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_order2 import * |
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47 | from domain_t2 import * |
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48 | from comp_flux_ext import * |
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49 | Generic_Domain = Domain #Rename |
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50 | |
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51 | #Shallow water domain |
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52 | class Domain(Generic_Domain): |
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53 | |
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54 | def __init__(self, coordinates, boundary = None, tagged_elements = None, |
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55 | geo_reference = None): |
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56 | |
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57 | conserved_quantities = ['stage', 'xmomentum'] |
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58 | other_quantities = ['elevation', 'friction'] |
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59 | Generic_Domain.__init__(self, coordinates, boundary, |
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60 | conserved_quantities, other_quantities, |
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61 | tagged_elements, geo_reference) |
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62 | |
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63 | from config import minimum_allowed_height, g |
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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 | |
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67 | #forcing terms not included in 1d domain ?WHy? |
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68 | self.forcing_terms.append(gravity) |
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69 | #self.forcing_terms.append(manning_friction) |
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70 | #print "\nI have Removed forcing terms line 64 1dsw" |
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71 | |
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72 | #Realtime visualisation |
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73 | self.visualiser = None |
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74 | self.visualise = False |
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75 | self.visualise_color_stage = False |
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76 | self.visualise_stage_range = 1.0 |
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77 | self.visualise_timer = True |
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78 | self.visualise_range_z = None |
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79 | |
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80 | #Stored output |
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81 | self.store = True |
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82 | self.format = 'sww' |
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83 | self.smooth = True |
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84 | |
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85 | #Evolve parametrs |
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86 | self.cfl = 1.0 |
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87 | |
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88 | #Reduction operation for get_vertex_values |
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89 | from util import mean |
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90 | self.reduction = mean |
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91 | #self.reduction = min #Looks better near steep slopes |
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92 | |
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93 | self.quantities_to_be_stored = ['stage','xmomentum'] |
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94 | |
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95 | |
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96 | def set_quantities_to_be_stored(self, q): |
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97 | """Specify which quantities will be stored in the sww file. |
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98 | |
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99 | q must be either: |
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100 | - the name of a quantity |
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101 | - a list of quantity names |
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102 | - None |
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103 | |
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104 | In the two first cases, the named quantities will be stored at each |
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105 | yieldstep |
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106 | (This is in addition to the quantities elevation and friction) |
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107 | If q is None, storage will be switched off altogether. |
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108 | """ |
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109 | |
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110 | |
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111 | if q is None: |
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112 | self.quantities_to_be_stored = [] |
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113 | self.store = False |
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114 | return |
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115 | |
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116 | if isinstance(q, basestring): |
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117 | q = [q] # Turn argument into a list |
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118 | |
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119 | #Check correcness |
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120 | for quantity_name in q: |
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121 | msg = 'Quantity %s is not a valid conserved quantity' %quantity_name |
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122 | assert quantity_name in self.conserved_quantities, msg |
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123 | |
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124 | self.quantities_to_be_stored = q |
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125 | |
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126 | |
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127 | def initialise_visualiser(self,scale_z=1.0,rect=None): |
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128 | #Realtime visualisation |
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129 | if self.visualiser is None: |
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130 | from realtime_visualisation_new import Visualiser |
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131 | self.visualiser = Visualiser(self,scale_z,rect) |
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132 | self.visualiser.setup['elevation']=True |
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133 | self.visualiser.updating['stage']=True |
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134 | self.visualise = True |
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135 | if self.visualise_color_stage == True: |
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136 | self.visualiser.coloring['stage'] = True |
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137 | self.visualiser.qcolor['stage'] = (0.0, 0.0, 0.8) |
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138 | print 'initialise visualiser' |
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139 | print self.visualiser.setup |
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140 | print self.visualiser.updating |
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141 | |
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142 | def check_integrity(self): |
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143 | Generic_Domain.check_integrity(self) |
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144 | #Check that we are solving the shallow water wave equation |
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145 | |
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146 | msg = 'First conserved quantity must be "stage"' |
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147 | assert self.conserved_quantities[0] == 'stage', msg |
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148 | msg = 'Second conserved quantity must be "xmomentum"' |
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149 | assert self.conserved_quantities[1] == 'xmomentum', msg |
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150 | |
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151 | def extrapolate_second_order_sw(self): |
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152 | #Call correct module function |
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153 | #(either from this module or C-extension) |
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154 | extrapolate_second_order_sw(self) |
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155 | |
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156 | def compute_fluxes(self): |
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157 | #Call correct module function |
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158 | #(either from this module or C-extension) |
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159 | compute_fluxes(self) |
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160 | |
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161 | def compute_timestep(self): |
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162 | #Call correct module function |
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163 | compute_timestep(self) |
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164 | |
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165 | def distribute_to_vertices_and_edges(self): |
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166 | #Call correct module function |
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167 | #(either from this module or C-extension) |
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168 | distribute_to_vertices_and_edges(self) |
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169 | |
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170 | def evolve(self, yieldstep = None, finaltime = None, |
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171 | skip_initial_step = False): |
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172 | """Specialisation of basic evolve method from parent class |
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173 | """ |
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174 | |
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175 | #Call check integrity here rather than from user scripts |
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176 | #self.check_integrity() |
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177 | |
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178 | #msg = 'Parameter beta_h must be in the interval [0, 1)' |
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179 | #assert 0 <= self.beta_h < 1.0, msg |
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180 | #msg = 'Parameter beta_w must be in the interval [0, 1)' |
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181 | #assert 0 <= self.beta_w < 1.0, msg |
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182 | |
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183 | |
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184 | #Initial update of vertex and edge values before any storage |
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185 | #and or visualisation |
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186 | |
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187 | self.distribute_to_vertices_and_edges() |
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188 | |
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189 | #Call basic machinery from parent class |
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190 | for t in Generic_Domain.evolve(self, yieldstep, finaltime, |
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191 | skip_initial_step): |
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192 | yield(t) |
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193 | |
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194 | def initialise_storage(self): |
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195 | """Create and initialise self.writer object for storing data. |
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196 | Also, save x and bed elevation |
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197 | """ |
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198 | |
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199 | import data_manager |
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200 | |
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201 | #Initialise writer |
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202 | self.writer = data_manager.get_dataobject(self, mode = 'w') |
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203 | |
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204 | #Store vertices and connectivity |
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205 | self.writer.store_connectivity() |
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206 | |
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207 | |
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208 | def store_timestep(self, name): |
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209 | """Store named quantity and time. |
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210 | |
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211 | Precondition: |
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212 | self.write has been initialised |
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213 | """ |
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214 | self.writer.store_timestep(name) |
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215 | |
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216 | |
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217 | #=============== End of Shallow Water Domain =============================== |
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218 | |
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219 | #Rotation of momentum vector |
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220 | def rotate(q, normal, direction = 1): |
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221 | """Rotate the momentum component q (q[1], q[2]) |
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222 | from x,y coordinates to coordinates based on normal vector. |
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223 | |
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224 | If direction is negative the rotation is inverted. |
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225 | |
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226 | Input vector is preserved |
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227 | |
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228 | This function is specific to the shallow water wave equation |
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229 | """ |
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230 | |
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231 | from Numeric import zeros, Float |
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232 | |
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233 | assert len(q) == 3,\ |
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234 | 'Vector of conserved quantities must have length 3'\ |
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235 | 'for 2D shallow water equation' |
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236 | |
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237 | try: |
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238 | l = len(normal) |
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239 | except: |
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240 | raise 'Normal vector must be an Numeric array' |
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241 | |
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242 | assert l == 2, 'Normal vector must have 2 components' |
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243 | |
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244 | |
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245 | n1 = normal[0] |
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246 | n2 = normal[1] |
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247 | |
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248 | r = zeros(len(q), Float) #Rotated quantities |
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249 | r[0] = q[0] #First quantity, height, is not rotated |
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250 | |
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251 | if direction == -1: |
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252 | n2 = -n2 |
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253 | |
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254 | |
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255 | r[1] = n1*q[1] + n2*q[2] |
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256 | r[2] = -n2*q[1] + n1*q[2] |
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257 | |
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258 | return r |
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259 | """++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++""" |
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260 | # Compute flux definition |
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261 | def compute_fluxes(domain): |
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262 | from Numeric import zeros, Float |
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263 | import sys |
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264 | |
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265 | timestep = float(sys.maxint) |
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266 | print 'timestep=',timestep |
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267 | print 'The type of timestep is',type(timestep) |
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268 | |
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269 | epsilon = domain.epsilon |
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270 | print 'epsilon=',epsilon |
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271 | print 'The type of epsilon is',type(epsilon) |
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272 | |
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273 | g = domain.g |
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274 | print 'g=',g |
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275 | print 'The type of g is',type(g) |
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276 | |
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277 | neighbours = domain.neighbours |
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278 | print 'neighbours=',neighbours |
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279 | print 'The type of neighbours is',type(neighbours) |
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280 | |
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281 | neighbour_vertices = domain.neighbour_vertices |
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282 | print 'neighbour_vertices=',neighbour_vertices |
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283 | print 'The type of neighbour_vertices is',type(neighbour_vertices) |
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284 | |
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285 | normals = domain.normals |
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286 | print 'normals=',normals |
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287 | print 'The type of normals is',type(normals) |
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288 | |
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289 | areas = domain.areas |
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290 | print 'areas=',areas |
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291 | print 'The type of areas is',type(areas) |
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292 | |
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293 | stage_edge_values = domain.quantities['stage'].vertex_values |
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294 | print 'stage_edge_values=',stage_edge_values |
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295 | print 'The type of stage_edge_values is',type(stage_edge_values) |
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296 | |
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297 | xmom_edge_values = domain.quantities['xmomentum'].vertex_values |
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298 | print 'xmom_edge_values=',xmom_edge_values |
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299 | print 'The type of xmom_edge_values is',type(xmom_edge_values) |
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300 | |
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301 | bed_edge_values = domain.quantities['elevation'].vertex_values |
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302 | print 'bed_edge_values=',bed_edge_values |
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303 | print 'The type of bed_edge_values is',type(bed_edge_values) |
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304 | |
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305 | stage_boundary_values = domain.quantities['stage'].boundary_values |
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306 | print 'stage_boundary_values=',stage_boundary_values |
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307 | print 'The type of stage_boundary_values is',type(stage_boundary_values) |
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308 | |
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309 | xmom_boundary_values = domain.quantities['xmomentum'].boundary_values |
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310 | print 'xmom_boundary_values=',xmom_boundary_values |
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311 | print 'The type of xmom_boundary_values is',type(xmom_boundary_values) |
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312 | |
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313 | stage_explicit_update = domain.quantities['stage'].explicit_update |
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314 | print 'stage_explicit_update=',stage_explicit_update |
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315 | print 'The type of stage_explicit_update is',type(stage_explicit_update) |
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316 | |
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317 | xmom_explicit_update = domain.quantities['xmomentum'].explicit_update |
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318 | print 'xmom_explicit_update=',xmom_explicit_update |
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319 | print 'The type of xmom_explicit_update is',type(xmom_explicit_update) |
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320 | |
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321 | number_of_elements = len(stage_edge_values) |
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322 | print 'number_of_elements=',number_of_elements |
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323 | print 'The type of number_of_elements is',type(number_of_elements) |
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324 | |
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325 | max_speed_array = zeros(number_of_elements, Float) |
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326 | print 'max_speed_array=',max_speed_array |
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327 | print 'The type of max_speed_array is',type(max_speed_array) |
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328 | |
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329 | return compute_fluxes_ext(timestep, epsilon, g, neighbours, neighbour_vertices, normals, areas, |
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330 | stage_edge_values, xmom_edge_values, bed_edge_values, stage_boundary_values, xmom_boundary_values, |
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331 | number_of_elements, max_speed_array) |
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332 | #################################### |
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333 | |
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334 | # Module functions for gradient limiting (distribute_to_vertices_and_edges) |
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335 | |
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336 | def distribute_to_vertices_and_edges(domain): |
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337 | """Distribution from centroids to vertices specific to the |
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338 | shallow water wave |
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339 | equation. |
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340 | |
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341 | It will ensure that h (w-z) is always non-negative even in the |
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342 | presence of steep bed-slopes by taking a weighted average between shallow |
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343 | and deep cases. |
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344 | |
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345 | In addition, all conserved quantities get distributed as per either a |
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346 | constant (order==1) or a piecewise linear function (order==2). |
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347 | |
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348 | FIXME: more explanation about removal of artificial variability etc |
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349 | |
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350 | Precondition: |
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351 | All quantities defined at centroids and bed elevation defined at |
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352 | vertices. |
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353 | |
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354 | Postcondition |
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355 | Conserved quantities defined at vertices |
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356 | |
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357 | """ |
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358 | |
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359 | #from config import optimised_gradient_limiter |
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360 | |
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361 | #Remove very thin layers of water |
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362 | protect_against_infinitesimal_and_negative_heights(domain) |
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363 | |
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364 | |
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365 | #Extrapolate all conserved quantities |
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366 | #if optimised_gradient_limiter: |
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367 | # #MH090605 if second order, |
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368 | # #perform the extrapolation and limiting on |
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369 | # #all of the conserved quantities |
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370 | |
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371 | # if (domain.order == 1): |
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372 | # for name in domain.conserved_quantities: |
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373 | # Q = domain.quantities[name] |
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374 | # Q.extrapolate_first_order() |
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375 | # elif domain.order == 2: |
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376 | # domain.extrapolate_second_order_sw() |
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377 | # else: |
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378 | # raise 'Unknown order' |
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379 | #else: |
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380 | #old code: |
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381 | |
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382 | for name in domain.conserved_quantities: |
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383 | Q = domain.quantities[name] |
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384 | if domain.order == 1: |
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385 | Q.extrapolate_first_order() |
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386 | elif domain.order == 2: |
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387 | #print "add extrapolate second order to shallow water" |
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388 | #if name != 'height': |
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389 | Q.extrapolate_second_order() |
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390 | #Q.limit() |
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391 | else: |
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392 | raise 'Unknown order' |
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393 | |
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394 | #Take bed elevation into account when water heights are small |
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395 | #balance_deep_and_shallow(domain) |
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396 | #protect_against_infinitesimal_and_negative_heights(domain) |
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397 | |
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398 | #Compute edge values by interpolation |
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399 | #for name in domain.conserved_quantities: |
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400 | # Q = domain.quantities[name] |
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401 | # Q.interpolate_from_vertices_to_edges() |
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402 | |
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403 | def protect_against_infinitesimal_and_negative_heights(domain): |
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404 | """Protect against infinitesimal heights and associated high velocities |
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405 | """ |
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406 | |
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407 | #Shortcuts |
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408 | wc = domain.quantities['stage'].centroid_values |
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409 | zc = domain.quantities['elevation'].centroid_values |
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410 | xmomc = domain.quantities['xmomentum'].centroid_values |
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411 | # ymomc = domain.quantities['ymomentum'].centroid_values |
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412 | hc = wc - zc #Water depths at centroids |
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413 | |
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414 | zv = domain.quantities['elevation'].vertex_values |
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415 | wv = domain.quantities['stage'].vertex_values |
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416 | hv = wv-zv |
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417 | xmomv = domain.quantities['xmomentum'].vertex_values |
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418 | #remove the above two lines and corresponding code below |
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419 | |
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420 | #Update |
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421 | for k in range(domain.number_of_elements): |
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422 | |
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423 | if hc[k] < domain.minimum_allowed_height: |
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424 | #Control stage |
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425 | if hc[k] < domain.epsilon: |
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426 | wc[k] = zc[k] # Contain 'lost mass' error |
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427 | wv[k,0] = zv[k,0] |
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428 | wv[k,1] = zv[k,1] |
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429 | |
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430 | xmomc[k] = 0.0 |
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431 | |
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432 | #N = domain.number_of_elements |
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433 | #if (k == 0) | (k==N-1): |
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434 | # wc[k] = zc[k] # Contain 'lost mass' error |
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435 | # wv[k,0] = zv[k,0] |
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436 | # wv[k,1] = zv[k,1] |
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437 | |
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438 | def h_limiter(domain): |
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439 | """Limit slopes for each volume to eliminate artificial variance |
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440 | introduced by e.g. second order extrapolator |
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441 | |
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442 | limit on h = w-z |
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443 | |
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444 | This limiter depends on two quantities (w,z) so it resides within |
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445 | this module rather than within quantity.py |
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446 | """ |
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447 | |
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448 | from Numeric import zeros, Float |
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449 | |
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450 | N = domain.number_of_elements |
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451 | beta_h = domain.beta_h |
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452 | |
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453 | #Shortcuts |
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454 | wc = domain.quantities['stage'].centroid_values |
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455 | zc = domain.quantities['elevation'].centroid_values |
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456 | hc = wc - zc |
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457 | |
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458 | wv = domain.quantities['stage'].vertex_values |
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459 | zv = domain.quantities['elevation'].vertex_values |
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460 | hv = wv-zv |
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461 | |
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462 | hvbar = zeros(hv.shape, Float) #h-limited values |
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463 | |
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464 | #Find min and max of this and neighbour's centroid values |
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465 | hmax = zeros(hc.shape, Float) |
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466 | hmin = zeros(hc.shape, Float) |
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467 | |
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468 | for k in range(N): |
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469 | hmax[k] = hmin[k] = hc[k] |
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470 | #for i in range(3): |
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471 | for i in range(2): |
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472 | n = domain.neighbours[k,i] |
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473 | if n >= 0: |
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474 | hn = hc[n] #Neighbour's centroid value |
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475 | |
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476 | hmin[k] = min(hmin[k], hn) |
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477 | hmax[k] = max(hmax[k], hn) |
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478 | |
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479 | |
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480 | #Diffences between centroids and maxima/minima |
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481 | dhmax = hmax - hc |
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482 | dhmin = hmin - hc |
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483 | |
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484 | #Deltas between vertex and centroid values |
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485 | dh = zeros(hv.shape, Float) |
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486 | #for i in range(3): |
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487 | for i in range(2): |
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488 | dh[:,i] = hv[:,i] - hc |
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489 | |
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490 | #Phi limiter |
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491 | for k in range(N): |
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492 | |
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493 | #Find the gradient limiter (phi) across vertices |
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494 | phi = 1.0 |
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495 | #for i in range(3): |
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496 | for i in range(2): |
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497 | r = 1.0 |
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498 | if (dh[k,i] > 0): r = dhmax[k]/dh[k,i] |
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499 | if (dh[k,i] < 0): r = dhmin[k]/dh[k,i] |
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500 | |
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501 | phi = min( min(r*beta_h, 1), phi ) |
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502 | |
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503 | #Then update using phi limiter |
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504 | #for i in range(3): |
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505 | for i in range(2): |
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506 | hvbar[k,i] = hc[k] + phi*dh[k,i] |
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507 | |
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508 | return hvbar |
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509 | |
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510 | def balance_deep_and_shallow(domain): |
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511 | """Compute linear combination between stage as computed by |
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512 | gradient-limiters limiting using w, and stage computed by |
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513 | gradient-limiters limiting using h (h-limiter). |
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514 | The former takes precedence when heights are large compared to the |
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515 | bed slope while the latter takes precedence when heights are |
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516 | relatively small. Anything in between is computed as a balanced |
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517 | linear combination in order to avoid numerical disturbances which |
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518 | would otherwise appear as a result of hard switching between |
---|
519 | modes. |
---|
520 | |
---|
521 | The h-limiter is always applied irrespective of the order. |
---|
522 | """ |
---|
523 | |
---|
524 | #Shortcuts |
---|
525 | wc = domain.quantities['stage'].centroid_values |
---|
526 | zc = domain.quantities['elevation'].centroid_values |
---|
527 | hc = wc - zc |
---|
528 | |
---|
529 | wv = domain.quantities['stage'].vertex_values |
---|
530 | zv = domain.quantities['elevation'].vertex_values |
---|
531 | hv = wv-zv |
---|
532 | |
---|
533 | #Limit h |
---|
534 | hvbar = h_limiter(domain) |
---|
535 | |
---|
536 | for k in range(domain.number_of_elements): |
---|
537 | #Compute maximal variation in bed elevation |
---|
538 | # This quantitiy is |
---|
539 | # dz = max_i abs(z_i - z_c) |
---|
540 | # and it is independent of dimension |
---|
541 | # In the 1d case zc = (z0+z1)/2 |
---|
542 | # In the 2d case zc = (z0+z1+z2)/3 |
---|
543 | |
---|
544 | dz = max(abs(zv[k,0]-zc[k]), |
---|
545 | abs(zv[k,1]-zc[k]))#, |
---|
546 | # abs(zv[k,2]-zc[k])) |
---|
547 | |
---|
548 | |
---|
549 | hmin = min( hv[k,:] ) |
---|
550 | |
---|
551 | #Create alpha in [0,1], where alpha==0 means using the h-limited |
---|
552 | #stage and alpha==1 means using the w-limited stage as |
---|
553 | #computed by the gradient limiter (both 1st or 2nd order) |
---|
554 | |
---|
555 | #If hmin > dz/2 then alpha = 1 and the bed will have no effect |
---|
556 | #If hmin < 0 then alpha = 0 reverting to constant height above bed. |
---|
557 | |
---|
558 | if dz > 0.0: |
---|
559 | alpha = max( min( 2*hmin/dz, 1.0), 0.0 ) |
---|
560 | else: |
---|
561 | #Flat bed |
---|
562 | alpha = 1.0 |
---|
563 | |
---|
564 | alpha = 0.0 |
---|
565 | #Let |
---|
566 | # |
---|
567 | # wvi be the w-limited stage (wvi = zvi + hvi) |
---|
568 | # wvi- be the h-limited state (wvi- = zvi + hvi-) |
---|
569 | # |
---|
570 | # |
---|
571 | #where i=0,1,2 denotes the vertex ids |
---|
572 | # |
---|
573 | #Weighted balance between w-limited and h-limited stage is |
---|
574 | # |
---|
575 | # wvi := (1-alpha)*(zvi+hvi-) + alpha*(zvi+hvi) |
---|
576 | # |
---|
577 | #It follows that the updated wvi is |
---|
578 | # wvi := zvi + (1-alpha)*hvi- + alpha*hvi |
---|
579 | # |
---|
580 | # Momentum is balanced between constant and limited |
---|
581 | |
---|
582 | |
---|
583 | #for i in range(3): |
---|
584 | # wv[k,i] = zv[k,i] + hvbar[k,i] |
---|
585 | |
---|
586 | #return |
---|
587 | |
---|
588 | if alpha < 1: |
---|
589 | |
---|
590 | #for i in range(3): |
---|
591 | for i in range(2): |
---|
592 | wv[k,i] = zv[k,i] + (1.0-alpha)*hvbar[k,i] + alpha*hv[k,i] |
---|
593 | |
---|
594 | #Momentums at centroids |
---|
595 | xmomc = domain.quantities['xmomentum'].centroid_values |
---|
596 | # ymomc = domain.quantities['ymomentum'].centroid_values |
---|
597 | |
---|
598 | #Momentums at vertices |
---|
599 | xmomv = domain.quantities['xmomentum'].vertex_values |
---|
600 | # ymomv = domain.quantities['ymomentum'].vertex_values |
---|
601 | |
---|
602 | # Update momentum as a linear combination of |
---|
603 | # xmomc and ymomc (shallow) and momentum |
---|
604 | # from extrapolator xmomv and ymomv (deep). |
---|
605 | xmomv[k,:] = (1.0-alpha)*xmomc[k] + alpha*xmomv[k,:] |
---|
606 | # ymomv[k,:] = (1-alpha)*ymomc[k] + alpha*ymomv[k,:] |
---|
607 | |
---|
608 | |
---|
609 | ############################################### |
---|
610 | #Boundaries - specific to the shallow water wave equation |
---|
611 | class Reflective_boundary(Boundary): |
---|
612 | """Reflective boundary returns same conserved quantities as |
---|
613 | those present in its neighbour volume but reflected. |
---|
614 | |
---|
615 | This class is specific to the shallow water equation as it |
---|
616 | works with the momentum quantities assumed to be the second |
---|
617 | and third conserved quantities. |
---|
618 | """ |
---|
619 | |
---|
620 | def __init__(self, domain = None): |
---|
621 | Boundary.__init__(self) |
---|
622 | |
---|
623 | if domain is None: |
---|
624 | msg = 'Domain must be specified for reflective boundary' |
---|
625 | raise msg |
---|
626 | |
---|
627 | #Handy shorthands |
---|
628 | #self.stage = domain.quantities['stage'].edge_values |
---|
629 | #self.xmom = domain.quantities['xmomentum'].edge_values |
---|
630 | #self.ymom = domain.quantities['ymomentum'].edge_values |
---|
631 | self.normals = domain.normals |
---|
632 | self.stage = domain.quantities['stage'].vertex_values |
---|
633 | self.xmom = domain.quantities['xmomentum'].vertex_values |
---|
634 | |
---|
635 | from Numeric import zeros, Float |
---|
636 | #self.conserved_quantities = zeros(3, Float) |
---|
637 | self.conserved_quantities = zeros(2, Float) |
---|
638 | |
---|
639 | def __repr__(self): |
---|
640 | return 'Reflective_boundary' |
---|
641 | |
---|
642 | |
---|
643 | def evaluate(self, vol_id, edge_id): |
---|
644 | """Reflective boundaries reverses the outward momentum |
---|
645 | of the volume they serve. |
---|
646 | """ |
---|
647 | |
---|
648 | q = self.conserved_quantities |
---|
649 | q[0] = self.stage[vol_id, edge_id] |
---|
650 | q[1] = self.xmom[vol_id, edge_id] |
---|
651 | #q[2] = self.ymom[vol_id, edge_id] |
---|
652 | #normal = self.normals[vol_id, 2*edge_id:2*edge_id+2] |
---|
653 | #normal = self.normals[vol_id, 2*edge_id:2*edge_id+1] |
---|
654 | normal = self.normals[vol_id,edge_id] |
---|
655 | |
---|
656 | #r = rotate(q, normal, direction = 1) |
---|
657 | #r[1] = -r[1] |
---|
658 | #q = rotate(r, normal, direction = -1) |
---|
659 | r = q |
---|
660 | r[1] = normal*r[1] |
---|
661 | r[1] = -r[1] |
---|
662 | r[1] = normal*r[1] |
---|
663 | q = r |
---|
664 | #For start interval there is no outward momentum so do not need to |
---|
665 | #reverse direction in this case |
---|
666 | |
---|
667 | return q |
---|
668 | |
---|
669 | class Dirichlet_boundary(Boundary): |
---|
670 | """Dirichlet boundary returns constant values for the |
---|
671 | conserved quantities |
---|
672 | """ |
---|
673 | |
---|
674 | |
---|
675 | def __init__(self, conserved_quantities=None): |
---|
676 | Boundary.__init__(self) |
---|
677 | |
---|
678 | if conserved_quantities is None: |
---|
679 | msg = 'Must specify one value for each conserved quantity' |
---|
680 | raise msg |
---|
681 | |
---|
682 | from Numeric import array, Float |
---|
683 | self.conserved_quantities=array(conserved_quantities).astype(Float) |
---|
684 | |
---|
685 | def __repr__(self): |
---|
686 | return 'Dirichlet boundary (%s)' %self.conserved_quantities |
---|
687 | |
---|
688 | def evaluate(self, vol_id=None, edge_id=None): |
---|
689 | return self.conserved_quantities |
---|
690 | |
---|
691 | |
---|
692 | ######################### |
---|
693 | #Standard forcing terms: |
---|
694 | # |
---|
695 | def gravity(domain): |
---|
696 | """Apply gravitational pull in the presence of bed slope |
---|
697 | """ |
---|
698 | |
---|
699 | from util import gradient |
---|
700 | from Numeric import zeros, Float, array, sum |
---|
701 | |
---|
702 | xmom = domain.quantities['xmomentum'].explicit_update |
---|
703 | stage = domain.quantities['stage'].explicit_update |
---|
704 | # ymom = domain.quantities['ymomentum'].explicit_update |
---|
705 | |
---|
706 | Stage = domain.quantities['stage'] |
---|
707 | Elevation = domain.quantities['elevation'] |
---|
708 | #h = Stage.edge_values - Elevation.edge_values |
---|
709 | h = Stage.vertex_values - Elevation.vertex_values |
---|
710 | b = Elevation.vertex_values |
---|
711 | w = Stage.vertex_values |
---|
712 | |
---|
713 | x = domain.get_vertex_coordinates() |
---|
714 | g = domain.g |
---|
715 | |
---|
716 | for k in range(domain.number_of_elements): |
---|
717 | # avg_h = sum( h[k,:] )/3 |
---|
718 | avg_h = sum( h[k,:] )/2 |
---|
719 | |
---|
720 | #Compute bed slope |
---|
721 | #x0, y0, x1, y1, x2, y2 = x[k,:] |
---|
722 | x0, x1 = x[k,:] |
---|
723 | #z0, z1, z2 = v[k,:] |
---|
724 | b0, b1 = b[k,:] |
---|
725 | |
---|
726 | w0, w1 = w[k,:] |
---|
727 | wx = gradient(x0, x1, w0, w1) |
---|
728 | |
---|
729 | #zx, zy = gradient(x0, y0, x1, y1, x2, y2, z0, z1, z2) |
---|
730 | bx = gradient(x0, x1, b0, b1) |
---|
731 | |
---|
732 | #Update momentum (explicit update is reset to source values) |
---|
733 | if domain.split == False: |
---|
734 | xmom[k] += -g*bx*avg_h |
---|
735 | #xmom[k] = -g*bx*avg_h |
---|
736 | #stage[k] = 0.0 |
---|
737 | elif domain.split == True: |
---|
738 | xmom[k] += -g*wx*avg_h |
---|
739 | #xmom[k] = -g*wx*avg_h |
---|
740 | #ymom[k] += -g*zy*avg_h |
---|
741 | |
---|
742 | def manning_friction(domain): |
---|
743 | """Apply (Manning) friction to water momentum |
---|
744 | """ |
---|
745 | |
---|
746 | from math import sqrt |
---|
747 | |
---|
748 | w = domain.quantities['stage'].centroid_values |
---|
749 | z = domain.quantities['elevation'].centroid_values |
---|
750 | h = w-z |
---|
751 | |
---|
752 | uh = domain.quantities['xmomentum'].centroid_values |
---|
753 | #vh = domain.quantities['ymomentum'].centroid_values |
---|
754 | eta = domain.quantities['friction'].centroid_values |
---|
755 | |
---|
756 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
---|
757 | #ymom_update = domain.quantities['ymomentum'].semi_implicit_update |
---|
758 | |
---|
759 | N = domain.number_of_elements |
---|
760 | eps = domain.minimum_allowed_height |
---|
761 | g = domain.g |
---|
762 | |
---|
763 | for k in range(N): |
---|
764 | if eta[k] >= eps: |
---|
765 | if h[k] >= eps: |
---|
766 | #S = -g * eta[k]**2 * sqrt((uh[k]**2 + vh[k]**2)) |
---|
767 | S = -g * eta[k]**2 * uh[k] |
---|
768 | S /= h[k]**(7.0/3) |
---|
769 | |
---|
770 | #Update momentum |
---|
771 | xmom_update[k] += S*uh[k] |
---|
772 | #ymom_update[k] += S*vh[k] |
---|
773 | |
---|
774 | def linear_friction(domain): |
---|
775 | """Apply linear friction to water momentum |
---|
776 | |
---|
777 | Assumes quantity: 'linear_friction' to be present |
---|
778 | """ |
---|
779 | |
---|
780 | from math import sqrt |
---|
781 | |
---|
782 | w = domain.quantities['stage'].centroid_values |
---|
783 | z = domain.quantities['elevation'].centroid_values |
---|
784 | h = w-z |
---|
785 | |
---|
786 | uh = domain.quantities['xmomentum'].centroid_values |
---|
787 | # vh = domain.quantities['ymomentum'].centroid_values |
---|
788 | tau = domain.quantities['linear_friction'].centroid_values |
---|
789 | |
---|
790 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
---|
791 | # ymom_update = domain.quantities['ymomentum'].semi_implicit_update |
---|
792 | |
---|
793 | N = domain.number_of_elements |
---|
794 | eps = domain.minimum_allowed_height |
---|
795 | g = domain.g #Not necessary? Why was this added? |
---|
796 | |
---|
797 | for k in range(N): |
---|
798 | if tau[k] >= eps: |
---|
799 | if h[k] >= eps: |
---|
800 | S = -tau[k]/h[k] |
---|
801 | |
---|
802 | #Update momentum |
---|
803 | xmom_update[k] += S*uh[k] |
---|
804 | # ymom_update[k] += S*vh[k] |
---|
805 | |
---|
806 | |
---|
807 | |
---|
808 | def check_forcefield(f): |
---|
809 | """Check that f is either |
---|
810 | 1: a callable object f(t,x,y), where x and y are vectors |
---|
811 | and that it returns an array or a list of same length |
---|
812 | as x and y |
---|
813 | 2: a scalar |
---|
814 | """ |
---|
815 | |
---|
816 | from Numeric import ones, Float, array |
---|
817 | |
---|
818 | |
---|
819 | if callable(f): |
---|
820 | #N = 3 |
---|
821 | N = 2 |
---|
822 | #x = ones(3, Float) |
---|
823 | #y = ones(3, Float) |
---|
824 | x = ones(2, Float) |
---|
825 | #y = ones(2, Float) |
---|
826 | |
---|
827 | try: |
---|
828 | #q = f(1.0, x=x, y=y) |
---|
829 | q = f(1.0, x=x) |
---|
830 | except Exception, e: |
---|
831 | msg = 'Function %s could not be executed:\n%s' %(f, e) |
---|
832 | #FIXME: Reconsider this semantics |
---|
833 | raise msg |
---|
834 | |
---|
835 | try: |
---|
836 | q = array(q).astype(Float) |
---|
837 | except: |
---|
838 | msg = 'Return value from vector function %s could ' %f |
---|
839 | msg += 'not be converted into a Numeric array of floats.\n' |
---|
840 | msg += 'Specified function should return either list or array.' |
---|
841 | raise msg |
---|
842 | |
---|
843 | #Is this really what we want? |
---|
844 | msg = 'Return vector from function %s ' %f |
---|
845 | msg += 'must have same lenght as input vectors' |
---|
846 | assert len(q) == N, msg |
---|
847 | |
---|
848 | else: |
---|
849 | try: |
---|
850 | f = float(f) |
---|
851 | except: |
---|
852 | msg = 'Force field %s must be either a scalar' %f |
---|
853 | msg += ' or a vector function' |
---|
854 | raise msg |
---|
855 | return f |
---|
856 | |
---|
857 | class Wind_stress: |
---|
858 | """Apply wind stress to water momentum in terms of |
---|
859 | wind speed [m/s] and wind direction [degrees] |
---|
860 | """ |
---|
861 | |
---|
862 | def __init__(self, *args, **kwargs): |
---|
863 | """Initialise windfield from wind speed s [m/s] |
---|
864 | and wind direction phi [degrees] |
---|
865 | |
---|
866 | Inputs v and phi can be either scalars or Python functions, e.g. |
---|
867 | |
---|
868 | W = Wind_stress(10, 178) |
---|
869 | |
---|
870 | #FIXME - 'normal' degrees are assumed for now, i.e. the |
---|
871 | vector (1,0) has zero degrees. |
---|
872 | We may need to convert from 'compass' degrees later on and also |
---|
873 | map from True north to grid north. |
---|
874 | |
---|
875 | Arguments can also be Python functions of t,x,y as in |
---|
876 | |
---|
877 | def speed(t,x,y): |
---|
878 | ... |
---|
879 | return s |
---|
880 | |
---|
881 | def angle(t,x,y): |
---|
882 | ... |
---|
883 | return phi |
---|
884 | |
---|
885 | where x and y are vectors. |
---|
886 | |
---|
887 | and then pass the functions in |
---|
888 | |
---|
889 | W = Wind_stress(speed, angle) |
---|
890 | |
---|
891 | The instantiated object W can be appended to the list of |
---|
892 | forcing_terms as in |
---|
893 | |
---|
894 | Alternatively, one vector valued function for (speed, angle) |
---|
895 | can be applied, providing both quantities simultaneously. |
---|
896 | As in |
---|
897 | W = Wind_stress(F), where returns (speed, angle) for each t. |
---|
898 | |
---|
899 | domain.forcing_terms.append(W) |
---|
900 | """ |
---|
901 | |
---|
902 | from config import rho_a, rho_w, eta_w |
---|
903 | from Numeric import array, Float |
---|
904 | |
---|
905 | if len(args) == 2: |
---|
906 | s = args[0] |
---|
907 | phi = args[1] |
---|
908 | elif len(args) == 1: |
---|
909 | #Assume vector function returning (s, phi)(t,x,y) |
---|
910 | vector_function = args[0] |
---|
911 | #s = lambda t,x,y: vector_function(t,x=x,y=y)[0] |
---|
912 | #phi = lambda t,x,y: vector_function(t,x=x,y=y)[1] |
---|
913 | s = lambda t,x: vector_function(t,x=x)[0] |
---|
914 | phi = lambda t,x: vector_function(t,x=x)[1] |
---|
915 | else: |
---|
916 | #Assume info is in 2 keyword arguments |
---|
917 | |
---|
918 | if len(kwargs) == 2: |
---|
919 | s = kwargs['s'] |
---|
920 | phi = kwargs['phi'] |
---|
921 | else: |
---|
922 | raise 'Assumes two keyword arguments: s=..., phi=....' |
---|
923 | |
---|
924 | print 'phi', phi |
---|
925 | self.speed = check_forcefield(s) |
---|
926 | self.phi = check_forcefield(phi) |
---|
927 | |
---|
928 | self.const = eta_w*rho_a/rho_w |
---|
929 | |
---|
930 | |
---|
931 | def __call__(self, domain): |
---|
932 | """Evaluate windfield based on values found in domain |
---|
933 | """ |
---|
934 | |
---|
935 | from math import pi, cos, sin, sqrt |
---|
936 | from Numeric import Float, ones, ArrayType |
---|
937 | |
---|
938 | xmom_update = domain.quantities['xmomentum'].explicit_update |
---|
939 | #ymom_update = domain.quantities['ymomentum'].explicit_update |
---|
940 | |
---|
941 | N = domain.number_of_elements |
---|
942 | t = domain.time |
---|
943 | |
---|
944 | if callable(self.speed): |
---|
945 | xc = domain.get_centroid_coordinates() |
---|
946 | #s_vec = self.speed(t, xc[:,0], xc[:,1]) |
---|
947 | s_vec = self.speed(t, xc) |
---|
948 | else: |
---|
949 | #Assume s is a scalar |
---|
950 | |
---|
951 | try: |
---|
952 | s_vec = self.speed * ones(N, Float) |
---|
953 | except: |
---|
954 | msg = 'Speed must be either callable or a scalar: %s' %self.s |
---|
955 | raise msg |
---|
956 | |
---|
957 | |
---|
958 | if callable(self.phi): |
---|
959 | xc = domain.get_centroid_coordinates() |
---|
960 | #phi_vec = self.phi(t, xc[:,0], xc[:,1]) |
---|
961 | phi_vec = self.phi(t, xc) |
---|
962 | else: |
---|
963 | #Assume phi is a scalar |
---|
964 | |
---|
965 | try: |
---|
966 | phi_vec = self.phi * ones(N, Float) |
---|
967 | except: |
---|
968 | msg = 'Angle must be either callable or a scalar: %s' %self.phi |
---|
969 | raise msg |
---|
970 | |
---|
971 | #assign_windfield_values(xmom_update, ymom_update, |
---|
972 | # s_vec, phi_vec, self.const) |
---|
973 | assign_windfield_values(xmom_update, s_vec, phi_vec, self.const) |
---|
974 | |
---|
975 | |
---|
976 | #def assign_windfield_values(xmom_update, ymom_update, |
---|
977 | # s_vec, phi_vec, const): |
---|
978 | def assign_windfield_values(xmom_update, s_vec, phi_vec, const): |
---|
979 | """Python version of assigning wind field to update vectors. |
---|
980 | A c version also exists (for speed) |
---|
981 | """ |
---|
982 | from math import pi, cos, sin, sqrt |
---|
983 | |
---|
984 | N = len(s_vec) |
---|
985 | for k in range(N): |
---|
986 | s = s_vec[k] |
---|
987 | phi = phi_vec[k] |
---|
988 | |
---|
989 | #Convert to radians |
---|
990 | phi = phi*pi/180 |
---|
991 | |
---|
992 | #Compute velocity vector (u, v) |
---|
993 | u = s*cos(phi) |
---|
994 | v = s*sin(phi) |
---|
995 | |
---|
996 | #Compute wind stress |
---|
997 | #S = const * sqrt(u**2 + v**2) |
---|
998 | S = const * u |
---|
999 | xmom_update[k] += S*u |
---|
1000 | #ymom_update[k] += S*v |
---|