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', 'height', 'velocity'] |
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56 | Generic_Domain.__init__(self, coordinates, boundary, |
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57 | conserved_quantities, other_quantities, |
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58 | tagged_elements) |
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59 | |
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60 | from config import minimum_allowed_height, g |
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61 | self.minimum_allowed_height = minimum_allowed_height |
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62 | self.g = g |
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63 | |
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64 | #forcing terms not included in 1d domain ? Why? |
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65 | self.forcing_terms.append(gravity) |
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66 | |
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67 | #Realtime visualisation |
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68 | self.visualiser = None |
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69 | self.visualise = False |
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70 | self.visualise_color_stage = False |
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71 | self.visualise_stage_range = 1.0 |
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72 | self.visualise_timer = True |
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73 | self.visualise_range_z = None |
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74 | |
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75 | #Stored output |
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76 | self.store = True |
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77 | self.format = 'sww' |
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78 | self.smooth = True |
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79 | |
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80 | #Evolve parametrs |
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81 | self.cfl = 1.0 |
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82 | |
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83 | #Reduction operation for get_vertex_values |
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84 | from util import mean |
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85 | self.reduction = mean |
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86 | #self.reduction = min #Looks better near steep slopes |
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87 | |
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88 | self.quantities_to_be_stored = ['stage', 'xmomentum', 'elevation'] |
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89 | |
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90 | self.__doc__ = 'shallow_water_domain_new' |
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91 | |
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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 initialise_visualiser(self,scale_z=1.0,rect=None): |
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125 | #Realtime visualisation |
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126 | if self.visualiser is None: |
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127 | from realtime_visualisation_new import Visualiser |
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128 | self.visualiser = Visualiser(self,scale_z,rect) |
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129 | self.visualiser.setup['elevation']=True |
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130 | self.visualiser.updating['stage']=True |
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131 | self.visualise = True |
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132 | if self.visualise_color_stage == True: |
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133 | self.visualiser.coloring['stage'] = True |
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134 | self.visualiser.qcolor['stage'] = (0.0, 0.0, 0.8) |
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135 | print 'initialise visualiser' |
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136 | print self.visualiser.setup |
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137 | print self.visualiser.updating |
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138 | |
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139 | def check_integrity(self): |
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140 | Generic_Domain.check_integrity(self) |
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141 | #Check that we are solving the shallow water wave equation |
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142 | |
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143 | msg = 'First conserved quantity must be "stage"' |
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144 | assert self.conserved_quantities[0] == 'stage', msg |
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145 | msg = 'Second conserved quantity must be "xmomentum"' |
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146 | assert self.conserved_quantities[1] == 'xmomentum', msg |
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147 | |
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148 | def extrapolate_second_order_sw(self): |
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149 | #Call correct module function |
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150 | #(either from this module or C-extension) |
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151 | extrapolate_second_order_sw(self) |
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152 | |
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153 | def compute_fluxes(self): |
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154 | #Call correct module function |
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155 | #(either from this module or C-extension) |
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156 | compute_fluxes_C_short(self) #compute_fluxes_C_wellbalanced(self) #compute_fluxes(self) #compute_fluxes_C_long(self) |
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157 | |
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158 | def compute_timestep(self): |
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159 | #Call correct module function |
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160 | compute_timestep(self) |
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161 | |
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162 | def distribute_to_vertices_and_edges(self): |
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163 | #Call correct module function |
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164 | #(either from this module or C-extension) |
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165 | distribute_to_vertices_and_edges(self) |
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166 | |
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167 | def evolve(self, yieldstep = None, |
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168 | finaltime = None, |
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169 | duration = None, |
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170 | skip_initial_step = False): |
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171 | """Specialisation of basic evolve method from parent class |
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172 | """ |
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173 | |
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174 | self.distribute_to_vertices_and_edges() |
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175 | |
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176 | for t in Generic_Domain.evolve(self, yieldstep, finaltime, duration, |
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177 | skip_initial_step): |
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178 | #Pass control on to outer loop for more specific actions |
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179 | yield(t) |
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180 | |
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181 | def initialise_storage(self): |
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182 | """Create and initialise self.writer object for storing data. |
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183 | Also, save x and bed elevation |
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184 | """ |
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185 | |
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186 | import data_manager |
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187 | |
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188 | #Initialise writer |
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189 | self.writer = data_manager.get_dataobject(self, mode = 'w') |
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190 | |
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191 | #Store vertices and connectivity |
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192 | self.writer.store_connectivity() |
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193 | |
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194 | |
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195 | def store_timestep(self, name): |
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196 | """Store named quantity and time. |
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197 | |
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198 | Precondition: |
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199 | self.write has been initialised |
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200 | """ |
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201 | self.writer.store_timestep(name) |
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202 | |
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203 | |
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204 | #=============== End of Shallow Water Domain =============================== |
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205 | def compute_timestep(domain): |
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206 | import sys |
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207 | from Numeric import zeros, Float |
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208 | |
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209 | N = domain.number_of_elements |
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210 | |
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211 | #Shortcuts |
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212 | Stage = domain.quantities['stage'] |
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213 | Xmom = domain.quantities['xmomentum'] |
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214 | Bed = domain.quantities['elevation'] |
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215 | |
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216 | stage = Stage.vertex_values |
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217 | xmom = Xmom.vertex_values |
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218 | bed = Bed.vertex_values |
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219 | |
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220 | stage_bdry = Stage.boundary_values |
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221 | xmom_bdry = Xmom.boundary_values |
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222 | |
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223 | flux = zeros(2, Float) #Work array for summing up fluxes |
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224 | ql = zeros(2, Float) |
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225 | qr = zeros(2, Float) |
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226 | |
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227 | #Loop |
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228 | timestep = float(sys.maxint) |
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229 | enter = True |
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230 | for k in range(N): |
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231 | |
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232 | flux[:] = 0. #Reset work array |
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233 | for i in range(2): |
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234 | #Quantities inside volume facing neighbour i |
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235 | ql = [stage[k, i], xmom[k, i]] |
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236 | zl = bed[k, i] |
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237 | |
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238 | #Quantities at neighbour on nearest face |
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239 | n = domain.neighbours[k,i] |
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240 | if n < 0: |
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241 | m = -n-1 #Convert negative flag to index |
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242 | qr[0] = stage_bdry[m] |
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243 | qr[1] = xmom_bdry[m] |
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244 | zr = zl #Extend bed elevation to boundary |
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245 | else: |
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246 | #m = domain.neighbour_edges[k,i] |
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247 | m = domain.neighbour_vertices[k,i] |
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248 | qr[0] = stage[n, m] |
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249 | qr[1] = xmom[n, m] |
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250 | zr = bed[n, m] |
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251 | |
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252 | |
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253 | #Outward pointing normal vector |
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254 | normal = domain.normals[k, i] |
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255 | |
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256 | #if domain.split == False: |
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257 | # edgeflux, max_speed = flux_function(normal, ql, qr, zl, zr) |
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258 | #elif domain.split == True: |
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259 | # edgeflux, max_speed = flux_function_split(normal, ql, qr, zl, zr) |
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260 | #Update optimal_timestep |
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261 | #try: |
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262 | # timestep = min(timestep, domain.cfl*0.5*domain.areas[k]/max_speed) |
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263 | #except ZeroDivisionError: |
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264 | # pass |
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265 | |
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266 | domain.timestep = timestep |
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267 | # |
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268 | def flux_function(normal, ql, qr, zl, zr): |
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269 | """Compute fluxes between volumes for the shallow water wave equation |
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270 | cast in terms of w = h+z using the 'central scheme' as described in |
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271 | |
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272 | Kurganov, Noelle, Petrova. 'Semidiscrete Central-Upwind Schemes For |
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273 | Hyperbolic Conservation Laws and Hamilton-Jacobi Equations'. |
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274 | Siam J. Sci. Comput. Vol. 23, No. 3, pp. 707-740. |
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275 | |
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276 | The implemented formula is given in equation (3.15) on page 714 |
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277 | |
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278 | Conserved quantities w, uh, are stored as elements 0 and 1 |
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279 | in the numerical vectors ql an qr. |
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280 | |
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281 | Bed elevations zl and zr. |
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282 | """ |
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283 | |
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284 | from config import g, epsilon |
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285 | from math import sqrt |
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286 | from Numeric import array |
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287 | |
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288 | #print 'ql',ql |
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289 | |
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290 | #Align momentums with x-axis |
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291 | q_left = ql |
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292 | q_left[1] = q_left[1]*normal |
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293 | q_right = qr |
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294 | q_right[1] = q_right[1]*normal |
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295 | |
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296 | z = 0.5*(zl+zr) #Take average of field values |
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297 | |
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298 | w_left = q_left[0] #w=h+z |
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299 | h_left = w_left-z |
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300 | uh_left = q_left[1] |
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301 | |
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302 | if h_left < epsilon: |
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303 | u_left = 0.0 #Could have been negative |
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304 | h_left = 0.0 |
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305 | else: |
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306 | u_left = uh_left/h_left |
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307 | |
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308 | |
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309 | w_right = q_right[0] #w=h+z |
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310 | h_right = w_right-z |
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311 | uh_right = q_right[1] |
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312 | |
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313 | |
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314 | if h_right < epsilon: |
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315 | u_right = 0.0 #Could have been negative |
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316 | h_right = 0.0 |
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317 | else: |
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318 | u_right = uh_right/h_right |
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319 | |
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320 | soundspeed_left = sqrt(g*h_left) |
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321 | soundspeed_right = sqrt(g*h_right) |
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322 | |
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323 | #Maximal wave speed |
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324 | s_max = max(u_left+soundspeed_left, u_right+soundspeed_right, 0) |
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325 | |
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326 | #Minimal wave speed |
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327 | s_min = min(u_left-soundspeed_left, u_right-soundspeed_right, 0) |
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328 | |
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329 | #Flux computation |
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330 | flux_left = array([u_left*h_left, |
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331 | u_left*uh_left + 0.5*g*h_left*h_left]) |
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332 | flux_right = array([u_right*h_right, |
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333 | u_right*uh_right + 0.5*g*h_right*h_right]) |
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334 | |
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335 | denom = s_max-s_min |
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336 | if denom == 0.0: |
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337 | edgeflux = array([0.0, 0.0]) |
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338 | max_speed = 0.0 |
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339 | else: |
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340 | edgeflux = (s_max*flux_left - s_min*flux_right)/denom |
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341 | edgeflux += s_max*s_min*(q_right-q_left)/denom |
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342 | |
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343 | edgeflux[1] = edgeflux[1]*normal |
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344 | |
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345 | max_speed = max(abs(s_max), abs(s_min)) |
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346 | |
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347 | return edgeflux, max_speed |
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348 | |
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349 | #The compute_fluxes is involving the flux_function above. |
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350 | def compute_fluxes(domain): |
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351 | """Compute all fluxes and the timestep suitable for all volumes |
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352 | in domain. |
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353 | |
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354 | Compute total flux for each conserved quantity using "flux_function" |
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355 | |
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356 | Fluxes across each edge are scaled by edgelengths and summed up |
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357 | Resulting flux is then scaled by area and stored in |
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358 | explicit_update for each of the three conserved quantities |
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359 | stage, xmomentum and ymomentum |
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360 | |
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361 | The maximal allowable speed computed by the flux_function for each volume |
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362 | is converted to a timestep that must not be exceeded. The minimum of |
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363 | those is computed as the next overall timestep. |
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364 | |
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365 | Post conditions: |
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366 | domain.explicit_update is reset to computed flux values |
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367 | domain.timestep is set to the largest step satisfying all volumes. |
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368 | """ |
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369 | |
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370 | import sys |
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371 | from Numeric import zeros, Float |
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372 | |
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373 | N = domain.number_of_elements |
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374 | |
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375 | #Shortcuts |
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376 | Stage = domain.quantities['stage'] |
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377 | Xmom = domain.quantities['xmomentum'] |
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378 | # Ymom = domain.quantities['ymomentum'] |
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379 | Bed = domain.quantities['elevation'] |
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380 | |
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381 | #Arrays |
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382 | stage = Stage.vertex_values |
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383 | xmom = Xmom.vertex_values |
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384 | bed = Bed.vertex_values |
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385 | |
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386 | stage_bdry = Stage.boundary_values |
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387 | xmom_bdry = Xmom.boundary_values |
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388 | |
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389 | flux = zeros(2, Float) #Work array for summing up fluxes |
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390 | ql = zeros(2, Float) |
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391 | qr = zeros(2, Float) |
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392 | |
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393 | #Loop |
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394 | timestep = float(sys.maxint) |
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395 | enter = True |
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396 | for k in range(N): |
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397 | |
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398 | flux[:] = 0. #Reset work array |
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399 | #for i in range(3): |
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400 | for i in range(2): |
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401 | #Quantities inside volume facing neighbour i |
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402 | ql = [stage[k, i], xmom[k, i]] |
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403 | zl = bed[k, i] |
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404 | |
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405 | #Quantities at neighbour on nearest face |
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406 | n = domain.neighbours[k,i] |
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407 | if n < 0: |
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408 | m = -n-1 #Convert negative flag to index |
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409 | qr[0] = stage_bdry[m] |
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410 | qr[1] = xmom_bdry[m] |
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411 | zr = zl #Extend bed elevation to boundary |
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412 | else: |
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413 | #m = domain.neighbour_edges[k,i] |
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414 | m = domain.neighbour_vertices[k,i] |
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415 | #qr = [stage[n, m], xmom[n, m], ymom[n, m]] |
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416 | qr[0] = stage[n, m] |
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417 | qr[1] = xmom[n, m] |
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418 | zr = bed[n, m] |
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419 | |
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420 | #Outward pointing normal vector |
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421 | normal = domain.normals[k, i] |
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422 | |
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423 | edgeflux, max_speed = flux_function(normal, ql, qr, zl, zr) |
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424 | |
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425 | # THIS IS THE LINE TO DEAL WITH LEFT AND RIGHT FLUXES |
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426 | # flux = edgefluxleft - edgefluxright |
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427 | flux -= edgeflux #* domain.edgelengths[k,i] |
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428 | #Update optimal_timestep |
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429 | try: |
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430 | #timestep = min(timestep, 0.5*domain.radii[k]/max_speed) |
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431 | timestep = min(timestep, domain.cfl*0.5*domain.areas[k]/max_speed) |
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432 | except ZeroDivisionError: |
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433 | pass |
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434 | |
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435 | #Normalise by area and store for when all conserved |
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436 | #quantities get updated |
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437 | flux /= domain.areas[k] |
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438 | |
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439 | Stage.explicit_update[k] = flux[0] |
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440 | Xmom.explicit_update[k] = flux[1] |
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441 | |
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442 | |
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443 | domain.flux_timestep = timestep |
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444 | #print domain.quantities['stage'].centroid_values |
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445 | |
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446 | |
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447 | # Compute flux definition |
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448 | def compute_fluxes_C_long(domain): |
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449 | from Numeric import zeros, Float |
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450 | import sys |
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451 | |
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452 | |
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453 | timestep = float(sys.maxint) |
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454 | epsilon = domain.epsilon |
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455 | g = domain.g |
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456 | neighbours = domain.neighbours |
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457 | neighbour_vertices = domain.neighbour_vertices |
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458 | normals = domain.normals |
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459 | areas = domain.areas |
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460 | stage_edge_values = domain.quantities['stage'].vertex_values |
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461 | xmom_edge_values = domain.quantities['xmomentum'].vertex_values |
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462 | bed_edge_values = domain.quantities['elevation'].vertex_values |
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463 | stage_boundary_values = domain.quantities['stage'].boundary_values |
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464 | xmom_boundary_values = domain.quantities['xmomentum'].boundary_values |
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465 | stage_explicit_update = domain.quantities['stage'].explicit_update |
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466 | xmom_explicit_update = domain.quantities['xmomentum'].explicit_update |
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467 | number_of_elements = len(stage_edge_values) |
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468 | max_speed_array = domain.max_speed_array |
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469 | |
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470 | from comp_flux_ext import compute_fluxes_ext |
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471 | |
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472 | domain.flux_timestep = compute_fluxes_ext(timestep, |
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473 | epsilon, |
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474 | g, |
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475 | neighbours, |
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476 | neighbour_vertices, |
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477 | normals, |
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478 | areas, |
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479 | stage_edge_values, |
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480 | xmom_edge_values, |
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481 | bed_edge_values, |
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482 | stage_boundary_values, |
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483 | xmom_boundary_values, |
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484 | stage_explicit_update, |
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485 | xmom_explicit_update, |
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486 | number_of_elements, |
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487 | max_speed_array) |
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488 | |
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489 | |
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490 | # Compute flux definition |
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491 | def compute_fluxes_C_short(domain): |
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492 | from Numeric import zeros, Float |
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493 | import sys |
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494 | |
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495 | |
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496 | timestep = float(sys.maxint) |
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497 | |
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498 | stage = domain.quantities['stage'] |
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499 | xmom = domain.quantities['xmomentum'] |
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500 | bed = domain.quantities['elevation'] |
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501 | |
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502 | |
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503 | from comp_flux_ext import compute_fluxes_ext_short |
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504 | |
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505 | domain.flux_timestep = compute_fluxes_ext_short(timestep,domain,stage,xmom,bed) |
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506 | |
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507 | |
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508 | def compute_fluxes_C_wellbalanced(domain): |
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509 | from Numeric import zeros, Float |
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510 | import sys |
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511 | |
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512 | |
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513 | timestep = float(sys.maxint) |
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514 | epsilon = domain.epsilon |
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515 | g = domain.g |
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516 | neighbours = domain.neighbours |
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517 | neighbour_vertices = domain.neighbour_vertices |
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518 | normals = domain.normals |
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519 | areas = domain.areas |
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520 | stage_edge_values = domain.quantities['stage'].vertex_values |
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521 | xmom_edge_values = domain.quantities['xmomentum'].vertex_values |
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522 | bed_edge_values = domain.quantities['elevation'].vertex_values |
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523 | stage_boundary_values = domain.quantities['stage'].boundary_values |
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524 | xmom_boundary_values = domain.quantities['xmomentum'].boundary_values |
---|
525 | stage_explicit_update = domain.quantities['stage'].explicit_update |
---|
526 | xmom_explicit_update = domain.quantities['xmomentum'].explicit_update |
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527 | number_of_elements = len(stage_edge_values) |
---|
528 | max_speed_array = domain.max_speed_array |
---|
529 | |
---|
530 | from comp_flux_ext_wellbalanced import compute_fluxes_ext_wellbalanced #from comp_flux_ext import compute_fluxes_ext |
---|
531 | |
---|
532 | domain.flux_timestep = compute_fluxes_ext_wellbalanced(timestep, |
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533 | epsilon, |
---|
534 | g, |
---|
535 | neighbours, |
---|
536 | neighbour_vertices, |
---|
537 | normals, |
---|
538 | areas, |
---|
539 | stage_edge_values, |
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540 | xmom_edge_values, |
---|
541 | bed_edge_values, |
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542 | stage_boundary_values, |
---|
543 | xmom_boundary_values, |
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544 | stage_explicit_update, |
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545 | xmom_explicit_update, |
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546 | number_of_elements, |
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547 | max_speed_array) |
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548 | |
---|
549 | # ################################### |
---|
550 | |
---|
551 | |
---|
552 | |
---|
553 | |
---|
554 | |
---|
555 | |
---|
556 | # Module functions for gradient limiting (distribute_to_vertices_and_edges) |
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557 | |
---|
558 | def distribute_to_vertices_and_edges(domain): |
---|
559 | """Distribution from centroids to vertices specific to the |
---|
560 | shallow water wave |
---|
561 | equation. |
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562 | |
---|
563 | It will ensure that h (w-z) is always non-negative even in the |
---|
564 | presence of steep bed-slopes by taking a weighted average between shallow |
---|
565 | and deep cases. |
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566 | |
---|
567 | In addition, all conserved quantities get distributed as per either a |
---|
568 | constant (order==1) or a piecewise linear function (order==2). |
---|
569 | |
---|
570 | FIXME: more explanation about removal of artificial variability etc |
---|
571 | |
---|
572 | Precondition: |
---|
573 | All quantities defined at centroids and bed elevation defined at |
---|
574 | vertices. |
---|
575 | |
---|
576 | Postcondition |
---|
577 | Conserved quantities defined at vertices |
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578 | |
---|
579 | """ |
---|
580 | |
---|
581 | #from config import optimised_gradient_limiter |
---|
582 | |
---|
583 | #Remove very thin layers of water |
---|
584 | protect_against_infinitesimal_and_negative_heights(domain) |
---|
585 | |
---|
586 | |
---|
587 | for name in domain.conserved_quantities: |
---|
588 | Q = domain.quantities[name] |
---|
589 | if domain.order == 1: |
---|
590 | Q.extrapolate_first_order() |
---|
591 | elif domain.order == 2: |
---|
592 | #print "add extrapolate second order to shallow water" |
---|
593 | #if name != 'height': |
---|
594 | Q.extrapolate_second_order() |
---|
595 | #Q.limit() |
---|
596 | else: |
---|
597 | raise 'Unknown order' |
---|
598 | |
---|
599 | |
---|
600 | def protect_against_infinitesimal_and_negative_heights(domain): |
---|
601 | """Protect against infinitesimal heights and associated high velocities |
---|
602 | """ |
---|
603 | |
---|
604 | #Shortcuts |
---|
605 | wc = domain.quantities['stage'].centroid_values |
---|
606 | zc = domain.quantities['elevation'].centroid_values |
---|
607 | xmomc = domain.quantities['xmomentum'].centroid_values |
---|
608 | # ymomc = domain.quantities['ymomentum'].centroid_values |
---|
609 | hc = wc - zc #Water depths at centroids |
---|
610 | |
---|
611 | zv = domain.quantities['elevation'].vertex_values |
---|
612 | wv = domain.quantities['stage'].vertex_values |
---|
613 | hv = wv-zv |
---|
614 | xmomv = domain.quantities['xmomentum'].vertex_values |
---|
615 | #remove the above two lines and corresponding code below |
---|
616 | |
---|
617 | #Update |
---|
618 | for k in range(domain.number_of_elements): |
---|
619 | |
---|
620 | if hc[k] < domain.minimum_allowed_height: |
---|
621 | #Control stage |
---|
622 | if hc[k] < domain.epsilon: |
---|
623 | wc[k] = zc[k] # Contain 'lost mass' error |
---|
624 | wv[k,0] = zv[k,0] |
---|
625 | wv[k,1] = zv[k,1] |
---|
626 | |
---|
627 | xmomc[k] = 0.0 |
---|
628 | |
---|
629 | |
---|
630 | |
---|
631 | def h_limiter(domain): |
---|
632 | """Limit slopes for each volume to eliminate artificial variance |
---|
633 | introduced by e.g. second order extrapolator |
---|
634 | |
---|
635 | limit on h = w-z |
---|
636 | |
---|
637 | This limiter depends on two quantities (w,z) so it resides within |
---|
638 | this module rather than within quantity.py |
---|
639 | """ |
---|
640 | |
---|
641 | from Numeric import zeros, Float |
---|
642 | |
---|
643 | N = domain.number_of_elements |
---|
644 | beta_h = domain.beta_h |
---|
645 | |
---|
646 | #Shortcuts |
---|
647 | wc = domain.quantities['stage'].centroid_values |
---|
648 | zc = domain.quantities['elevation'].centroid_values |
---|
649 | hc = wc - zc |
---|
650 | |
---|
651 | wv = domain.quantities['stage'].vertex_values |
---|
652 | zv = domain.quantities['elevation'].vertex_values |
---|
653 | hv = wv-zv |
---|
654 | |
---|
655 | hvbar = zeros(hv.shape, Float) #h-limited values |
---|
656 | |
---|
657 | #Find min and max of this and neighbour's centroid values |
---|
658 | hmax = zeros(hc.shape, Float) |
---|
659 | hmin = zeros(hc.shape, Float) |
---|
660 | |
---|
661 | for k in range(N): |
---|
662 | hmax[k] = hmin[k] = hc[k] |
---|
663 | #for i in range(3): |
---|
664 | for i in range(2): |
---|
665 | n = domain.neighbours[k,i] |
---|
666 | if n >= 0: |
---|
667 | hn = hc[n] #Neighbour's centroid value |
---|
668 | |
---|
669 | hmin[k] = min(hmin[k], hn) |
---|
670 | hmax[k] = max(hmax[k], hn) |
---|
671 | |
---|
672 | |
---|
673 | #Diffences between centroids and maxima/minima |
---|
674 | dhmax = hmax - hc |
---|
675 | dhmin = hmin - hc |
---|
676 | |
---|
677 | #Deltas between vertex and centroid values |
---|
678 | dh = zeros(hv.shape, Float) |
---|
679 | #for i in range(3): |
---|
680 | for i in range(2): |
---|
681 | dh[:,i] = hv[:,i] - hc |
---|
682 | |
---|
683 | #Phi limiter |
---|
684 | for k in range(N): |
---|
685 | |
---|
686 | #Find the gradient limiter (phi) across vertices |
---|
687 | phi = 1.0 |
---|
688 | #for i in range(3): |
---|
689 | for i in range(2): |
---|
690 | r = 1.0 |
---|
691 | if (dh[k,i] > 0): r = dhmax[k]/dh[k,i] |
---|
692 | if (dh[k,i] < 0): r = dhmin[k]/dh[k,i] |
---|
693 | |
---|
694 | phi = min( min(r*beta_h, 1), phi ) |
---|
695 | |
---|
696 | #Then update using phi limiter |
---|
697 | #for i in range(3): |
---|
698 | for i in range(2): |
---|
699 | hvbar[k,i] = hc[k] + phi*dh[k,i] |
---|
700 | |
---|
701 | return hvbar |
---|
702 | |
---|
703 | def balance_deep_and_shallow(domain): |
---|
704 | """Compute linear combination between stage as computed by |
---|
705 | gradient-limiters limiting using w, and stage computed by |
---|
706 | gradient-limiters limiting using h (h-limiter). |
---|
707 | The former takes precedence when heights are large compared to the |
---|
708 | bed slope while the latter takes precedence when heights are |
---|
709 | relatively small. Anything in between is computed as a balanced |
---|
710 | linear combination in order to avoid numerical disturbances which |
---|
711 | would otherwise appear as a result of hard switching between |
---|
712 | modes. |
---|
713 | |
---|
714 | The h-limiter is always applied irrespective of the order. |
---|
715 | """ |
---|
716 | |
---|
717 | #Shortcuts |
---|
718 | wc = domain.quantities['stage'].centroid_values |
---|
719 | zc = domain.quantities['elevation'].centroid_values |
---|
720 | hc = wc - zc |
---|
721 | |
---|
722 | wv = domain.quantities['stage'].vertex_values |
---|
723 | zv = domain.quantities['elevation'].vertex_values |
---|
724 | hv = wv-zv |
---|
725 | |
---|
726 | #Limit h |
---|
727 | hvbar = h_limiter(domain) |
---|
728 | |
---|
729 | for k in range(domain.number_of_elements): |
---|
730 | |
---|
731 | dz = max(abs(zv[k,0]-zc[k]), |
---|
732 | abs(zv[k,1]-zc[k]))#, |
---|
733 | # abs(zv[k,2]-zc[k])) |
---|
734 | |
---|
735 | |
---|
736 | hmin = min( hv[k,:] ) |
---|
737 | |
---|
738 | if dz > 0.0: |
---|
739 | alpha = max( min( 2*hmin/dz, 1.0), 0.0 ) |
---|
740 | else: |
---|
741 | #Flat bed |
---|
742 | alpha = 1.0 |
---|
743 | |
---|
744 | alpha = 0.0 |
---|
745 | |
---|
746 | if alpha < 1: |
---|
747 | |
---|
748 | #for i in range(3): |
---|
749 | for i in range(2): |
---|
750 | wv[k,i] = zv[k,i] + (1.0-alpha)*hvbar[k,i] + alpha*hv[k,i] |
---|
751 | |
---|
752 | #Momentums at centroids |
---|
753 | xmomc = domain.quantities['xmomentum'].centroid_values |
---|
754 | # ymomc = domain.quantities['ymomentum'].centroid_values |
---|
755 | |
---|
756 | #Momentums at vertices |
---|
757 | xmomv = domain.quantities['xmomentum'].vertex_values |
---|
758 | # ymomv = domain.quantities['ymomentum'].vertex_values |
---|
759 | |
---|
760 | # Update momentum as a linear combination of |
---|
761 | # xmomc and ymomc (shallow) and momentum |
---|
762 | # from extrapolator xmomv and ymomv (deep). |
---|
763 | xmomv[k,:] = (1.0-alpha)*xmomc[k] + alpha*xmomv[k,:] |
---|
764 | # ymomv[k,:] = (1-alpha)*ymomc[k] + alpha*ymomv[k,:] |
---|
765 | |
---|
766 | |
---|
767 | # ############################################## |
---|
768 | #Boundaries - specific to the shallow water wave equation |
---|
769 | class Reflective_boundary(Boundary): |
---|
770 | """Reflective boundary returns same conserved quantities as |
---|
771 | those present in its neighbour volume but reflected. |
---|
772 | |
---|
773 | This class is specific to the shallow water equation as it |
---|
774 | works with the momentum quantities assumed to be the second |
---|
775 | and third conserved quantities. |
---|
776 | """ |
---|
777 | |
---|
778 | def __init__(self, domain = None): |
---|
779 | Boundary.__init__(self) |
---|
780 | |
---|
781 | if domain is None: |
---|
782 | msg = 'Domain must be specified for reflective boundary' |
---|
783 | raise msg |
---|
784 | |
---|
785 | #Handy shorthands |
---|
786 | self.normals = domain.normals |
---|
787 | self.stage = domain.quantities['stage'].vertex_values |
---|
788 | self.xmom = domain.quantities['xmomentum'].vertex_values |
---|
789 | |
---|
790 | from Numeric import zeros, Float |
---|
791 | #self.conserved_quantities = zeros(3, Float) |
---|
792 | self.conserved_quantities = zeros(2, Float) |
---|
793 | |
---|
794 | def __repr__(self): |
---|
795 | return 'Reflective_boundary' |
---|
796 | |
---|
797 | |
---|
798 | def evaluate(self, vol_id, edge_id): |
---|
799 | """Reflective boundaries reverses the outward momentum |
---|
800 | of the volume they serve. |
---|
801 | """ |
---|
802 | |
---|
803 | q = self.conserved_quantities |
---|
804 | q[0] = self.stage[vol_id, edge_id] |
---|
805 | q[1] = self.xmom[vol_id, edge_id] |
---|
806 | normal = self.normals[vol_id,edge_id] |
---|
807 | |
---|
808 | r = q |
---|
809 | r[1] = normal*r[1] |
---|
810 | r[1] = -r[1] |
---|
811 | r[1] = normal*r[1] |
---|
812 | q = r |
---|
813 | #For start interval there is no outward momentum so do not need to |
---|
814 | #reverse direction in this case |
---|
815 | |
---|
816 | return q |
---|
817 | |
---|
818 | class Dirichlet_boundary(Boundary): |
---|
819 | """Dirichlet boundary returns constant values for the |
---|
820 | conserved quantities |
---|
821 | """ |
---|
822 | |
---|
823 | |
---|
824 | def __init__(self, conserved_quantities=None): |
---|
825 | Boundary.__init__(self) |
---|
826 | |
---|
827 | if conserved_quantities is None: |
---|
828 | msg = 'Must specify one value for each conserved quantity' |
---|
829 | raise msg |
---|
830 | |
---|
831 | from Numeric import array, Float |
---|
832 | self.conserved_quantities=array(conserved_quantities).astype(Float) |
---|
833 | |
---|
834 | def __repr__(self): |
---|
835 | return 'Dirichlet boundary (%s)' %self.conserved_quantities |
---|
836 | |
---|
837 | def evaluate(self, vol_id=None, edge_id=None): |
---|
838 | return self.conserved_quantities |
---|
839 | |
---|
840 | |
---|
841 | # ######################## |
---|
842 | #Standard forcing terms: |
---|
843 | def gravity(domain): |
---|
844 | """Apply gravitational pull in the presence of bed slope |
---|
845 | """ |
---|
846 | |
---|
847 | from util import gradient |
---|
848 | from Numeric import zeros, Float, array, sum |
---|
849 | |
---|
850 | xmom = domain.quantities['xmomentum'].explicit_update |
---|
851 | stage = domain.quantities['stage'].explicit_update |
---|
852 | # ymom = domain.quantities['ymomentum'].explicit_update |
---|
853 | |
---|
854 | Stage = domain.quantities['stage'] |
---|
855 | Elevation = domain.quantities['elevation'] |
---|
856 | #h = Stage.edge_values - Elevation.edge_values |
---|
857 | h = Stage.vertex_values - Elevation.vertex_values |
---|
858 | b = Elevation.vertex_values |
---|
859 | w = Stage.vertex_values |
---|
860 | |
---|
861 | x = domain.get_vertex_coordinates() |
---|
862 | g = domain.g |
---|
863 | |
---|
864 | for k in range(domain.number_of_elements): |
---|
865 | # avg_h = sum( h[k,:] )/3 |
---|
866 | avg_h = sum( h[k,:] )/2 |
---|
867 | |
---|
868 | #Compute bed slope |
---|
869 | #x0, y0, x1, y1, x2, y2 = x[k,:] |
---|
870 | x0, x1 = x[k,:] |
---|
871 | #z0, z1, z2 = v[k,:] |
---|
872 | b0, b1 = b[k,:] |
---|
873 | |
---|
874 | w0, w1 = w[k,:] |
---|
875 | wx = gradient(x0, x1, w0, w1) |
---|
876 | |
---|
877 | #zx, zy = gradient(x0, y0, x1, y1, x2, y2, z0, z1, z2) |
---|
878 | bx = gradient(x0, x1, b0, b1) |
---|
879 | |
---|
880 | #Update momentum (explicit update is reset to source values) |
---|
881 | xmom[k] += -g*bx*avg_h |
---|
882 | #xmom[k] = -g*bx*avg_h |
---|
883 | #stage[k] = 0.0 |
---|
884 | |
---|
885 | |
---|
886 | |
---|
887 | def check_forcefield(f): |
---|
888 | """Check that f is either |
---|
889 | 1: a callable object f(t,x,y), where x and y are vectors |
---|
890 | and that it returns an array or a list of same length |
---|
891 | as x and y |
---|
892 | 2: a scalar |
---|
893 | """ |
---|
894 | |
---|
895 | from Numeric import ones, Float, array |
---|
896 | |
---|
897 | |
---|
898 | if callable(f): |
---|
899 | #N = 3 |
---|
900 | N = 2 |
---|
901 | #x = ones(3, Float) |
---|
902 | #y = ones(3, Float) |
---|
903 | x = ones(2, Float) |
---|
904 | #y = ones(2, Float) |
---|
905 | |
---|
906 | try: |
---|
907 | #q = f(1.0, x=x, y=y) |
---|
908 | q = f(1.0, x=x) |
---|
909 | except Exception, e: |
---|
910 | msg = 'Function %s could not be executed:\n%s' %(f, e) |
---|
911 | #FIXME: Reconsider this semantics |
---|
912 | raise msg |
---|
913 | |
---|
914 | try: |
---|
915 | q = array(q).astype(Float) |
---|
916 | except: |
---|
917 | msg = 'Return value from vector function %s could ' %f |
---|
918 | msg += 'not be converted into a Numeric array of floats.\n' |
---|
919 | msg += 'Specified function should return either list or array.' |
---|
920 | raise msg |
---|
921 | |
---|
922 | #Is this really what we want? |
---|
923 | msg = 'Return vector from function %s ' %f |
---|
924 | msg += 'must have same lenght as input vectors' |
---|
925 | assert len(q) == N, msg |
---|
926 | |
---|
927 | else: |
---|
928 | try: |
---|
929 | f = float(f) |
---|
930 | except: |
---|
931 | msg = 'Force field %s must be either a scalar' %f |
---|
932 | msg += ' or a vector function' |
---|
933 | raise msg |
---|
934 | return f |
---|