_bdry = Xmom.boundary_values |
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495 | #print 'stage_bdry',stage_bdry |
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496 | #print 'xmom_bdry', xmom_bdry |
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497 | # ymom_bdry = Ymom.boundary_values |
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498 | |
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499 | # flux = zeros(3, Float) #Work array for summing up fluxes |
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500 | flux = zeros(2, Float) #Work array for summing up fluxes |
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501 | ql = zeros(2, Float) |
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502 | qr = zeros(2, Float) |
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503 | |
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504 | #Loop |
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505 | timestep = float(sys.maxint) |
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506 | enter = True |
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507 | for k in range(N): |
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508 | |
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509 | flux[:] = 0. #Reset work array |
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510 | #for i in range(3): |
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511 | for i in range(2): |
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512 | #Quantities inside volume facing neighbour i |
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513 | #ql[0] = stage[k, i] |
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514 | #ql[1] = xmom[k, i] |
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515 | ql = [stage[k, i], xmom[k, i]] |
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516 | zl = bed[k, i] |
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517 | |
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518 | #Quantities at neighbour on nearest face |
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519 | n = domain.neighbours[k,i] |
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520 | if n < 0: |
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521 | m = -n-1 #Convert negative flag to index |
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522 | qr[0] = stage_bdry[m] |
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523 | qr[1] = xmom_bdry[m] |
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524 | zr = zl #Extend bed elevation to boundary |
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525 | else: |
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526 | #m = domain.neighbour_edges[k,i] |
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527 | m = domain.neighbour_vertices[k,i] |
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528 | #qr = [stage[n, m], xmom[n, m], ymom[n, m]] |
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529 | qr[0] = stage[n, m] |
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530 | qr[1] = xmom[n, m] |
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531 | zr = bed[n, m] |
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532 | |
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533 | |
---|
534 | #Outward pointing normal vector |
---|
535 | normal = domain.normals[k, i] |
---|
536 | |
---|
537 | #Flux computation using provided function |
---|
538 | #edgeflux, max_speed = flux_function(normal, ql, qr, zl, zr) |
---|
539 | #print 'ql',ql |
---|
540 | #print 'qr',qr |
---|
541 | |
---|
542 | |
---|
543 | edgeflux, max_speed = flux_function(normal, ql, qr, zl, zr) |
---|
544 | |
---|
545 | #print 'edgeflux', edgeflux |
---|
546 | |
---|
547 | # THIS IS THE LINE TO DEAL WITH LEFT AND RIGHT FLUXES |
---|
548 | # flux = edgefluxleft - edgefluxright |
---|
549 | flux -= edgeflux #* domain.edgelengths[k,i] |
---|
550 | #Update optimal_timestep |
---|
551 | try: |
---|
552 | #timestep = min(timestep, 0.5*domain.radii[k]/max_speed) |
---|
553 | timestep = min(timestep, domain.cfl*0.5*domain.areas[k]/max_speed) |
---|
554 | except ZeroDivisionError: |
---|
555 | pass |
---|
556 | |
---|
557 | #Normalise by area and store for when all conserved |
---|
558 | #quantities get updated |
---|
559 | flux /= domain.areas[k] |
---|
560 | |
---|
561 | Stage.explicit_update[k] = flux[0] |
---|
562 | Xmom.explicit_update[k] = flux[1] |
---|
563 | #Ymom.explicit_update[k] = flux[2] |
---|
564 | #print "flux cell",k,flux[0] |
---|
565 | |
---|
566 | domain.flux_timestep = timestep |
---|
567 | #print domain.quantities['stage'].centroid_values |
---|
568 | |
---|
569 | |
---|
570 | # Compute flux definition |
---|
571 | def compute_fluxes_C_long(domain): |
---|
572 | from Numeric import zeros, Float |
---|
573 | import sys |
---|
574 | |
---|
575 | cfl = domain.get_CFL() |
---|
576 | |
---|
577 | timestep = float(sys.maxint) |
---|
578 | #print 'timestep=',timestep |
---|
579 | #print 'The type of timestep is',type(timestep) |
---|
580 | |
---|
581 | epsilon = domain.epsilon |
---|
582 | #print 'epsilon=',epsilon |
---|
583 | #print 'The type of epsilon is',type(epsilon) |
---|
584 | |
---|
585 | g = domain.g |
---|
586 | #print 'g=',g |
---|
587 | #print 'The type of g is',type(g) |
---|
588 | |
---|
589 | h0 = domain.h0 |
---|
590 | |
---|
591 | neighbours = domain.neighbours |
---|
592 | #print 'neighbours=',neighbours |
---|
593 | #print 'The type of neighbours is',type(neighbours) |
---|
594 | |
---|
595 | neighbour_vertices = domain.neighbour_vertices |
---|
596 | #print 'neighbour_vertices=',neighbour_vertices |
---|
597 | #print 'The type of neighbour_vertices is',type(neighbour_vertices) |
---|
598 | |
---|
599 | normals = domain.normals |
---|
600 | #print 'normals=',normals |
---|
601 | #print 'The type of normals is',type(normals) |
---|
602 | |
---|
603 | areas = domain.areas |
---|
604 | #print 'areas=',areas |
---|
605 | #print 'The type of areas is',type(areas) |
---|
606 | |
---|
607 | stage_edge_values = domain.quantities['stage'].vertex_values |
---|
608 | #print 'stage_edge_values=',stage_edge_values |
---|
609 | #print 'The type of stage_edge_values is',type(stage_edge_values) |
---|
610 | |
---|
611 | xmom_edge_values = domain.quantities['xmomentum'].vertex_values |
---|
612 | #print 'xmom_edge_values=',xmom_edge_values |
---|
613 | #print 'The type of xmom_edge_values is',type(xmom_edge_values) |
---|
614 | |
---|
615 | bed_edge_values = domain.quantities['elevation'].vertex_values |
---|
616 | #print 'bed_edge_values=',bed_edge_values |
---|
617 | #print 'The type of bed_edge_values is',type(bed_edge_values) |
---|
618 | |
---|
619 | stage_boundary_values = domain.quantities['stage'].boundary_values |
---|
620 | #print 'stage_boundary_values=',stage_boundary_values |
---|
621 | #print 'The type of stage_boundary_values is',type(stage_boundary_values) |
---|
622 | |
---|
623 | xmom_boundary_values = domain.quantities['xmomentum'].boundary_values |
---|
624 | #print 'xmom_boundary_values=',xmom_boundary_values |
---|
625 | #print 'The type of xmom_boundary_values is',type(xmom_boundary_values) |
---|
626 | |
---|
627 | stage_explicit_update = domain.quantities['stage'].explicit_update |
---|
628 | #print 'stage_explicit_update=',stage_explicit_update |
---|
629 | #print 'The type of stage_explicit_update is',type(stage_explicit_update) |
---|
630 | |
---|
631 | xmom_explicit_update = domain.quantities['xmomentum'].explicit_update |
---|
632 | #print 'xmom_explicit_update=',xmom_explicit_update |
---|
633 | #print 'The type of xmom_explicit_update is',type(xmom_explicit_update) |
---|
634 | |
---|
635 | number_of_elements = len(stage_edge_values) |
---|
636 | #print 'number_of_elements=',number_of_elements |
---|
637 | #print 'The type of number_of_elements is',type(number_of_elements) |
---|
638 | |
---|
639 | max_speed_array = domain.max_speed_array |
---|
640 | #print 'max_speed_array=',max_speed_array |
---|
641 | #print 'The type of max_speed_array is',type(max_speed_array) |
---|
642 | |
---|
643 | |
---|
644 | from comp_flux_ext import compute_fluxes_ext |
---|
645 | |
---|
646 | domain.flux_timestep = compute_fluxes_ext(cfl, |
---|
647 | timestep, |
---|
648 | epsilon, |
---|
649 | g, |
---|
650 | h0, |
---|
651 | neighbours, |
---|
652 | neighbour_vertices, |
---|
653 | normals, |
---|
654 | areas, |
---|
655 | stage_edge_values, |
---|
656 | xmom_edge_values, |
---|
657 | bed_edge_values, |
---|
658 | stage_boundary_values, |
---|
659 | xmom_boundary_values, |
---|
660 | stage_explicit_update, |
---|
661 | xmom_explicit_update, |
---|
662 | number_of_elements, |
---|
663 | max_speed_array) |
---|
664 | |
---|
665 | |
---|
666 | # Compute flux definition |
---|
667 | def compute_fluxes_C_short(domain): |
---|
668 | from Numeric import zeros, Float |
---|
669 | import sys |
---|
670 | |
---|
671 | |
---|
672 | timestep = float(sys.maxint) |
---|
673 | |
---|
674 | stage = domain.quantities['stage'] |
---|
675 | xmom = domain.quantities['xmomentum'] |
---|
676 | bed = domain.quantities['elevation'] |
---|
677 | |
---|
678 | |
---|
679 | from comp_flux_ext import compute_fluxes_ext_short |
---|
680 | |
---|
681 | domain.flux_timestep = compute_fluxes_ext_short(timestep,domain,stage,xmom,bed) |
---|
682 | |
---|
683 | |
---|
684 | |
---|
685 | #################################### |
---|
686 | |
---|
687 | |
---|
688 | |
---|
689 | |
---|
690 | |
---|
691 | |
---|
692 | # Module functions for gradient limiting (distribute_to_vertices_and_edges) |
---|
693 | |
---|
694 | def distribute_to_vertices_and_edges(domain): |
---|
695 | """Distribution from centroids to vertices specific to the |
---|
696 | shallow water wave |
---|
697 | equation. |
---|
698 | |
---|
699 | It will ensure that h (w-z) is always non-negative even in the |
---|
700 | presence of steep bed-slopes by taking a weighted average between shallow |
---|
701 | and deep cases. |
---|
702 | |
---|
703 | In addition, all conserved quantities get distributed as per either a |
---|
704 | constant (order==1) or a piecewise linear function (order==2). |
---|
705 | |
---|
706 | FIXME: more explanation about removal of artificial variability etc |
---|
707 | |
---|
708 | Precondition: |
---|
709 | All quantities defined at centroids and bed elevation defined at |
---|
710 | vertices. |
---|
711 | |
---|
712 | Postcondition |
---|
713 | Conserved quantities defined at vertices |
---|
714 | |
---|
715 | """ |
---|
716 | |
---|
717 | #from config import optimised_gradient_limiter |
---|
718 | |
---|
719 | #Remove very thin layers of water |
---|
720 | protect_against_infinitesimal_and_negative_heights(domain) |
---|
721 | |
---|
722 | |
---|
723 | #Extrapolate all conserved quantities |
---|
724 | #if optimised_gradient_limiter: |
---|
725 | # #MH090605 if second order, |
---|
726 | # #perform the extrapolation and limiting on |
---|
727 | # #all of the conserved quantities |
---|
728 | |
---|
729 | # if (domain.order == 1): |
---|
730 | # for name in domain.conserved_quantities: |
---|
731 | # Q = domain.quantities[name] |
---|
732 | # Q.extrapolate_first_order() |
---|
733 | # elif domain.order == 2: |
---|
734 | # domain.extrapolate_second_order_sw() |
---|
735 | # else: |
---|
736 | # raise 'Unknown order' |
---|
737 | #else: |
---|
738 | #old code: |
---|
739 | |
---|
740 | for name in domain.conserved_quantities: |
---|
741 | Q = domain.quantities[name] |
---|
742 | if domain.order == 1: |
---|
743 | Q.extrapolate_first_order() |
---|
744 | elif domain.order == 2: |
---|
745 | #print "add extrapolate second order to shallow water" |
---|
746 | #if name != 'height': |
---|
747 | Q.extrapolate_second_order() |
---|
748 | #Q.limit() |
---|
749 | else: |
---|
750 | raise 'Unknown order' |
---|
751 | |
---|
752 | #Take bed elevation into account when water heights are small |
---|
753 | #balance_deep_and_shallow(domain) |
---|
754 | #protect_against_infinitesimal_and_negative_heights(domain) |
---|
755 | |
---|
756 | #Compute edge values by interpolation |
---|
757 | #for name in domain.conserved_quantities: |
---|
758 | # Q = domain.quantities[name] |
---|
759 | # Q.interpolate_from_vertices_to_edges() |
---|
760 | |
---|
761 | def protect_against_infinitesimal_and_negative_heights(domain): |
---|
762 | """Protect against infinitesimal heights and associated high velocities |
---|
763 | """ |
---|
764 | |
---|
765 | #Shortcuts |
---|
766 | wc = domain.quantities['stage'].centroid_values |
---|
767 | zc = domain.quantities['elevation'].centroid_values |
---|
768 | xmomc = domain.quantities['xmomentum'].centroid_values |
---|
769 | # ymomc = domain.quantities['ymomentum'].centroid_values |
---|
770 | hc = wc - zc #Water depths at centroids |
---|
771 | |
---|
772 | zv = domain.quantities['elevation'].vertex_values |
---|
773 | wv = domain.quantities['stage'].vertex_values |
---|
774 | hv = wv-zv |
---|
775 | xmomv = domain.quantities['xmomentum'].vertex_values |
---|
776 | #remove the above two lines and corresponding code below |
---|
777 | |
---|
778 | #Update |
---|
779 | for k in range(domain.number_of_elements): |
---|
780 | |
---|
781 | if hc[k] < domain.minimum_allowed_height: |
---|
782 | #Control stage |
---|
783 | if hc[k] < domain.epsilon: |
---|
784 | wc[k] = zc[k] # Contain 'lost mass' error |
---|
785 | wv[k,0] = zv[k,0] |
---|
786 | wv[k,1] = zv[k,1] |
---|
787 | |
---|
788 | xmomc[k] = 0.0 |
---|
789 | |
---|
790 | #N = domain.number_of_elements |
---|
791 | #if (k == 0) | (k==N-1): |
---|
792 | # wc[k] = zc[k] # Contain 'lost mass' error |
---|
793 | # wv[k,0] = zv[k,0] |
---|
794 | # wv[k,1] = zv[k,1] |
---|
795 | |
---|
796 | def h_limiter(domain): |
---|
797 | """Limit slopes for each volume to eliminate artificial variance |
---|
798 | introduced by e.g. second order extrapolator |
---|
799 | |
---|
800 | limit on h = w-z |
---|
801 | |
---|
802 | This limiter depends on two quantities (w,z) so it resides within |
---|
803 | this module rather than within quantity.py |
---|
804 | """ |
---|
805 | |
---|
806 | from Numeric import zeros, Float |
---|
807 | |
---|
808 | N = domain.number_of_elements |
---|
809 | beta_h = domain.beta_h |
---|
810 | |
---|
811 | #Shortcuts |
---|
812 | wc = domain.quantities['stage'].centroid_values |
---|
813 | zc = domain.quantities['elevation'].centroid_values |
---|
814 | hc = wc - zc |
---|
815 | |
---|
816 | wv = domain.quantities['stage'].vertex_values |
---|
817 | zv = domain.quantities['elevation'].vertex_values |
---|
818 | hv = wv-zv |
---|
819 | |
---|
820 | hvbar = zeros(hv.shape, Float) #h-limited values |
---|
821 | |
---|
822 | #Find min and max of this and neighbour's centroid values |
---|
823 | hmax = zeros(hc.shape, Float) |
---|
824 | hmin = zeros(hc.shape, Float) |
---|
825 | |
---|
826 | for k in range(N): |
---|
827 | hmax[k] = hmin[k] = hc[k] |
---|
828 | #for i in range(3): |
---|
829 | for i in range(2): |
---|
830 | n = domain.neighbours[k,i] |
---|
831 | if n >= 0: |
---|
832 | hn = hc[n] #Neighbour's centroid value |
---|
833 | |
---|
834 | hmin[k] = min(hmin[k], hn) |
---|
835 | hmax[k] = max(hmax[k], hn) |
---|
836 | |
---|
837 | |
---|
838 | #Diffences between centroids and maxima/minima |
---|
839 | dhmax = hmax - hc |
---|
840 | dhmin = hmin - hc |
---|
841 | |
---|
842 | #Deltas between vertex and centroid values |
---|
843 | dh = zeros(hv.shape, Float) |
---|
844 | #for i in range(3): |
---|
845 | for i in range(2): |
---|
846 | dh[:,i] = hv[:,i] - hc |
---|
847 | |
---|
848 | #Phi limiter |
---|
849 | for k in range(N): |
---|
850 | |
---|
851 | #Find the gradient limiter (phi) across vertices |
---|
852 | phi = 1.0 |
---|
853 | #for i in range(3): |
---|
854 | for i in range(2): |
---|
855 | r = 1.0 |
---|
856 | if (dh[k,i] > 0): r = dhmax[k]/dh[k,i] |
---|
857 | if (dh[k,i] < 0): r = dhmin[k]/dh[k,i] |
---|
858 | |
---|
859 | phi = min( min(r*beta_h, 1), phi ) |
---|
860 | |
---|
861 | #Then update using phi limiter |
---|
862 | #for i in range(3): |
---|
863 | for i in range(2): |
---|
864 | hvbar[k,i] = hc[k] + phi*dh[k,i] |
---|
865 | |
---|
866 | return hvbar |
---|
867 | |
---|
868 | def balance_deep_and_shallow(domain): |
---|
869 | """Compute linear combination between stage as computed by |
---|
870 | gradient-limiters limiting using w, and stage computed by |
---|
871 | gradient-limiters limiting using h (h-limiter). |
---|
872 | The former takes precedence when heights are large compared to the |
---|
873 | bed slope while the latter takes precedence when heights are |
---|
874 | relatively small. Anything in between is computed as a balanced |
---|
875 | linear combination in order to avoid numerical disturbances which |
---|
876 | would otherwise appear as a result of hard switching between |
---|
877 | modes. |
---|
878 | |
---|
879 | The h-limiter is always applied irrespective of the order. |
---|
880 | """ |
---|
881 | |
---|
882 | #Shortcuts |
---|
883 | wc = domain.quantities['stage'].centroid_values |
---|
884 | zc = domain.quantities['elevation'].centroid_values |
---|
885 | hc = wc - zc |
---|
886 | |
---|
887 | wv = domain.quantities['stage'].vertex_values |
---|
888 | zv = domain.quantities['elevation'].vertex_values |
---|
889 | hv = wv-zv |
---|
890 | |
---|
891 | #Limit h |
---|
892 | hvbar = h_limiter(domain) |
---|
893 | |
---|
894 | for k in range(domain.number_of_elements): |
---|
895 | #Compute maximal variation in bed elevation |
---|
896 | # This quantitiy is |
---|
897 | # dz = max_i abs(z_i - z_c) |
---|
898 | # and it is independent of dimension |
---|
899 | # In the 1d case zc = (z0+z1)/2 |
---|
900 | # In the 2d case zc = (z0+z1+z2)/3 |
---|
901 | |
---|
902 | dz = max(abs(zv[k,0]-zc[k]), |
---|
903 | abs(zv[k,1]-zc[k]))#, |
---|
904 | # abs(zv[k,2]-zc[k])) |
---|
905 | |
---|
906 | |
---|
907 | hmin = min( hv[k,:] ) |
---|
908 | |
---|
909 | #Create alpha in [0,1], where alpha==0 means using the h-limited |
---|
910 | #stage and alpha==1 means using the w-limited stage as |
---|
911 | #computed by the gradient limiter (both 1st or 2nd order) |
---|
912 | |
---|
913 | #If hmin > dz/2 then alpha = 1 and the bed will have no effect |
---|
914 | #If hmin < 0 then alpha = 0 reverting to constant height above bed. |
---|
915 | |
---|
916 | if dz > 0.0: |
---|
917 | alpha = max( min( 2*hmin/dz, 1.0), 0.0 ) |
---|
918 | else: |
---|
919 | #Flat bed |
---|
920 | alpha = 1.0 |
---|
921 | |
---|
922 | alpha = 0.0 |
---|
923 | #Let |
---|
924 | # |
---|
925 | # wvi be the w-limited stage (wvi = zvi + hvi) |
---|
926 | # wvi- be the h-limited state (wvi- = zvi + hvi-) |
---|
927 | # |
---|
928 | # |
---|
929 | #where i=0,1,2 denotes the vertex ids |
---|
930 | # |
---|
931 | #Weighted balance between w-limited and h-limited stage is |
---|
932 | # |
---|
933 | # wvi := (1-alpha)*(zvi+hvi-) + alpha*(zvi+hvi) |
---|
934 | # |
---|
935 | #It follows that the updated wvi is |
---|
936 | # wvi := zvi + (1-alpha)*hvi- + alpha*hvi |
---|
937 | # |
---|
938 | # Momentum is balanced between constant and limited |
---|
939 | |
---|
940 | |
---|
941 | #for i in range(3): |
---|
942 | # wv[k,i] = zv[k,i] + hvbar[k,i] |
---|
943 | |
---|
944 | #return |
---|
945 | |
---|
946 | if alpha < 1: |
---|
947 | |
---|
948 | #for i in range(3): |
---|
949 | for i in range(2): |
---|
950 | wv[k,i] = zv[k,i] + (1.0-alpha)*hvbar[k,i] + alpha*hv[k,i] |
---|
951 | |
---|
952 | #Momentums at centroids |
---|
953 | xmomc = domain.quantities['xmomentum'].centroid_values |
---|
954 | # ymomc = domain.quantities['ymomentum'].centroid_values |
---|
955 | |
---|
956 | #Momentums at vertices |
---|
957 | xmomv = domain.quantities['xmomentum'].vertex_values |
---|
958 | # ymomv = domain.quantities['ymomentum'].vertex_values |
---|
959 | |
---|
960 | # Update momentum as a linear combination of |
---|
961 | # xmomc and ymomc (shallow) and momentum |
---|
962 | # from extrapolator xmomv and ymomv (deep). |
---|
963 | xmomv[k,:] = (1.0-alpha)*xmomc[k] + alpha*xmomv[k,:] |
---|
964 | # ymomv[k,:] = (1-alpha)*ymomc[k] + alpha*ymomv[k,:] |
---|
965 | |
---|
966 | |
---|
967 | ############################################### |
---|
968 | #Boundaries - specific to the shallow water wave equation |
---|
969 | class Reflective_boundary(Boundary): |
---|
970 | """Reflective boundary returns same conserved quantities as |
---|
971 | those present in its neighbour volume but reflected. |
---|
972 | |
---|
973 | This class is specific to the shallow water equation as it |
---|
974 | works with the momentum quantities assumed to be the second |
---|
975 | and third conserved quantities. |
---|
976 | """ |
---|
977 | |
---|
978 | def __init__(self, domain = None): |
---|
979 | Boundary.__init__(self) |
---|
980 | |
---|
981 | if domain is None: |
---|
982 | msg = 'Domain must be specified for reflective boundary' |
---|
983 | raise msg |
---|
984 | |
---|
985 | #Handy shorthands |
---|
986 | #self.stage = domain.quantities['stage'].edge_values |
---|
987 | #self.xmom = domain.quantities['xmomentum'].edge_values |
---|
988 | #self.ymom = domain.quantities['ymomentum'].edge_values |
---|
989 | self.normals = domain.normals |
---|
990 | self.stage = domain.quantities['stage'].vertex_values |
---|
991 | self.xmom = domain.quantities['xmomentum'].vertex_values |
---|
992 | |
---|
993 | from Numeric import zeros, Float |
---|
994 | #self.conserved_quantities = zeros(3, Float) |
---|
995 | self.conserved_quantities = zeros(2, Float) |
---|
996 | |
---|
997 | def __repr__(self): |
---|
998 | return 'Reflective_boundary' |
---|
999 | |
---|
1000 | |
---|
1001 | def evaluate(self, vol_id, edge_id): |
---|
1002 | """Reflective boundaries reverses the outward momentum |
---|
1003 | of the volume they serve. |
---|
1004 | """ |
---|
1005 | |
---|
1006 | q = self.conserved_quantities |
---|
1007 | q[0] = self.stage[vol_id, edge_id] |
---|
1008 | q[1] = self.xmom[vol_id, edge_id] |
---|
1009 | #q[2] = self.ymom[vol_id, edge_id] |
---|
1010 | #normal = self.normals[vol_id, 2*edge_id:2*edge_id+2] |
---|
1011 | #normal = self.normals[vol_id, 2*edge_id:2*edge_id+1] |
---|
1012 | normal = self.normals[vol_id,edge_id] |
---|
1013 | |
---|
1014 | #r = rotate(q, normal, direction = 1) |
---|
1015 | #r[1] = -r[1] |
---|
1016 | #q = rotate(r, normal, direction = -1) |
---|
1017 | r = q |
---|
1018 | r[1] = normal*r[1] |
---|
1019 | r[1] = -r[1] |
---|
1020 | r[1] = normal*r[1] |
---|
1021 | q = r |
---|
1022 | #For start interval there is no outward momentum so do not need to |
---|
1023 | #reverse direction in this case |
---|
1024 | |
---|
1025 | return q |
---|
1026 | |
---|
1027 | class Dirichlet_boundary(Boundary): |
---|
1028 | """Dirichlet boundary returns constant values for the |
---|
1029 | conserved quantities |
---|
1030 | """ |
---|
1031 | |
---|
1032 | |
---|
1033 | def __init__(self, conserved_quantities=None): |
---|
1034 | Boundary.__init__(self) |
---|
1035 | |
---|
1036 | if conserved_quantities is None: |
---|
1037 | msg = 'Must specify one value for each conserved quantity' |
---|
1038 | raise msg |
---|
1039 | |
---|
1040 | from Numeric import array, Float |
---|
1041 | self.conserved_quantities=array(conserved_quantities).astype(Float) |
---|
1042 | |
---|
1043 | def __repr__(self): |
---|
1044 | return 'Dirichlet boundary (%s)' %self.conserved_quantities |
---|
1045 | |
---|
1046 | def evaluate(self, vol_id=None, edge_id=None): |
---|
1047 | return self.conserved_quantities |
---|
1048 | |
---|
1049 | |
---|
1050 | ######################### |
---|
1051 | #Standard forcing terms: |
---|
1052 | # |
---|
1053 | def gravity(domain): |
---|
1054 | """Apply gravitational pull in the presence of bed slope |
---|
1055 | """ |
---|
1056 | |
---|
1057 | from util import gradient |
---|
1058 | from Numeric import zeros, Float, array, sum |
---|
1059 | |
---|
1060 | xmom = domain.quantities['xmomentum'].explicit_update |
---|
1061 | stage = domain.quantities['stage'].explicit_update |
---|
1062 | # ymom = domain.quantities['ymomentum'].explicit_update |
---|
1063 | |
---|
1064 | Stage = domain.quantities['stage'] |
---|
1065 | Elevation = domain.quantities['elevation'] |
---|
1066 | #h = Stage.edge_values - Elevation.edge_values |
---|
1067 | h = Stage.vertex_values - Elevation.vertex_values |
---|
1068 | b = Elevation.vertex_values |
---|
1069 | w = Stage.vertex_values |
---|
1070 | |
---|
1071 | x = domain.get_vertex_coordinates() |
---|
1072 | g = domain.g |
---|
1073 | |
---|
1074 | for k in range(domain.number_of_elements): |
---|
1075 | # avg_h = sum( h[k,:] )/3 |
---|
1076 | avg_h = sum( h[k,:] )/2 |
---|
1077 | |
---|
1078 | #Compute bed slope |
---|
1079 | #x0, y0, x1, y1, x2, y2 = x[k,:] |
---|
1080 | x0, x1 = x[k,:] |
---|
1081 | #z0, z1, z2 = v[k,:] |
---|
1082 | b0, b1 = b[k,:] |
---|
1083 | |
---|
1084 | w0, w1 = w[k,:] |
---|
1085 | wx = gradient(x0, x1, w0, w1) |
---|
1086 | |
---|
1087 | #zx, zy = gradient(x0, y0, x1, y1, x2, y2, z0, z1, z2) |
---|
1088 | bx = gradient(x0, x1, b0, b1) |
---|
1089 | |
---|
1090 | #Update momentum (explicit update is reset to source values) |
---|
1091 | xmom[k] += -g*bx*avg_h |
---|
1092 | #xmom[k] = -g*bx*avg_h |
---|
1093 | #stage[k] = 0.0 |
---|
1094 | |
---|
1095 | |
---|
1096 | def manning_friction(domain): |
---|
1097 | """Apply (Manning) friction to water momentum |
---|
1098 | """ |
---|
1099 | |
---|
1100 | from math import sqrt |
---|
1101 | |
---|
1102 | w = domain.quantities['stage'].centroid_values |
---|
1103 | z = domain.quantities['elevation'].centroid_values |
---|
1104 | h = w-z |
---|
1105 | |
---|
1106 | uh = domain.quantities['xmomentum'].centroid_values |
---|
1107 | #vh = domain.quantities['ymomentum'].centroid_values |
---|
1108 | eta = domain.quantities['friction'].centroid_values |
---|
1109 | |
---|
1110 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
---|
1111 | #ymom_update = domain.quantities['ymomentum'].semi_implicit_update |
---|
1112 | |
---|
1113 | N = domain.number_of_elements |
---|
1114 | eps = domain.minimum_allowed_height |
---|
1115 | g = domain.g |
---|
1116 | |
---|
1117 | for k in range(N): |
---|
1118 | if eta[k] >= eps: |
---|
1119 | if h[k] >= eps: |
---|
1120 | #S = -g * eta[k]**2 * sqrt((uh[k]**2 + vh[k]**2)) |
---|
1121 | S = -g * eta[k]**2 * uh[k] |
---|
1122 | S /= h[k]**(7.0/3) |
---|
1123 | |
---|
1124 | #Update momentum |
---|
1125 | xmom_update[k] += S*uh[k] |
---|
1126 | #ymom_update[k] += S*vh[k] |
---|
1127 | |
---|
1128 | def linear_friction(domain): |
---|
1129 | """Apply linear friction to water momentum |
---|
1130 | |
---|
1131 | Assumes quantity: 'linear_friction' to be present |
---|
1132 | """ |
---|
1133 | |
---|
1134 | from math import sqrt |
---|
1135 | |
---|
1136 | w = domain.quantities['stage'].centroid_values |
---|
1137 | z = domain.quantities['elevation'].centroid_values |
---|
1138 | h = w-z |
---|
1139 | |
---|
1140 | uh = domain.quantities['xmomentum'].centroid_values |
---|
1141 | # vh = domain.quantities['ymomentum'].centroid_values |
---|
1142 | tau = domain.quantities['linear_friction'].centroid_values |
---|
1143 | |
---|
1144 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
---|
1145 | # ymom_update = domain.quantities['ymomentum'].semi_implicit_update |
---|
1146 | |
---|
1147 | N = domain.number_of_elements |
---|
1148 | eps = domain.minimum_allowed_height |
---|
1149 | g = domain.g #Not necessary? Why was this added? |
---|
1150 | |
---|
1151 | for k in range(N): |
---|
1152 | if tau[k] >= eps: |
---|
1153 | if h[k] >= eps: |
---|
1154 | S = -tau[k]/h[k] |
---|
1155 | |
---|
1156 | #Update momentum |
---|
1157 | xmom_update[k] += S*uh[k] |
---|
1158 | # ymom_update[k] += S*vh[k] |
---|
1159 | |
---|
1160 | |
---|
1161 | |
---|
1162 | def check_forcefield(f): |
---|
1163 | """Check that f is either |
---|
1164 | 1: a callable object f(t,x,y), where x and y are vectors |
---|
1165 | and that it returns an array or a list of same length |
---|
1166 | as x and y |
---|
1167 | 2: a scalar |
---|
1168 | """ |
---|
1169 | |
---|
1170 | from Numeric import ones, Float, array |
---|
1171 | |
---|
1172 | |
---|
1173 | if callable(f): |
---|
1174 | #N = 3 |
---|
1175 | N = 2 |
---|
1176 | #x = ones(3, Float) |
---|
1177 | #y = ones(3, Float) |
---|
1178 | x = ones(2, Float) |
---|
1179 | #y = ones(2, Float) |
---|
1180 | |
---|
1181 | try: |
---|
1182 | #q = f(1.0, x=x, y=y) |
---|
1183 | q = f(1.0, x=x) |
---|
1184 | except Exception, e: |
---|
1185 | msg = 'Function %s could not be executed:\n%s' %(f, e) |
---|
1186 | #FIXME: Reconsider this semantics |
---|
1187 | raise msg |
---|
1188 | |
---|
1189 | try: |
---|
1190 | q = array(q).astype(Float) |
---|
1191 | except: |
---|
1192 | msg = 'Return value from vector function %s could ' %f |
---|
1193 | msg += 'not be converted into a Numeric array of floats.\n' |
---|
1194 | msg += 'Specified function should return either list or array.' |
---|
1195 | raise msg |
---|
1196 | |
---|
1197 | #Is this really what we want? |
---|
1198 | msg = 'Return vector from function %s ' %f |
---|
1199 | msg += 'must have same lenght as input vectors' |
---|
1200 | assert len(q) == N, msg |
---|
1201 | |
---|
1202 | else: |
---|
1203 | try: |
---|
1204 | f = float(f) |
---|
1205 | except: |
---|
1206 | msg = 'Force field %s must be either a scalar' %f |
---|
1207 | msg += ' or a vector function' |
---|
1208 | raise msg |
---|
1209 | return f |
---|
1210 | |
---|
1211 | class Wind_stress: |
---|
1212 | """Apply wind stress to water momentum in terms of |
---|
1213 | wind speed [m/s] and wind direction [degrees] |
---|
1214 | """ |
---|
1215 | |
---|
1216 | def __init__(self, *args, **kwargs): |
---|
1217 | """Initialise windfield from wind speed s [m/s] |
---|
1218 | and wind direction phi [degrees] |
---|
1219 | |
---|
1220 | Inputs v and phi can be either scalars or Python functions, e.g. |
---|
1221 | |
---|
1222 | W = Wind_stress(10, 178) |
---|
1223 | |
---|
1224 | #FIXME - 'normal' degrees are assumed for now, i.e. the |
---|
1225 | vector (1,0) has zero degrees. |
---|
1226 | We may need to convert from 'compass' degrees later on and also |
---|
1227 | map from True north to grid north. |
---|
1228 | |
---|
1229 | Arguments can also be Python functions of t,x,y as in |
---|
1230 | |
---|
1231 | def speed(t,x,y): |
---|
1232 | ... |
---|
1233 | return s |
---|
1234 | |
---|
1235 | def angle(t,x,y): |
---|
1236 | ... |
---|
1237 | return phi |
---|
1238 | |
---|
1239 | where x and y are vectors. |
---|
1240 | |
---|
1241 | and then pass the functions in |
---|
1242 | |
---|
1243 | W = Wind_stress(speed, angle) |
---|
1244 | |
---|
1245 | The instantiated object W can be appended to the list of |
---|
1246 | forcing_terms as in |
---|
1247 | |
---|
1248 | Alternatively, one vector valued function for (speed, angle) |
---|
1249 | can be applied, providing both quantities simultaneously. |
---|
1250 | As in |
---|
1251 | W = Wind_stress(F), where returns (speed, angle) for each t. |
---|
1252 | |
---|
1253 | domain.forcing_terms.append(W) |
---|
1254 | """ |
---|
1255 | |
---|
1256 | from config import rho_a, rho_w, eta_w |
---|
1257 | from Numeric import array, Float |
---|
1258 | |
---|
1259 | if len(args) == 2: |
---|
1260 | s = args[0] |
---|
1261 | phi = args[1] |
---|
1262 | elif len(args) == 1: |
---|
1263 | #Assume vector function returning (s, phi)(t,x,y) |
---|
1264 | vector_function = args[0] |
---|
1265 | #s = lambda t,x,y: vector_function(t,x=x,y=y)[0] |
---|
1266 | #phi = lambda t,x,y: vector_function(t,x=x,y=y)[1] |
---|
1267 | s = lambda t,x: vector_function(t,x=x)[0] |
---|
1268 | phi = lambda t,x: vector_function(t,x=x)[1] |
---|
1269 | else: |
---|
1270 | #Assume info is in 2 keyword arguments |
---|
1271 | |
---|
1272 | if len(kwargs) == 2: |
---|
1273 | s = kwargs['s'] |
---|
1274 | phi = kwargs['phi'] |
---|
1275 | else: |
---|
1276 | raise 'Assumes two keyword arguments: s=..., phi=....' |
---|
1277 | |
---|
1278 | print 'phi', phi |
---|
1279 | self.speed = check_forcefield(s) |
---|
1280 | self.phi = check_forcefield(phi) |
---|
1281 | |
---|
1282 | self.const = eta_w*rho_a/rho_w |
---|
1283 | |
---|
1284 | |
---|
1285 | def __call__(self, domain): |
---|
1286 | """Evaluate windfield based on values found in domain |
---|
1287 | """ |
---|
1288 | |
---|
1289 | from math import pi, cos, sin, sqrt |
---|
1290 | from Numeric import Float, ones, ArrayType |
---|
1291 | |
---|
1292 | xmom_update = domain.quantities['xmomentum'].explicit_update |
---|
1293 | #ymom_update = domain.quantities['ymomentum'].explicit_update |
---|
1294 | |
---|
1295 | N = domain.number_of_elements |
---|
1296 | t = domain.time |
---|
1297 | |
---|
1298 | if callable(self.speed): |
---|
1299 | xc = domain.get_centroid_coordinates() |
---|
1300 | #s_vec = self.speed(t, xc[:,0], xc[:,1]) |
---|
1301 | s_vec = self.speed(t, xc) |
---|
1302 | else: |
---|
1303 | #Assume s is a scalar |
---|
1304 | |
---|
1305 | try: |
---|
1306 | s_vec = self.speed * ones(N, Float) |
---|
1307 | except: |
---|
1308 | msg = 'Speed must be either callable or a scalar: %s' %self.s |
---|
1309 | raise msg |
---|
1310 | |
---|
1311 | |
---|
1312 | if callable(self.phi): |
---|
1313 | xc = domain.get_centroid_coordinates() |
---|
1314 | #phi_vec = self.phi(t, xc[:,0], xc[:,1]) |
---|
1315 | phi_vec = self.phi(t, xc) |
---|
1316 | else: |
---|
1317 | #Assume phi is a scalar |
---|
1318 | |
---|
1319 | try: |
---|
1320 | phi_vec = self.phi * ones(N, Float) |
---|
1321 | except: |
---|
1322 | msg = 'Angle must be either callable or a scalar: %s' %self.phi |
---|
1323 | raise msg |
---|
1324 | |
---|
1325 | #assign_windfield_values(xmom_update, ymom_update, |
---|
1326 | # s_vec, phi_vec, self.const) |
---|
1327 | assign_windfield_values(xmom_update, s_vec, phi_vec, self.const) |
---|
1328 | |
---|
1329 | |
---|
1330 | #def assign_windfield_values(xmom_update, ymom_update, |
---|
1331 | # s_vec, phi_vec, const): |
---|
1332 | def assign_windfield_values(xmom_update, s_vec, phi_vec, const): |
---|
1333 | """Python version of assigning wind field to update vectors. |
---|
1334 | A c version also exists (for speed) |
---|
1335 | """ |
---|
1336 | from math import pi, cos, sin, sqrt |
---|
1337 | |
---|
1338 | N = len(s_vec) |
---|
1339 | for k in range(N): |
---|
1340 | s = s_vec[k] |
---|
1341 | phi = phi_vec[k] |
---|
1342 | |
---|
1343 | #Convert to radians |
---|
1344 | phi = phi*pi/180 |
---|
1345 | |
---|
1346 | #Compute velocity vector (u, v) |
---|
1347 | u = s*cos(phi) |
---|
1348 | v = s*sin(phi) |
---|
1349 | |
---|
1350 | #Compute wind stress |
---|
1351 | #S = const * sqrt(u**2 + v**2) |
---|
1352 | S = const * u |
---|
1353 | xmom_update[k] += S*u |
---|
1354 | #ymom_update[k] += S*v |
---|