[1290] | 1 | """Example of shallow water wave equation. |
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| 2 | |
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| 3 | This is called Netherlands because it shows a dam with a gap in it and |
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| 4 | stylised housed behind it and below the water surface. |
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| 5 | |
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| 6 | """ |
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| 7 | |
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| 8 | ###################### |
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| 9 | # Module imports |
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| 10 | # |
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| 11 | from shallow_water import Domain, Reflective_boundary, Dirichlet_boundary,\ |
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| 12 | Transmissive_boundary, Constant_height |
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| 13 | |
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| 14 | from mesh_factory import rectangular |
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| 15 | from Numeric import array |
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| 16 | |
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| 17 | |
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| 18 | class Weir: |
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| 19 | """Set a bathymetry for simple weir with a hole. |
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| 20 | x,y are assumed to be in the unit square |
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| 21 | """ |
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| 22 | |
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| 23 | def __init__(self, stage): |
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| 24 | self.inflow_stage = stage |
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| 25 | |
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| 26 | def __call__(self, x, y): |
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| 27 | from Numeric import zeros, Float |
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| 28 | |
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| 29 | N = len(x) |
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| 30 | assert N == len(y) |
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| 31 | |
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| 32 | z = zeros(N, Float) |
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| 33 | for i in range(N): |
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| 34 | z[i] = -x[i]/20 #General slope |
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| 35 | |
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| 36 | #Flattish bit to the left |
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| 37 | if x[i] <= 0.3: |
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| 38 | #z[i] = -x[i]/5 |
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| 39 | z[i] = -x[i]/20 |
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| 40 | |
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| 41 | |
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| 42 | #Weir |
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| 43 | if x[i] > 0.3 and x[i] < 0.4: |
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| 44 | z[i] = -x[i]/20+1.2 |
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| 45 | |
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| 46 | #Dip |
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| 47 | #if x[i] > 0.6 and x[i] < 0.9: |
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| 48 | # z[i] = -x[i]/20-0.5 #-y[i]/5 |
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| 49 | |
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| 50 | #Hole in weir |
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| 51 | #if x[i] > 0.3 and x[i] < 0.4 and y[i] > 0.2 and y[i] < 0.4: |
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| 52 | if x[i] > 0.3 and x[i] < 0.4 and y[i] > 0.4 and y[i] < 0.6: |
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| 53 | #z[i] = -x[i]/5 |
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| 54 | z[i] = -x[i]/20 |
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| 55 | |
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| 56 | #Poles |
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| 57 | #if x[i] > 0.65 and x[i] < 0.8 and y[i] > 0.55 and y[i] < 0.65 or\ |
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| 58 | # x[i] > 0.75 and x[i] < 0.9 and y[i] > 0.35 and y[i] < 0.45: |
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| 59 | # z[i] = -x[i]/20+0.4 |
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| 60 | |
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| 61 | if (x[i] - 0.72)**2 + (y[i] - 0.6)**2 < 0.05**2:# or\ |
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| 62 | #x[i] > 0.75 and x[i] < 0.9 and y[i] > 0.35 and y[i] < 0.45: |
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| 63 | z[i] = -x[i]/20+0.4 |
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| 64 | |
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| 65 | #Wall |
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| 66 | if x[i] > 0.995: |
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| 67 | z[i] = -x[i]/20+0.3 |
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| 68 | |
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| 69 | return z/2 |
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| 70 | |
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| 71 | |
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| 72 | |
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| 73 | ###################### |
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| 74 | # Domain |
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| 75 | # |
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| 76 | |
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| 77 | N = 250 |
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| 78 | #N= 8 |
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| 79 | N = 16 |
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| 80 | #N = 4 |
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| 81 | #N = 102 |
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| 82 | N = 25 |
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| 83 | N = 16 |
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| 84 | N = 60 |
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| 85 | N = 150 #size = 45000 |
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| 86 | N = 130 #size = 33800 |
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| 87 | #N = 60 |
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| 88 | #N = 40 |
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| 89 | N = 260 |
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| 90 | #N = 150 |
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| 91 | N = 264 |
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| 92 | |
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| 93 | N = 600 #Size = 720000 |
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| 94 | N = 20 |
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| 95 | #N = 150 |
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| 96 | N = 110 |
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| 97 | N = 60 |
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| 98 | |
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| 99 | <<<<<<< .mine |
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| 100 | N = 4 |
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| 101 | ======= |
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| 102 | #N = 140 |
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| 103 | >>>>>>> .r817 |
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| 104 | |
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| 105 | #N = 15 |
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| 106 | |
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| 107 | print 'Creating domain' |
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| 108 | #Create basic mesh |
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| 109 | points, vertices, boundary = rectangular(N, N) |
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| 110 | |
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| 111 | #Create shallow water domain |
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| 112 | domain = Domain(points, vertices, boundary) |
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| 113 | |
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| 114 | domain.check_integrity() |
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| 115 | domain.default_order = 2 |
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| 116 | #domain.beta_h=0 |
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| 117 | |
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| 118 | #Output params |
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| 119 | domain.smooth = True |
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| 120 | domain.reduction = min #Looks a lot better on top of steep slopes |
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| 121 | |
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| 122 | print "Number of triangles = ", len(domain) |
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| 123 | |
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| 124 | |
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| 125 | if N > 40: |
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| 126 | domain.visualise = False |
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| 127 | domain.checkpoint = False |
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| 128 | domain.store = True #Store for visualisation purposes |
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| 129 | domain.format = 'sww' #Native netcdf visualisation format |
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| 130 | import sys, os |
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| 131 | #FIXME: This was os.path.splitext but caused weird filenames based on root |
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| 132 | base = os.path.basename(sys.argv[0]) |
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| 133 | domain.filename, _ = os.path.splitext(base) |
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| 134 | else: |
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| 135 | domain.visualise = False |
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| 136 | domain.checkpoint = False |
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| 137 | domain.store = False |
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| 138 | |
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| 139 | |
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| 140 | #Set bed-slope and friction |
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| 141 | inflow_stage = 0.08 |
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| 142 | manning = 0.02 |
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| 143 | Z = Weir(inflow_stage) |
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| 144 | |
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| 145 | print 'Field values' |
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| 146 | domain.set_quantity('elevation', Z) |
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| 147 | domain.set_quantity('friction', manning) |
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| 148 | |
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| 149 | |
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| 150 | ###################### |
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| 151 | # Boundary conditions |
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| 152 | # |
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| 153 | print 'Boundaries' |
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| 154 | Br = Reflective_boundary(domain) |
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| 155 | Bt = Transmissive_boundary(domain) |
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| 156 | |
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| 157 | #Constant inflow |
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| 158 | Bd = Dirichlet_boundary([2*inflow_stage, 0.0, 0.0]) |
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| 159 | |
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| 160 | |
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| 161 | #Set boundary conditions |
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| 162 | domain.set_boundary({'left': Bd, 'right': Br, 'bottom': Br, 'top': Br}) |
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| 163 | |
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| 164 | |
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| 165 | ###################### |
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| 166 | #Initial condition |
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| 167 | # |
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| 168 | print 'Initial condition' |
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| 169 | domain.set_quantity('stage', Constant_height(Z, 0.)) |
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| 170 | |
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| 171 | #Evolve |
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| 172 | import time |
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| 173 | t0 = time.time() |
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| 174 | |
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| 175 | for t in domain.evolve(yieldstep = 0.5, finaltime = 1.0): |
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| 176 | domain.write_time() |
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| 177 | |
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| 178 | |
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| 179 | |
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| 180 | |
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| 181 | print 'That took %.2f seconds' %(time.time()-t0) |
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| 182 | print 'time', domain.write_time() |
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| 183 | |
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| 184 | print domain.coordinates |
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| 185 | print '*****' |
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| 186 | print domain.vertex_coordinates |
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| 187 | print '*****' |
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| 188 | print domain.quantities['xmomentum'].centroid_values |
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| 189 | print '*****' |
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| 190 | print domain.quantities['xmomentum'].edge_values |
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| 191 | print '*****' |
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| 192 | print domain.quantities['stage'].vertex_values |
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| 193 | print '*****' |
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| 194 | print domain.quantities['stage'].explicit_update |
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| 195 | |
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| 196 | from shallow_water import * |
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| 197 | |
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| 198 | def compute_fluxes_python(domain): |
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| 199 | """Compute all fluxes and the timestep suitable for all volumes |
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| 200 | in domain. |
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| 201 | |
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| 202 | Compute total flux for each conserved quantity using "flux_function" |
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| 203 | |
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| 204 | Fluxes across each edge are scaled by edgelengths and summed up |
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| 205 | Resulting flux is then scaled by area and stored in |
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| 206 | explicit_update for each of the three conserved quantities |
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| 207 | stage, xmomentum and ymomentum |
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| 208 | |
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| 209 | The maximal allowable speed computed by the flux_function for each volume |
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| 210 | is converted to a timestep that must not be exceeded. The minimum of |
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| 211 | those is computed as the next overall timestep. |
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| 212 | |
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| 213 | Post conditions: |
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| 214 | domain.explicit_update is reset to computed flux values |
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| 215 | domain.timestep is set to the largest step satisfying all volumes. |
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| 216 | """ |
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| 217 | |
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| 218 | import sys |
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| 219 | from Numeric import zeros, Float |
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| 220 | |
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| 221 | N = domain.number_of_elements |
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| 222 | |
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| 223 | #Shortcuts |
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| 224 | Stage = domain.quantities['stage'] |
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| 225 | Xmom = domain.quantities['xmomentum'] |
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| 226 | Ymom = domain.quantities['ymomentum'] |
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| 227 | Bed = domain.quantities['elevation'] |
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| 228 | |
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| 229 | #Arrays |
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| 230 | stage = Stage.edge_values |
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| 231 | xmom = Xmom.edge_values |
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| 232 | ymom = Ymom.edge_values |
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| 233 | bed = Bed.edge_values |
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| 234 | |
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| 235 | stage_bdry = Stage.boundary_values |
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| 236 | xmom_bdry = Xmom.boundary_values |
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| 237 | ymom_bdry = Ymom.boundary_values |
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| 238 | |
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| 239 | flux = zeros((N,3), Float) #Work array for summing up fluxes |
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| 240 | |
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| 241 | #Loop |
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| 242 | timestep = float(sys.maxint) |
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| 243 | for k in range(N): |
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| 244 | |
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| 245 | for i in range(3): |
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| 246 | #Quantities inside volume facing neighbour i |
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| 247 | ql = [stage[k, i], xmom[k, i], ymom[k, i]] |
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| 248 | zl = bed[k, i] |
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| 249 | |
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| 250 | #Quantities at neighbour on nearest face |
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| 251 | n = domain.neighbours[k,i] |
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| 252 | if n < 0: |
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| 253 | m = -n-1 #Convert negative flag to index |
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| 254 | qr = [stage_bdry[m], xmom_bdry[m], ymom_bdry[m]] |
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| 255 | zr = zl #Extend bed elevation to boundary |
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| 256 | else: |
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| 257 | m = domain.neighbour_edges[k,i] |
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| 258 | qr = [stage[n, m], xmom[n, m], ymom[n, m]] |
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| 259 | zr = bed[n, m] |
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| 260 | |
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| 261 | |
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| 262 | #Outward pointing normal vector |
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| 263 | normal = domain.normals[k, 2*i:2*i+2] |
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| 264 | |
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| 265 | #Flux computation using provided function |
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| 266 | edgeflux, max_speed = flux_function(normal, ql, qr, zl, zr) |
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| 267 | |
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| 268 | flux[k,:] = edgeflux |
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| 269 | |
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| 270 | return flux |
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| 271 | |
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| 272 | flux = compute_fluxes_python(domain) |
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| 273 | print 'flux' |
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| 274 | print flux |
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| 275 | |
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| 276 | |
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| 277 | # THis was pulled out of |
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