[4959] | 1 | import os |
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| 2 | from math import sqrt, pi, sin, cos |
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| 3 | from shallow_water_adjust import * |
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| 4 | from Numeric import allclose, array, zeros, ones, Float, take, sqrt |
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| 5 | from config import g, epsilon |
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| 6 | |
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| 7 | def newLinePlot(title='Simple Plot'): |
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| 8 | import Gnuplot |
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| 9 | g = Gnuplot.Gnuplot(persist=0) |
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| 10 | g.title(title) |
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| 11 | g('set data style linespoints') |
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| 12 | g.xlabel('x') |
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| 13 | g.ylabel('y') |
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| 14 | return g |
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| 15 | |
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| 16 | def linePlot(g,x1,y1,x2,y2,x3,y3): |
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| 17 | import Gnuplot |
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| 18 | plot1 = Gnuplot.PlotItems.Data(x1.flat,y1.flat,with="lines 2") |
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| 19 | plot2 = Gnuplot.PlotItems.Data(x2.flat,y2.flat,with="lines 3") |
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| 20 | plot3 = Gnuplot.PlotItems.Data(x3.flat,y3.flat,with="linespoints 1") |
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| 21 | g.plot(plot1,plot2,plot3) |
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| 22 | |
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| 23 | |
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| 24 | def analytic_cannal(C,t): |
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| 25 | N = len(C) |
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| 26 | u = zeros(N,Float) ## water velocity |
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| 27 | h = zeros(N,Float) ## water depth |
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| 28 | x = C |
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| 29 | g = 9.81 |
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| 30 | |
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| 31 | |
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| 32 | ## Define Basin Bathymetry |
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| 33 | z_b = zeros(N,Float) ## elevation of basin |
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| 34 | z = zeros(N,Float) ## elevation of water surface |
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| 35 | z_infty = 10.0 ## max equilibrium water depth at lowest point. |
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| 36 | L_x = 2500.0 ## width of channel |
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| 37 | |
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| 38 | A0 = 0.5*L_x ## determines amplitudes of oscillations |
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| 39 | omega = sqrt(2*g*z_infty)/L_x ## angular frequency of osccilation |
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| 40 | |
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| 41 | #x1 = A0*cos(omega*t)-L_x # left shoreline |
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| 42 | #x2 = A0*cos(omega*t)+L_x # right shoreline |
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| 43 | |
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| 44 | for i in range(N): |
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| 45 | z_b[i] = z_infty*(x[i]**2/L_x**2) |
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| 46 | u[i] = -A0*omega*sin(omega*t) |
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| 47 | z[i] = z_infty+2*A0*z_infty/L_x*cos(omega*t)*(x[i]/L_x-0.5*A0/(L_x)*cos(omega*t)) |
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| 48 | |
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| 49 | h = z-z_b |
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| 50 | return u,h,z,z_b |
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| 51 | |
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| 52 | |
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| 53 | #plot2 = newLinePlot("Momentum") |
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| 54 | |
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| 55 | L_x = 2500.0 # Length of channel (m) |
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| 56 | N = 400 # Number of compuational cells |
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| 57 | cell_len = 4*L_x/N # Origin = 0.0 |
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| 58 | |
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| 59 | points = zeros(N+1,Float) |
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| 60 | for i in range(N+1): |
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| 61 | points[i] = -2*L_x +i*cell_len |
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| 62 | |
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| 63 | domain = Domain(points) |
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| 64 | |
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| 65 | domain.order = 2 #make this unnecessary |
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| 66 | domain.default_order = 2 |
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| 67 | domain.default_time_order = 1 |
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| 68 | domain.cfl = 1.0 |
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| 69 | domain.beta = 1.0 |
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| 70 | #domain.limiter = "minmod_kurganov" |
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| 71 | domain.limiter = "vanleer" |
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| 72 | #domain.limiter = "vanalbada" |
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| 73 | #domain.limiter = "superbee" |
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| 74 | #domain.limiter = "minmod" |
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| 75 | |
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| 76 | def stage(x): |
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| 77 | |
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| 78 | z_infty = 10.0 ## max equilibrium water depth at lowest point. |
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| 79 | L_x = 2500.0 ## width of channel |
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| 80 | A0 = 0.5*L_x ## determines amplitudes of oscillations |
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| 81 | omega = sqrt(2*g*z_infty)/L_x ## angular frequency of osccilation |
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| 82 | t=0.0 |
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| 83 | y = zeros(len(x),Float) |
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| 84 | for i in range(len(x)): |
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| 85 | y[i] = z_infty+2*A0*z_infty/L_x*cos(omega*t)*(x[i]/L_x-0.5*A0/(L_x)*cos(omega*t)) |
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| 86 | return y |
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| 87 | |
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| 88 | def elevation(x): |
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| 89 | N = len(x) |
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| 90 | z_infty = 10.0 |
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| 91 | z = zeros(N,Float) |
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| 92 | L_x = 2500.0 |
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| 93 | A0 = 0.5*L_x |
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| 94 | omega = sqrt(2*g*z_infty)/L_x |
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| 95 | for i in range(N): |
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| 96 | z[i] = z_infty*(x[i]**2/L_x**2) |
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| 97 | return z |
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| 98 | |
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| 99 | def height(x): |
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| 100 | z_infty = 10.0 ## max equilibrium water depth at lowest point. |
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| 101 | L_x = 2500.0 ## width of channel |
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| 102 | A0 = 0.5*L_x ## determines amplitudes of oscillations |
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| 103 | omega = sqrt(2*g*z_infty)/L_x ## angular frequency of osccilation |
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| 104 | t=0.0 |
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| 105 | y = zeros(len(x),Float) |
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| 106 | for i in range(len(x)): |
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| 107 | y[i] = max(z_infty+2*A0*z_infty/L_x*cos(omega*t)*(x[i]/L_x-0.5*A0/(L_x)*cos(omega*t))-z_infty*(x[i]**2/L_x**2),0.0) |
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| 108 | return y |
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| 109 | |
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| 110 | |
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| 111 | domain.set_quantity('stage', stage) |
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| 112 | domain.set_quantity('elevation',elevation) |
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| 113 | #domain.set_quantity('height',height) |
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| 114 | |
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| 115 | domain.set_boundary({'exterior': Reflective_boundary(domain)}) |
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| 116 | |
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| 117 | import time |
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| 118 | t0 = time.time() |
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| 119 | #yieldstep = 50.0 |
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| 120 | #yieldstep = 10.0 |
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| 121 | #yieldstep = 1122.0 |
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| 122 | |
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| 123 | #finaltime = 1122.0*0.999488 |
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| 124 | finaltime=0.75*1122.0 |
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| 125 | yieldstep = finaltime |
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| 126 | #yieldstep = finaltime |
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| 127 | #finaltime = 1122.0*4.0 |
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| 128 | #finaltime = 2000.0 |
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| 129 | |
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| 130 | plot1 = newLinePlot("Stage") |
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| 131 | plot2 = newLinePlot("Xmomentum") |
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| 132 | C = domain.centroids |
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| 133 | X = domain.vertices |
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| 134 | |
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| 135 | ElevationQ = domain.quantities['elevation'].vertex_values |
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| 136 | StageQ = domain.quantities['stage'].vertex_values |
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| 137 | XmomQ = domain.quantities['xmomentum'].vertex_values |
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| 138 | #HeightC = domain.quantities['stage'].centroid_values-domain.quantities['elevation'].centroid_values |
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| 139 | HeightC = domain.quantities['height'].centroid_values |
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| 140 | XmomC = domain.quantities['xmomentum'].centroid_values |
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| 141 | from util import calculate_wetted_area |
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| 142 | import time |
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| 143 | |
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| 144 | t0 = time.time() |
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| 145 | for t in domain.evolve(yieldstep = yieldstep, finaltime = finaltime): |
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| 146 | pass |
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| 147 | #print StageQ |
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| 148 | #print "integral %f"%domain.quantities['height'].get_integral() |
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| 149 | #if t == 0.0: |
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| 150 | # initial_integral = domain.quantities['height'].get_integral() |
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| 151 | #assert(allclose(initial_integral,domain.quantities['height'].get_integral())) |
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| 152 | #domain.write_time() |
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| 153 | u,h,z,z_b = analytic_cannal(X.flat,t) |
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| 154 | linePlot(plot1,X,z,X,z_b,X,StageQ) |
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| 155 | linePlot(plot2,X,u*h,X,u*h,X,XmomQ) |
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| 156 | #HeightQ = domain.quantities['stage'].centroid_values-domain.quantities['elevation'].centroid_values |
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| 157 | #u,hc,z,z_b = analytic_cannal(C,t) |
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| 158 | #for k in range(N): |
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| 159 | # if hc[k] < 0.0: |
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| 160 | # hc[k] = 0.0 |
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| 161 | #error = 1.0/(N)*sum(abs(hc-HeightQ)) |
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| 162 | #print 'Error measured at centroids', error |
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| 163 | |
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| 164 | #assert(allclose(initial_integral,domain.quantities['height'].get_integral())) |
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| 165 | |
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| 166 | u,h,z,z_b = analytic_cannal(C.flat,t) |
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| 167 | z_infty = 10.0 |
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| 168 | L_x = 2500.0 |
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| 169 | A0 = 0.5*L_x |
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| 170 | omega = sqrt(2*g*z_infty)/L_x |
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| 171 | x1 = A0*cos(omega*t)-L_x # left shoreline |
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| 172 | x2 = A0*cos(omega*t)+L_x # right shoreline |
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| 173 | for j in range(N): |
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| 174 | if (C[j]<x1) | (C[j] > x2): |
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| 175 | u[j] = 0.0 |
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| 176 | h[j] = 0.0 |
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| 177 | #print h |
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| 178 | #print HeightC |
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| 179 | h_error = 1.0/(N)*sum(abs(h-HeightC)) |
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| 180 | uh_error = 1.0/(N)*sum(abs(u*h-XmomC)) |
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| 181 | print "h_error %.10f" %(h_error) |
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| 182 | print "uh_error %.10f"% (uh_error) |
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| 183 | |
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| 184 | from pylab import plot,title,xlabel,ylabel,legend,savefig,show,hold,subplot,rc |
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| 185 | rc('text', usetex=True) |
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| 186 | X = domain.vertices |
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| 187 | u,h,z,z_b = analytic_cannal(X.flat,domain.time) |
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| 188 | StageQ = domain.quantities['stage'].vertex_values |
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| 189 | XmomQ = domain.quantities['xmomentum'].vertex_values |
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| 190 | hold(False) |
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| 191 | plot1 = subplot(211) |
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| 192 | z_infty = 10.0 |
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| 193 | L_x = 2500.0 |
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| 194 | A0 = 0.5*L_x |
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| 195 | omega = sqrt(2*g*z_infty)/L_x |
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| 196 | x1 = A0*cos(omega*t)-L_x # left shoreline |
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| 197 | x2 = A0*cos(omega*t)+L_x # right shoreline |
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| 198 | for n in range(N): |
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| 199 | m = 2*n |
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| 200 | for j in range(2): |
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| 201 | if (X.flat[m+j]<x1) | (X.flat[m+j] > x2): |
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| 202 | u[m+j] = 0.0 |
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| 203 | plot(X,z,X,StageQ,X,z_b) |
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| 204 | #plot1.set_ylim([4,11]) |
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| 205 | #title('Free Surface Elevation of a Dry Dam-Break') |
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| 206 | #xlabel('x (m)') |
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| 207 | ylabel('Stage (m)') |
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| 208 | legend(('Analytical Solution', 'Numerical Solution'), |
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| 209 | 'upper right', shadow=True) |
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| 210 | plot2 = subplot(212) |
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| 211 | plot(X,u*h,X,XmomQ) |
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| 212 | #plot2.set_ylim([-1,25]) |
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| 213 | #title('Xmomentum Profile of a Dry Dam-Break') |
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| 214 | xlabel('x (m)') |
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| 215 | ylabel(r'x-momentum ($m^2/s$)') |
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| 216 | filename = "parabolic_adjust_no_fix_" |
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| 217 | filename += domain.limiter |
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| 218 | filename += str(finaltime) |
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| 219 | filename += ".eps" |
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| 220 | print filename |
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| 221 | savefig(filename) |
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| 222 | show() |
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| 223 | |
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| 224 | """ |
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| 225 | parabolic_adjust_no_fix_vanleer1121.425536.eps |
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| 226 | h_error 0.0620113496 |
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| 227 | uh_error 0.7105544340 |
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| 228 | parabolic_adjust_anlty_mom_fix_vanleer1121.425536.eps |
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| 229 | h_error 0.4820676350 |
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| 230 | uh_error 2.4370614797 |
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| 231 | parabolic_adjust_mom_fix_vanleer1121.425536.eps |
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| 232 | h_error 0.1460889018 |
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| 233 | uh_error 1.2977862625 |
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| 234 | parabolic_adjust_no_fix_vanleer841.5.eps |
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| 235 | error 0.0613796233 |
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| 236 | uh_error 0.4579430471 |
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| 237 | |
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| 238 | """ |
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