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 | John Jakeman, Ole Nielsen, Stephen Roberts, Duncan Gray, Christopher Zoppou |
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41 | Geoscience Australia, 2006 |
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42 | |
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43 | Sudi Mungkasi, ANU, 2010 |
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44 | """ |
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45 | |
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46 | |
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47 | from domain import * |
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48 | Generic_Domain = Domain #Rename |
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49 | |
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50 | #Shallow water domain |
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51 | class Domain(Generic_Domain): |
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52 | |
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53 | def __init__(self, coordinates, boundary = None, tagged_elements = None): |
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54 | conserved_quantities = ['stage', 'xmomentum'] #['height', 'xmomentum'] |
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55 | evolved_quantities = ['stage', 'xmomentum', 'elevation', 'height', 'velocity'] |
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56 | other_quantities = ['friction'] |
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57 | Generic_Domain.__init__(self, coordinates, boundary, |
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58 | conserved_quantities, evolved_quantities, other_quantities, |
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59 | tagged_elements) |
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60 | |
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61 | from config import minimum_allowed_height, g, h0 |
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62 | self.minimum_allowed_height = minimum_allowed_height |
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63 | self.g = g |
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64 | self.h0 = h0 |
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65 | |
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66 | self.forcing_terms.append(gravity_F2) |
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67 | #self.forcing_terms.append(manning_friction) |
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68 | |
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69 | #Realtime visualisation |
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70 | self.visualiser = None |
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71 | self.visualise = False |
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72 | self.visualise_color_stage = False |
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73 | self.visualise_stage_range = 1.0 |
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74 | self.visualise_timer = True |
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75 | self.visualise_range_z = None |
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76 | |
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77 | #Stored output |
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78 | self.store = True |
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79 | self.format = 'sww' |
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80 | self.smooth = True |
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81 | |
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82 | #Evolve parametrs |
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83 | self.cfl = 1.0 |
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84 | |
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85 | #Reduction operation for get_vertex_values |
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86 | from util import mean |
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87 | self.reduction = mean |
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88 | #self.reduction = min #Looks better near steep slopes |
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89 | |
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90 | self.quantities_to_be_stored = ['stage','xmomentum'] |
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91 | |
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92 | self.__doc__ = 'sww_domain_simplified' |
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93 | self.check_integrity() |
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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 | if q is None: |
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111 | self.quantities_to_be_stored = [] |
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112 | self.store = False |
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113 | return |
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114 | |
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115 | if isinstance(q, basestring): |
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116 | q = [q] # Turn argument into a list |
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117 | |
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118 | #Check correcness |
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119 | for quantity_name in q: |
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120 | msg = 'Quantity %s is not a valid conserved quantity' %quantity_name |
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121 | assert quantity_name in self.conserved_quantities, msg |
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122 | |
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123 | self.quantities_to_be_stored = q |
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124 | |
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125 | |
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126 | def initialise_visualiser(self,scale_z=1.0,rect=None): |
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127 | #Realtime visualisation |
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128 | if self.visualiser is None: |
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129 | from realtime_visualisation_new import Visualiser |
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130 | self.visualiser = Visualiser(self,scale_z,rect) |
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131 | self.visualiser.setup['elevation']=True |
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132 | self.visualiser.updating['stage']=True |
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133 | self.visualise = True |
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134 | if self.visualise_color_stage == True: |
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135 | self.visualiser.coloring['stage'] = True |
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136 | self.visualiser.qcolor['stage'] = (0.0, 0.0, 0.8) |
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137 | print 'initialise visualiser' |
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138 | print self.visualiser.setup |
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139 | print self.visualiser.updating |
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140 | |
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141 | def check_integrity(self): |
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142 | Generic_Domain.check_integrity(self) |
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143 | #Check that we are solving the shallow water wave equation |
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144 | |
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145 | msg = 'First conserved quantity must be "stage"' |
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146 | assert self.conserved_quantities[0] == 'stage', msg |
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147 | msg = 'Second conserved quantity must be "xmomentum"' |
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148 | assert self.conserved_quantities[1] == 'xmomentum', msg |
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149 | |
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150 | msg = 'First evolved quantity must be "stage"' |
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151 | assert self.evolved_quantities[0] == 'stage', msg |
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152 | msg = 'Second evolved quantity must be "xmomentum"' |
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153 | assert self.evolved_quantities[1] == 'xmomentum', msg |
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154 | msg = 'Third evolved quantity must be "elevation"' |
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155 | assert self.evolved_quantities[2] == 'elevation', msg |
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156 | msg = 'Fourth evolved quantity must be "height"' |
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157 | assert self.evolved_quantities[3] == 'height', msg |
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158 | msg = 'Fifth evolved quantity must be "velocity"' |
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159 | assert self.evolved_quantities[4] == 'velocity', msg |
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160 | |
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161 | def extrapolate_second_order_sw(self): |
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162 | #Call correct module function |
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163 | #(either from this module or C-extension) |
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164 | extrapolate_second_order_sw(self) |
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165 | |
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166 | def compute_fluxes(self): |
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167 | #Call correct module function(either from this module or C-extension) |
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168 | compute_fluxes_C_wellbalanced(self) |
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169 | #compute_fluxes_C_nonwellbalanced2(self) |
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170 | |
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171 | def compute_timestep(self): |
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172 | #Call correct module function |
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173 | compute_timestep(self) |
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174 | |
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175 | def distribute_to_vertices_and_edges(self): |
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176 | #Call correct module function(either from this module or C-extension) |
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177 | #distribute_to_vertices_and_edges_shv(self) |
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178 | distribute_to_vertices_and_edges_shm(self) |
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179 | |
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180 | def evolve(self, yieldstep = None, finaltime = None, duration = None, skip_initial_step = False): |
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181 | #Call basic machinery from parent class |
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182 | for t in Generic_Domain.evolve(self, yieldstep, finaltime, duration, skip_initial_step): |
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183 | yield(t) |
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184 | |
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185 | def initialise_storage(self): |
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186 | """Create and initialise self.writer object for storing data. |
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187 | Also, save x and bed elevation |
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188 | """ |
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189 | |
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190 | import data_manager |
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191 | |
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192 | #Initialise writer |
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193 | self.writer = data_manager.get_dataobject(self, mode = 'w') |
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194 | |
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195 | #Store vertices and connectivity |
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196 | self.writer.store_connectivity() |
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197 | |
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198 | |
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199 | def store_timestep(self, name): |
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200 | """Store named quantity and time. |
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201 | |
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202 | Precondition: |
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203 | self.write has been initialised |
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204 | """ |
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205 | self.writer.store_timestep(name) |
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206 | |
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207 | |
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208 | #=============== End of Shallow Water Domain =============================== |
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209 | |
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210 | # Compute flux definition |
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211 | # ################################### |
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212 | def compute_fluxes_C_wellbalanced(domain): |
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213 | import sys |
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214 | from Numeric import Float |
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215 | from numpy import zeros |
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216 | |
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217 | N = domain.number_of_elements |
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218 | timestep = float(sys.maxint) |
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219 | epsilon = domain.epsilon |
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220 | g = domain.g |
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221 | neighbours = domain.neighbours |
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222 | neighbour_vertices = domain.neighbour_vertices |
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223 | normals = domain.normals |
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224 | areas = domain.areas |
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225 | |
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226 | Stage = domain.quantities['stage'] |
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227 | Xmom = domain.quantities['xmomentum'] |
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228 | Bed = domain.quantities['elevation'] |
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229 | Height = domain.quantities['height'] |
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230 | Velocity = domain.quantities['velocity'] |
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231 | |
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232 | |
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233 | stage_boundary_values = Stage.boundary_values |
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234 | xmom_boundary_values = Xmom.boundary_values |
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235 | bed_boundary_values = Bed.boundary_values |
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236 | height_boundary_values= Height.boundary_values |
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237 | vel_boundary_values = Velocity.boundary_values |
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238 | |
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239 | stage_explicit_update = Stage.explicit_update |
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240 | xmom_explicit_update = Xmom.explicit_update |
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241 | bed_explicit_values = Bed.explicit_update |
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242 | height_explicit_values= Height.explicit_update |
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243 | vel_explicit_values = Velocity.explicit_update |
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244 | |
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245 | max_speed_array = domain.max_speed_array |
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246 | |
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247 | domain.distribute_to_vertices_and_edges() |
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248 | domain.update_boundary() |
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249 | |
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250 | stage_V = Stage.vertex_values |
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251 | xmom_V = Xmom.vertex_values |
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252 | bed_V = Bed.vertex_values |
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253 | height_V= Height.vertex_values |
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254 | vel_V = Velocity.vertex_values |
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255 | |
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256 | number_of_elements = len(stage_V) |
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257 | |
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258 | from comp_flux_ext_wellbalanced import compute_fluxes_ext_wellbalanced |
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259 | domain.flux_timestep = compute_fluxes_ext_wellbalanced(timestep, |
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260 | epsilon, |
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261 | g, |
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262 | |
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263 | neighbours, |
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264 | neighbour_vertices, |
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265 | normals, |
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266 | areas, |
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267 | |
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268 | stage_V, |
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269 | xmom_V, |
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270 | bed_V, |
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271 | height_V, |
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272 | vel_V, |
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273 | |
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274 | stage_boundary_values, |
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275 | xmom_boundary_values, |
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276 | bed_boundary_values, |
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277 | height_boundary_values, |
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278 | vel_boundary_values, |
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279 | |
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280 | stage_explicit_update, |
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281 | xmom_explicit_update, |
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282 | bed_explicit_values, |
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283 | height_explicit_values, |
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284 | vel_explicit_values, |
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285 | |
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286 | number_of_elements, |
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287 | max_speed_array) |
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288 | |
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289 | |
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290 | # ################################### |
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291 | # Module functions for gradient limiting (distribute_to_vertices_and_edges) |
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292 | def distribute_to_vertices_and_edges_shv(domain): |
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293 | """Distribution from centroids to vertices specific to the |
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294 | shallow water wave |
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295 | equation. |
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296 | |
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297 | It will ensure that h (w-z) is always non-negative even in the |
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298 | presence of steep bed-slopes by taking a weighted average between shallow |
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299 | and deep cases. |
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300 | |
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301 | In addition, all conserved quantities get distributed as per either a |
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302 | constant (order==1) or a piecewise linear function (order==2). |
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303 | |
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304 | FIXME: more explanation about removal of artificial variability etc |
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305 | |
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306 | Precondition: |
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307 | All quantities defined at centroids and bed elevation defined at |
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308 | vertices. |
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309 | |
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310 | Postcondition |
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311 | Conserved quantities defined at vertices |
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312 | |
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313 | """ |
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314 | |
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315 | #from config import optimised_gradient_limiter |
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316 | |
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317 | #Remove very thin layers of water |
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318 | #protect_against_infinitesimal_and_negative_heights(domain) |
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319 | |
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320 | import sys |
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321 | from Numeric import Float |
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322 | from numpy import zeros |
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323 | from config import epsilon, h0 |
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324 | |
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325 | N = domain.number_of_elements |
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326 | |
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327 | #Shortcuts |
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328 | Stage = domain.quantities['stage'] |
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329 | Xmom = domain.quantities['xmomentum'] |
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330 | Bed = domain.quantities['elevation'] |
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331 | Height = domain.quantities['height'] |
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332 | Velocity = domain.quantities['velocity'] |
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333 | |
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334 | #Arrays |
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335 | w_C = Stage.centroid_values |
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336 | uh_C = Xmom.centroid_values |
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337 | z_C = Bed.centroid_values |
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338 | h_C = Height.centroid_values |
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339 | u_C = Velocity.centroid_values |
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340 | |
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341 | for i in range(N): |
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342 | h_C[i] = w_C[i] - z_C[i] |
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343 | if h_C[i] <= epsilon: |
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344 | uh_C[i] = 0.0 |
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345 | u_C[i] = 0.0 |
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346 | #w_C[i] = z_C[i] |
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347 | else: |
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348 | u_C[i] = uh_C[i]/(h_C[i] + h0/h_C[i]) |
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349 | |
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350 | for name in ['stage', 'height', 'velocity']: |
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351 | Q = domain.quantities[name] |
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352 | if domain.order == 1: |
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353 | Q.extrapolate_first_order() |
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354 | elif domain.order == 2: |
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355 | Q.extrapolate_second_order() |
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356 | else: |
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357 | raise 'Unknown order' |
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358 | |
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359 | stage_V = domain.quantities['stage'].vertex_values |
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360 | bed_V = domain.quantities['elevation'].vertex_values |
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361 | h_V = domain.quantities['height'].vertex_values |
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362 | u_V = domain.quantities['velocity'].vertex_values |
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363 | xmom_V = domain.quantities['xmomentum'].vertex_values |
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364 | |
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365 | bed_V[:] = stage_V - h_V |
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366 | xmom_V[:] = u_V * h_V |
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367 | |
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368 | return |
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369 | |
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370 | def distribute_to_vertices_and_edges_shm(domain): |
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371 | # shm stands for STAGE, HEIGHT, MOMENTUM |
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372 | """Distribution from centroids to vertices specific to the |
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373 | shallow water wave |
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374 | equation. |
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375 | |
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376 | It will ensure that h (w-z) is always non-negative even in the |
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377 | presence of steep bed-slopes by taking a weighted average between shallow |
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378 | and deep cases. |
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379 | |
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380 | In addition, all conserved quantities get distributed as per either a |
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381 | constant (order==1) or a piecewise linear function (order==2). |
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382 | |
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383 | FIXME: more explanation about removal of artificial variability etc |
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384 | |
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385 | Precondition: |
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386 | All quantities defined at centroids and bed elevation defined at |
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387 | vertices. |
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388 | |
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389 | Postcondition |
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390 | Conserved quantities defined at vertices |
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391 | |
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392 | """ |
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393 | |
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394 | #from config import optimised_gradient_limiter |
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395 | |
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396 | #Remove very thin layers of water |
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397 | #protect_against_infinitesimal_and_negative_heights(domain) |
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398 | |
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399 | import sys |
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400 | from Numeric import Float |
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401 | from numpy import array, zeros |
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402 | from config import epsilon, h0 |
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403 | |
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404 | N = domain.number_of_elements |
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405 | |
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406 | #Shortcuts |
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407 | Stage = domain.quantities['stage'] |
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408 | Xmom = domain.quantities['xmomentum'] |
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409 | Bed = domain.quantities['elevation'] |
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410 | Height = domain.quantities['height'] |
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411 | Velocity = domain.quantities['velocity'] |
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412 | |
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413 | #Arrays |
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414 | w_C = Stage.centroid_values |
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415 | uh_C = Xmom.centroid_values |
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416 | z_C = Bed.centroid_values |
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417 | h_C = Height.centroid_values |
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418 | u_C = Velocity.centroid_values |
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419 | |
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420 | |
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421 | for i in range(N): |
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422 | h_C[i] = w_C[i] - z_C[i] |
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423 | if h_C[i] <= epsilon: |
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424 | uh_C[i] = 0.0 |
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425 | u_C[i] = 0.0 |
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426 | else: |
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427 | u_C[i] = uh_C[i]/(h_C[i] + h0/h_C[i]) |
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428 | |
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429 | for name in ['stage', 'height', 'xmomentum']: |
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430 | Q = domain.quantities[name] |
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431 | if domain.order == 1: |
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432 | Q.extrapolate_first_order() |
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433 | elif domain.order == 2: |
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434 | Q.extrapolate_second_order() |
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435 | else: |
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436 | raise 'Unknown order' |
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437 | |
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438 | stage_V = domain.quantities['stage'].vertex_values |
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439 | bed_V = domain.quantities['elevation'].vertex_values |
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440 | h_V = domain.quantities['height'].vertex_values |
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441 | u_V = domain.quantities['velocity'].vertex_values |
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442 | xmom_V = domain.quantities['xmomentum'].vertex_values |
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443 | |
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444 | bed_V[:] = stage_V - h_V |
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445 | |
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446 | for i in range(N): |
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447 | if min(h_V[i]) <= 0.0: |
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448 | h_V[i] = array([0.0, 0.0]) |
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449 | stage_V[i] = bed_V[i] |
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450 | xmom_V[i] = array([0.0, 0.0]) |
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451 | |
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452 | u_V[:] = xmom_V/(h_V + h0/h_V) |
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453 | |
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454 | return |
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455 | |
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456 | |
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457 | |
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458 | # |
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459 | def protect_against_infinitesimal_and_negative_heights(domain): |
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460 | """Protect against infinitesimal heights and associated high velocities |
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461 | """ |
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462 | |
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463 | #Shortcuts |
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464 | wc = domain.quantities['stage'].centroid_values |
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465 | zc = domain.quantities['elevation'].centroid_values |
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466 | xmomc = domain.quantities['xmomentum'].centroid_values |
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467 | hc = wc - zc #Water depths at centroids |
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468 | |
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469 | zv = domain.quantities['elevation'].vertex_values |
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470 | wv = domain.quantities['stage'].vertex_values |
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471 | hv = wv-zv |
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472 | xmomv = domain.quantities['xmomentum'].vertex_values |
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473 | #remove the above two lines and corresponding code below |
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474 | |
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475 | #Update |
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476 | for k in range(domain.number_of_elements): |
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477 | |
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478 | if hc[k] < domain.minimum_allowed_height: |
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479 | #Control stage |
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480 | if hc[k] < domain.epsilon: |
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481 | wc[k] = zc[k] # Contain 'lost mass' error |
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482 | wv[k,0] = zv[k,0] |
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483 | wv[k,1] = zv[k,1] |
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484 | |
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485 | xmomc[k] = 0.0 |
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486 | |
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487 | |
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488 | |
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489 | |
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490 | |
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491 | ######################### |
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492 | #Standard forcing terms: |
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493 | # |
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494 | def gravity(domain): |
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495 | """Apply gravitational pull in the presence of bed slope |
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496 | """ |
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497 | |
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498 | from util import gradient |
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499 | from Numeric import Float |
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500 | from numpy import zeros, array, sum |
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501 | |
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502 | xmom = domain.quantities['xmomentum'].explicit_update |
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503 | stage = domain.quantities['stage'].explicit_update |
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504 | |
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505 | Stage = domain.quantities['stage'] |
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506 | Elevation = domain.quantities['elevation'] |
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507 | h = Stage.vertex_values - Elevation.vertex_values |
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508 | b = Elevation.vertex_values |
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509 | w = Stage.vertex_values |
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510 | |
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511 | x = domain.get_vertex_coordinates() |
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512 | g = domain.g |
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513 | |
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514 | for k in range(domain.number_of_elements): |
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515 | avg_h = sum( h[k,:] )/2 |
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516 | |
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517 | #Compute bed slope |
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518 | x0, x1 = x[k,:] |
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519 | b0, b1 = b[k,:] |
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520 | |
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521 | w0, w1 = w[k,:] |
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522 | wx = gradient(x0, x1, w0, w1) |
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523 | bx = gradient(x0, x1, b0, b1) |
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524 | |
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525 | #Update momentum (explicit update is reset to source values) |
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526 | xmom[k] += -g*bx*avg_h |
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527 | |
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528 | def gravity_F2(domain): |
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529 | """Apply gravitational pull in the presence of bed slope |
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530 | """ |
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531 | |
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532 | from util import gradient |
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533 | from Numeric import Float |
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534 | from numpy import zeros, array, sum |
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535 | from parameters import F2#This is an additional friction!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
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536 | |
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537 | xmom = domain.quantities['xmomentum'].explicit_update |
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538 | stage = domain.quantities['stage'].explicit_update |
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539 | |
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540 | Stage = domain.quantities['stage'] |
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541 | Elevation = domain.quantities['elevation'] |
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542 | h = Stage.vertex_values - Elevation.vertex_values |
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543 | b = Elevation.vertex_values |
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544 | w = Stage.vertex_values |
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545 | |
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546 | x = domain.get_vertex_coordinates() |
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547 | g = domain.g |
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548 | |
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549 | for k in range(domain.number_of_elements): |
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550 | avg_h = sum( h[k,:] )/2 |
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551 | |
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552 | #Compute bed slope |
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553 | x0, x1 = x[k,:] |
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554 | b0, b1 = b[k,:] |
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555 | |
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556 | w0, w1 = w[k,:] |
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557 | wx = gradient(x0, x1, w0, w1) |
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558 | bx = gradient(x0, x1, b0, b1) |
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559 | |
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560 | #Update momentum (explicit update is reset to source values) |
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561 | xmom[k] += -g*bx*avg_h + avg_h*F2#This is an additional friction!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
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562 | |
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563 | |
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564 | def manning_friction(domain): |
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565 | """Apply (Manning) friction to water momentum |
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566 | """ |
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567 | |
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568 | from math import sqrt |
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569 | |
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570 | w = domain.quantities['stage'].centroid_values |
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571 | z = domain.quantities['elevation'].centroid_values |
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572 | h = w-z |
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573 | |
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574 | uh = domain.quantities['xmomentum'].centroid_values |
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575 | eta = domain.quantities['friction'].centroid_values |
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576 | |
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577 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
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578 | |
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579 | N = domain.number_of_elements |
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580 | eps = domain.minimum_allowed_height |
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581 | g = domain.g |
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582 | |
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583 | for k in range(N): |
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584 | if eta[k] >= eps: |
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585 | if h[k] >= eps: |
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586 | S = -g * eta[k]**2 * uh[k] |
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587 | S /= h[k]**(7.0/3) |
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588 | |
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589 | #Update momentum |
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590 | xmom_update[k] += S*uh[k] |
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