[7839] | 1 | #! /usr/bin/python |
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| 2 | |
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| 3 | |
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| 4 | """ |
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| 5 | Forcing terms for the shallow water equations, gravity, friction etc |
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| 6 | """ |
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| 7 | |
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| 8 | __author__="Stephen Roberts" |
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| 9 | __date__ ="$05/06/2010 5:49:35 PM$" |
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| 10 | |
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| 11 | |
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| 12 | def gravity(domain): |
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| 13 | """Apply gravitational pull in the presence of bed slope |
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| 14 | """ |
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| 15 | |
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| 16 | from flow_1d.utilities.util import gradient |
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| 17 | |
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| 18 | xmom = domain.quantities['xmomentum'].explicit_update |
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| 19 | stage = domain.quantities['stage'].explicit_update |
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| 20 | # ymom = domain.quantities['ymomentum'].explicit_update |
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| 21 | |
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| 22 | Stage = domain.quantities['stage'] |
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| 23 | Elevation = domain.quantities['elevation'] |
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| 24 | #h = Stage.edge_values - Elevation.edge_values |
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| 25 | h = Stage.vertex_values - Elevation.vertex_values |
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| 26 | b = Elevation.vertex_values |
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| 27 | w = Stage.vertex_values |
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| 28 | |
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| 29 | x = domain.get_vertex_coordinates() |
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| 30 | g = domain.g |
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| 31 | |
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| 32 | for k in range(domain.number_of_elements): |
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| 33 | # avg_h = sum( h[k,:] )/3 |
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| 34 | avg_h = sum( h[k,:] )/2 |
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| 35 | |
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| 36 | #Compute bed slope |
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| 37 | #x0, y0, x1, y1, x2, y2 = x[k,:] |
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| 38 | x0, x1 = x[k,:] |
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| 39 | #z0, z1, z2 = v[k,:] |
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| 40 | b0, b1 = b[k,:] |
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| 41 | |
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| 42 | w0, w1 = w[k,:] |
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| 43 | wx = gradient(x0, x1, w0, w1) |
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| 44 | |
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| 45 | #zx, zy = gradient(x0, y0, x1, y1, x2, y2, z0, z1, z2) |
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| 46 | bx = gradient(x0, x1, b0, b1) |
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| 47 | |
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| 48 | #Update momentum (explicit update is reset to source values) |
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| 49 | xmom[k] += -g*bx*avg_h |
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| 50 | #xmom[k] = -g*bx*avg_h |
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| 51 | #stage[k] = 0.0 |
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| 52 | |
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| 53 | |
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| 54 | def manning_friction(domain): |
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| 55 | """Apply (Manning) friction to water momentum |
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| 56 | """ |
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| 57 | |
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| 58 | from math import sqrt |
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| 59 | |
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| 60 | w = domain.quantities['stage'].centroid_values |
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| 61 | z = domain.quantities['elevation'].centroid_values |
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| 62 | h = w-z |
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| 63 | |
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| 64 | uh = domain.quantities['xmomentum'].centroid_values |
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| 65 | #vh = domain.quantities['ymomentum'].centroid_values |
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| 66 | eta = domain.quantities['friction'].centroid_values |
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| 67 | |
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| 68 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
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| 69 | #ymom_update = domain.quantities['ymomentum'].semi_implicit_update |
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| 70 | |
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| 71 | N = domain.number_of_elements |
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| 72 | eps = domain.minimum_allowed_height |
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| 73 | g = domain.g |
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| 74 | |
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| 75 | for k in range(N): |
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| 76 | if eta[k] >= eps: |
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| 77 | if h[k] >= eps: |
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| 78 | #S = -g * eta[k]**2 * sqrt((uh[k]**2 + vh[k]**2)) |
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| 79 | S = -g * eta[k]**2 * uh[k] |
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| 80 | S /= h[k]**(7.0/3) |
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| 81 | |
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| 82 | #Update momentum |
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| 83 | xmom_update[k] += S*uh[k] |
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| 84 | #ymom_update[k] += S*vh[k] |
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| 85 | |
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| 86 | def linear_friction(domain): |
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| 87 | """Apply linear friction to water momentum |
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| 88 | |
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| 89 | Assumes quantity: 'linear_friction' to be present |
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| 90 | """ |
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| 91 | |
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| 92 | from math import sqrt |
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| 93 | |
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| 94 | w = domain.quantities['stage'].centroid_values |
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| 95 | z = domain.quantities['elevation'].centroid_values |
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| 96 | h = w-z |
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| 97 | |
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| 98 | uh = domain.quantities['xmomentum'].centroid_values |
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| 99 | # vh = domain.quantities['ymomentum'].centroid_values |
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| 100 | tau = domain.quantities['linear_friction'].centroid_values |
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| 101 | |
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| 102 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
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| 103 | # ymom_update = domain.quantities['ymomentum'].semi_implicit_update |
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| 104 | |
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| 105 | N = domain.number_of_elements |
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| 106 | eps = domain.minimum_allowed_height |
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| 107 | g = domain.g #Not necessary? Why was this added? |
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| 108 | |
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| 109 | for k in range(N): |
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| 110 | if tau[k] >= eps: |
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| 111 | if h[k] >= eps: |
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| 112 | S = -tau[k]/h[k] |
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| 113 | |
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| 114 | #Update momentum |
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| 115 | xmom_update[k] += S*uh[k] |
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| 116 | # ymom_update[k] += S*vh[k] |
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| 117 | |
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| 118 | |
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| 119 | |
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| 120 | def check_forcefield(f): |
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| 121 | """Check that f is either |
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| 122 | 1: a callable object f(t,x,y), where x and y are vectors |
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| 123 | and that it returns an array or a list of same length |
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| 124 | as x and y |
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| 125 | 2: a scalar |
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| 126 | """ |
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| 127 | |
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| 128 | |
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| 129 | if callable(f): |
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| 130 | #N = 3 |
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| 131 | N = 2 |
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| 132 | #x = ones(3, numpy.float) |
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| 133 | #y = ones(3, numpy.float) |
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| 134 | x = ones(2, numpy.float) |
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| 135 | #y = ones(2, numpy.float) |
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| 136 | |
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| 137 | try: |
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| 138 | #q = f(1.0, x=x, y=y) |
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| 139 | q = f(1.0, x=x) |
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| 140 | except Exception, e: |
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| 141 | msg = 'Function %s could not be executed:\n%s' %(f, e) |
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| 142 | #FIXME: Reconsider this semantics |
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| 143 | raise msg |
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| 144 | |
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| 145 | try: |
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| 146 | q = numpy.array(q, numpy.float) |
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| 147 | except: |
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| 148 | msg = 'Return value from vector function %s could ' %f |
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| 149 | msg += 'not be converted into a numpy array of numpy.floats.\n' |
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| 150 | msg += 'Specified function should return either list or array.' |
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| 151 | raise msg |
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| 152 | |
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| 153 | #Is this really what we want? |
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| 154 | msg = 'Return vector from function %s ' %f |
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| 155 | msg += 'must have same lenght as input vectors' |
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| 156 | assert len(q) == N, msg |
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| 157 | |
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| 158 | else: |
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| 159 | try: |
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| 160 | f = float(f) |
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| 161 | except: |
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| 162 | msg = 'Force field %s must be either a scalar' %f |
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| 163 | msg += ' or a vector function' |
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| 164 | raise msg |
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| 165 | return f |
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| 166 | |
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| 167 | |
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