| 1 | #!/usr/bin/env python |
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| 2 | |
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| 3 | import unittest |
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| 4 | from math import sqrt, pi |
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| 5 | |
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| 6 | |
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| 7 | from shallow_water_domain import * |
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| 8 | from shallow_water_domain import flux_function as domain_flux_function |
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| 9 | |
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| 10 | |
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| 11 | |
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| 12 | from Numeric import allclose, array, ones, Float, maximum, zeros |
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| 13 | |
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| 14 | |
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| 15 | class Test_Shallow_Water(unittest.TestCase): |
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| 16 | def setUp(self): |
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| 17 | self.points = [0.0, 1.0, 2.0, 3.0] |
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| 18 | self.vertex_values = [[1.0,2.0],[4.0,5.0],[-1.0,2.0]] |
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| 19 | self.points2 = [0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0] |
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| 20 | |
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| 21 | def tearDown(self): |
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| 22 | pass |
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| 23 | #print " Tearing down" |
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| 24 | |
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| 25 | |
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| 26 | def test_creation(self): |
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| 27 | domain = Domain(self.points) |
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| 28 | assert allclose(domain.centroids, [0.5, 1.5, 2.5]) |
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| 29 | |
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| 30 | def test_compute_fluxes(self): |
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| 31 | """ |
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| 32 | Compare shallow_water_domain flux calculation against a previous |
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| 33 | Python implementation (defined in this file) |
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| 34 | """ |
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| 35 | domain = Domain(self.points) |
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| 36 | domain.set_quantity('stage',2.0) |
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| 37 | domain.set_boundary({'exterior' : Reflective_boundary(domain)}) |
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| 38 | |
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| 39 | stage_ud, xmom_ud = local_compute_fluxes(domain) |
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| 40 | |
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| 41 | domain.distribute_to_vertices_and_edges() |
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| 42 | domain.compute_fluxes() |
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| 43 | |
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| 44 | print domain.quantities['stage'].explicit_update |
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| 45 | print domain.quantities['xmomentum'].explicit_update |
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| 46 | print stage_ud |
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| 47 | print xmom_ud |
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| 48 | |
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| 49 | assert allclose( domain.quantities['stage'].explicit_update, stage_ud ) |
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| 50 | assert allclose( domain.quantities['xmomentum'].explicit_update, xmom_ud ) |
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| 51 | |
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| 52 | |
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| 53 | def test_local_flux_function(self): |
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| 54 | normal = 1.0 |
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| 55 | ql = array([1.0, 2.0],Float) |
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| 56 | qr = array([1.0, 2.0],Float) |
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| 57 | zl = 0.0 |
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| 58 | zr = 0.0 |
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| 59 | |
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| 60 | #This assumes h0 = 1.0e-3!! |
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| 61 | edgeflux, maxspeed = local_flux_function(normal, ql,qr,zl,zr) |
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| 62 | #print maxspeed |
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| 63 | #print edgeflux |
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| 64 | |
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| 65 | assert allclose(array([2.0, 8.9],Float), edgeflux, rtol=1.0e-005) |
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| 66 | assert allclose(5.1305, maxspeed, rtol=1.0e-005) |
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| 67 | |
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| 68 | normal = -1.0 |
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| 69 | ql = array([1.0, 2.0],Float) |
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| 70 | qr = array([1.0, 2.0],Float) |
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| 71 | zl = 0.0 |
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| 72 | zr = 0.0 |
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| 73 | |
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| 74 | edgeflux, maxspeed = local_flux_function(normal, ql,qr,zl,zr) |
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| 75 | |
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| 76 | |
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| 77 | #print maxspeed |
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| 78 | #print edgeflux |
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| 79 | |
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| 80 | assert allclose(array([-2.0, -8.9],Float), edgeflux, rtol=1.0e-005) |
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| 81 | assert allclose(5.1305, maxspeed, rtol=1.0e-005) |
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| 82 | |
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| 83 | def test_domain_flux_function(self): |
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| 84 | normal = 1.0 |
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| 85 | ql = array([1.0, 2.0],Float) |
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| 86 | qr = array([1.0, 2.0],Float) |
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| 87 | zl = 0.0 |
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| 88 | zr = 0.0 |
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| 89 | |
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| 90 | edgeflux, maxspeed = local_flux_function(normal, ql,qr,zl,zr) |
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| 91 | |
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| 92 | #print edgeflux |
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| 93 | |
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| 94 | |
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| 95 | |
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| 96 | domainedgeflux, domainmaxspeed = domain_flux_function(normal, ql,qr,zl,zr) |
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| 97 | |
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| 98 | #print domainedgeflux |
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| 99 | |
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| 100 | assert allclose(domainedgeflux, edgeflux) |
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| 101 | assert allclose(domainmaxspeed, maxspeed) |
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| 102 | |
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| 103 | def test_gravity(self): |
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| 104 | """ |
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| 105 | Compare shallow_water_domain gravity calculation |
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| 106 | """ |
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| 107 | |
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| 108 | def slope_one(x): |
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| 109 | return x |
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| 110 | |
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| 111 | domain = Domain(self.points) |
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| 112 | domain.set_quantity('stage',4.0) |
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| 113 | domain.set_quantity('elevation',slope_one) |
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| 114 | domain.set_boundary({'exterior' : Reflective_boundary(domain)}) |
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| 115 | |
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| 116 | gravity(domain) |
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| 117 | |
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| 118 | #print domain.quantities['stage'].vertex_values |
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| 119 | #print domain.quantities['elevation'].vertex_values |
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| 120 | #print domain.quantities['xmomentum'].explicit_update |
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| 121 | |
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| 122 | assert allclose( array([-34.3, -24.5, -14.7], Float), domain.quantities['xmomentum'].explicit_update ) |
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| 123 | |
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| 124 | |
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| 125 | def test_evolve_first_order(self): |
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| 126 | """ |
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| 127 | Compare still lake solution for various versions of shallow_water_domain |
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| 128 | """ |
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| 129 | |
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| 130 | def slope_square(x): |
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| 131 | return maximum(4.0-(x-5.0)*(x-5.0), 0.0) |
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| 132 | |
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| 133 | domain = Domain(self.points2) |
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| 134 | domain.set_quantity('stage',10.0) |
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| 135 | domain.set_quantity('elevation',slope_square) |
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| 136 | domain.set_boundary({'exterior' : Reflective_boundary(domain)}) |
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| 137 | |
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| 138 | domain.default_order = 1 |
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| 139 | domain.set_timestepping_method('euler') |
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| 140 | |
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| 141 | yieldstep=1.0 |
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| 142 | finaltime=1.0 |
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| 143 | |
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| 144 | for t in domain.evolve(yieldstep=yieldstep, finaltime=finaltime): |
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| 145 | pass |
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| 146 | |
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| 147 | ## print domain.quantities['stage'].vertex_values |
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| 148 | ## print domain.quantities['elevation'].vertex_values |
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| 149 | ## print domain.quantities['xmomentum'].vertex_values |
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| 150 | ## |
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| 151 | ## |
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| 152 | ## print domain.quantities['stage'].centroid_values |
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| 153 | ## print domain.quantities['elevation'].centroid_values |
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| 154 | ## print domain.quantities['xmomentum'].centroid_values |
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| 155 | |
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| 156 | assert allclose( 10.0*ones(10), domain.quantities['stage'].centroid_values ) |
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| 157 | assert allclose( zeros(10), domain.quantities['xmomentum'].centroid_values ) |
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| 158 | |
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| 159 | |
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| 160 | def test_evolve_euler_second_order_space(self): |
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| 161 | """ |
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| 162 | Compare still lake solution for various versions of shallow_water_domain |
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| 163 | """ |
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| 164 | |
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| 165 | def slope_square(x): |
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| 166 | return maximum(4.0-(x-5.0)*(x-5.0), 0.0) |
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| 167 | |
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| 168 | domain = Domain(self.points2) |
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| 169 | domain.set_quantity('stage',10.0) |
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| 170 | domain.set_quantity('elevation',slope_square) |
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| 171 | domain.set_boundary({'exterior' : Reflective_boundary(domain)}) |
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| 172 | |
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| 173 | domain.default_order = 2 |
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| 174 | domain.set_timestepping_method('rk2') |
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| 175 | yieldstep=1.0 |
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| 176 | finaltime=1.0 |
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| 177 | |
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| 178 | for t in domain.evolve(yieldstep=yieldstep, finaltime=finaltime): |
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| 179 | pass |
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| 180 | |
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| 181 | assert allclose( 10.0*ones(10), domain.quantities['stage'].centroid_values ) |
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| 182 | assert allclose( zeros(10), domain.quantities['xmomentum'].centroid_values ) |
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| 183 | |
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| 184 | def test_evolve_second_order_space_time(self): |
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| 185 | """ |
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| 186 | Compare still lake solution for various versions of shallow_water_domain |
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| 187 | """ |
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| 188 | |
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| 189 | def slope_square(x): |
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| 190 | return maximum(4.0-(x-5.0)*(x-5.0), 0.0) |
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| 191 | |
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| 192 | domain = Domain(self.points2) |
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| 193 | domain.set_quantity('stage',10.0) |
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| 194 | domain.set_quantity('elevation',slope_square) |
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| 195 | domain.set_boundary({'exterior' : Reflective_boundary(domain)}) |
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| 196 | |
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| 197 | domain.default_order = 2 |
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| 198 | domain.set_timestepping_method('rk3') |
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| 199 | |
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| 200 | yieldstep=1.0 |
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| 201 | finaltime=1.0 |
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| 202 | |
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| 203 | for t in domain.evolve(yieldstep=yieldstep, finaltime=finaltime): |
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| 204 | pass |
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| 205 | |
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| 206 | assert allclose( 10.0*ones(10), domain.quantities['stage'].centroid_values ) |
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| 207 | assert allclose( zeros(10), domain.quantities['xmomentum'].centroid_values ) |
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| 208 | |
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| 209 | |
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| 210 | |
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| 211 | #============================================================================== |
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| 212 | |
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| 213 | def local_compute_fluxes(domain): |
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| 214 | """Compute all fluxes and the timestep suitable for all volumes |
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| 215 | in domain. |
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| 216 | |
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| 217 | Compute total flux for each conserved quantity using "flux_function" |
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| 218 | |
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| 219 | Fluxes across each edge are scaled by edgelengths and summed up |
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| 220 | Resulting flux is then scaled by area and stored in |
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| 221 | explicit_update for each of the three conserved quantities |
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| 222 | stage, xmomentum and ymomentum |
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| 223 | |
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| 224 | The maximal allowable speed computed by the flux_function for each volume |
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| 225 | is converted to a timestep that must not be exceeded. The minimum of |
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| 226 | those is computed as the next overall timestep. |
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| 227 | |
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| 228 | Post conditions: |
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| 229 | domain.explicit_update is reset to computed flux values |
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| 230 | domain.timestep is set to the largest step satisfying all volumes. |
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| 231 | """ |
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| 232 | |
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| 233 | import sys |
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| 234 | from Numeric import zeros, Float |
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| 235 | |
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| 236 | N = domain.number_of_elements |
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| 237 | |
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| 238 | tmp0 = zeros(N,Float) |
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| 239 | tmp1 = zeros(N,Float) |
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| 240 | |
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| 241 | #Shortcuts |
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| 242 | Stage = domain.quantities['stage'] |
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| 243 | Xmom = domain.quantities['xmomentum'] |
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| 244 | # Ymom = domain.quantities['ymomentum'] |
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| 245 | Bed = domain.quantities['elevation'] |
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| 246 | |
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| 247 | #Arrays |
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| 248 | #stage = Stage.edge_values |
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| 249 | #xmom = Xmom.edge_values |
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| 250 | # ymom = Ymom.edge_values |
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| 251 | #bed = Bed.edge_values |
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| 252 | |
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| 253 | stage = Stage.vertex_values |
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| 254 | xmom = Xmom.vertex_values |
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| 255 | bed = Bed.vertex_values |
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| 256 | |
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| 257 | #print 'stage edge values', stage |
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| 258 | #print 'xmom edge values', xmom |
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| 259 | #print 'bed values', bed |
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| 260 | |
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| 261 | stage_bdry = Stage.boundary_values |
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| 262 | xmom_bdry = Xmom.boundary_values |
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| 263 | #print 'stage_bdry',stage_bdry |
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| 264 | #print 'xmom_bdry', xmom_bdry |
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| 265 | # ymom_bdry = Ymom.boundary_values |
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| 266 | |
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| 267 | # flux = zeros(3, Float) #Work array for summing up fluxes |
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| 268 | flux = zeros(2, Float) #Work array for summing up fluxes |
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| 269 | ql = zeros(2, Float) |
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| 270 | qr = zeros(2, Float) |
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| 271 | |
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| 272 | #Loop |
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| 273 | timestep = float(sys.maxint) |
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| 274 | enter = True |
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| 275 | for k in range(N): |
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| 276 | |
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| 277 | flux[:,] = 0. #Reset work array |
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| 278 | #for i in range(3): |
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| 279 | for i in range(2): |
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| 280 | #Quantities inside volume facing neighbour i |
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| 281 | #ql[0] = stage[k, i] |
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| 282 | #ql[1] = xmom[k, i] |
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| 283 | ql = [stage[k, i], xmom[k, i]] |
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| 284 | zl = bed[k, i] |
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| 285 | |
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| 286 | #Quantities at neighbour on nearest face |
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| 287 | n = domain.neighbours[k,i] |
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| 288 | if n < 0: |
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| 289 | m = -n-1 #Convert negative flag to index |
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| 290 | qr[0] = stage_bdry[m] |
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| 291 | qr[1] = xmom_bdry[m] |
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| 292 | zr = zl #Extend bed elevation to boundary |
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| 293 | else: |
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| 294 | #m = domain.neighbour_edges[k,i] |
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| 295 | m = domain.neighbour_vertices[k,i] |
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| 296 | #print i, ' ' , m |
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| 297 | #qr = [stage[n, m], xmom[n, m], ymom[n, m]] |
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| 298 | qr[0] = stage[n, m] |
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| 299 | qr[1] = xmom[n, m] |
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| 300 | zr = bed[n, m] |
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| 301 | |
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| 302 | |
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| 303 | #Outward pointing normal vector |
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| 304 | normal = domain.normals[k, i] |
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| 305 | |
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| 306 | #Flux computation using provided function |
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| 307 | #edgeflux, max_speed = flux_function(normal, ql, qr, zl, zr) |
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| 308 | #print 'ql',ql |
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| 309 | #print 'qr',qr |
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| 310 | |
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| 311 | |
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| 312 | edgeflux, max_speed = flux_function(normal, ql, qr, zl, zr) |
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| 313 | |
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| 314 | #print 'edgeflux', edgeflux |
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| 315 | |
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| 316 | # THIS IS THE LINE TO DEAL WITH LEFT AND RIGHT FLUXES |
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| 317 | # flux = edgefluxleft - edgefluxright |
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| 318 | flux -= edgeflux #* domain.edgelengths[k,i] |
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| 319 | #Update optimal_timestep |
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| 320 | try: |
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| 321 | #timestep = min(timestep, 0.5*domain.radii[k]/max_speed) |
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| 322 | timestep = min(timestep, domain.CFL*0.5*domain.areas[k]/max_speed) |
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| 323 | except ZeroDivisionError: |
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| 324 | pass |
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| 325 | |
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| 326 | #Normalise by area and store for when all conserved |
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| 327 | #quantities get updated |
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| 328 | flux /= domain.areas[k] |
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| 329 | |
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| 330 | #Stage.explicit_update[k] = flux[0] |
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| 331 | tmp0[k] = flux[0] |
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| 332 | tmp1[k] = flux[1] |
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| 333 | |
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| 334 | |
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| 335 | return tmp0, tmp1 |
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| 336 | |
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| 337 | |
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| 338 | def local_flux_function(normal, ql, qr, zl, zr): |
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| 339 | """Compute fluxes between volumes for the shallow water wave equation |
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| 340 | cast in terms of w = h+z using the 'central scheme' as described in |
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| 341 | |
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| 342 | Kurganov, Noelle, Petrova. 'Semidiscrete Central-Upwind Schemes For |
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| 343 | Hyperbolic Conservation Laws and Hamilton-Jacobi Equations'. |
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| 344 | Siam J. Sci. Comput. Vol. 23, No. 3, pp. 707-740. |
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| 345 | |
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| 346 | The implemented formula is given in equation (3.15) on page 714 |
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| 347 | |
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| 348 | Conserved quantities w, uh, are stored as elements 0 and 1 |
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| 349 | in the numerical vectors ql an qr. |
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| 350 | |
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| 351 | Bed elevations zl and zr. |
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| 352 | """ |
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| 353 | |
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| 354 | from config import g, epsilon, h0 |
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| 355 | from math import sqrt |
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| 356 | from Numeric import array |
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| 357 | |
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| 358 | #print 'ql',ql |
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| 359 | |
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| 360 | #Align momentums with x-axis |
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| 361 | #q_left = rotate(ql, normal, direction = 1) |
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| 362 | #q_right = rotate(qr, normal, direction = 1) |
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| 363 | q_left = ql |
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| 364 | q_left[1] = q_left[1]*normal |
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| 365 | q_right = qr |
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| 366 | q_right[1] = q_right[1]*normal |
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| 367 | |
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| 368 | #z = (zl+zr)/2 #Take average of field values |
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| 369 | z = 0.5*(zl+zr) #Take average of field values |
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| 370 | |
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| 371 | w_left = q_left[0] #w=h+z |
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| 372 | h_left = w_left-z |
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| 373 | uh_left = q_left[1] |
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| 374 | |
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| 375 | if h_left < epsilon: |
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| 376 | u_left = 0.0 #Could have been negative |
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| 377 | h_left = 0.0 |
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| 378 | else: |
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| 379 | u_left = uh_left/(h_left + h0/h_left) |
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| 380 | |
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| 381 | |
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| 382 | uh_left = u_left*h_left |
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| 383 | |
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| 384 | w_right = q_right[0] #w=h+z |
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| 385 | h_right = w_right-z |
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| 386 | uh_right = q_right[1] |
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| 387 | |
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| 388 | |
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| 389 | if h_right < epsilon: |
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| 390 | u_right = 0.0 #Could have been negative |
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| 391 | h_right = 0.0 |
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| 392 | else: |
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| 393 | u_right = uh_right/(h_right + h0/h_right) |
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| 394 | |
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| 395 | uh_right = u_right*h_right |
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| 396 | |
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| 397 | #vh_left = q_left[2] |
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| 398 | #vh_right = q_right[2] |
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| 399 | |
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| 400 | #print h_right |
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| 401 | #print u_right |
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| 402 | #print h_left |
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| 403 | #print u_right |
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| 404 | |
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| 405 | soundspeed_left = sqrt(g*h_left) |
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| 406 | soundspeed_right = sqrt(g*h_right) |
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| 407 | |
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| 408 | #Maximal wave speed |
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| 409 | s_max = max(u_left+soundspeed_left, u_right+soundspeed_right, 0) |
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| 410 | |
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| 411 | #Minimal wave speed |
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| 412 | s_min = min(u_left-soundspeed_left, u_right-soundspeed_right, 0) |
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| 413 | |
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| 414 | #Flux computation |
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| 415 | |
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| 416 | #flux_left = array([u_left*h_left, |
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| 417 | # u_left*uh_left + 0.5*g*h_left**2]) |
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| 418 | #flux_right = array([u_right*h_right, |
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| 419 | # u_right*uh_right + 0.5*g*h_right**2]) |
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| 420 | flux_left = array([u_left*h_left, |
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| 421 | u_left*uh_left + 0.5*g*h_left*h_left]) |
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| 422 | flux_right = array([u_right*h_right, |
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| 423 | u_right*uh_right + 0.5*g*h_right*h_right]) |
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| 424 | |
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| 425 | denom = s_max-s_min |
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| 426 | if denom == 0.0: |
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| 427 | edgeflux = array([0.0, 0.0]) |
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| 428 | max_speed = 0.0 |
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| 429 | else: |
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| 430 | edgeflux = (s_max*flux_left - s_min*flux_right)/denom |
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| 431 | edgeflux += s_max*s_min*(q_right-q_left)/denom |
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| 432 | |
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| 433 | edgeflux[1] = edgeflux[1]*normal |
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| 434 | |
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| 435 | max_speed = max(abs(s_max), abs(s_min)) |
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| 436 | |
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| 437 | return edgeflux, max_speed |
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| 438 | |
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| 439 | |
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| 440 | #------------------------------------------------------------- |
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| 441 | if __name__ == "__main__": |
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| 442 | suite = unittest.makeSuite(Test_Shallow_Water, 'test') |
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| 443 | #suite = unittest.makeSuite(Test_Quantity, 'test_set_values_from_file_using_polygon') |
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| 444 | |
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| 445 | #suite = unittest.makeSuite(Test_Quantity, 'test_set_vertex_values_using_general_interface_with_subset') |
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| 446 | #print "restricted test" |
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| 447 | #suite = unittest.makeSuite(Test_Quantity,'verbose_test_set_values_from_UTM_pts') |
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| 448 | runner = unittest.TextTestRunner() |
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| 449 | runner.run(suite) |
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