1 | import os |
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2 | from math import sqrt, pi, sin, cos |
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3 | from shallow_water_1d 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 = 8 # 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 = 2 |
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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 = "steve_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 | #xy[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 | y[i] = 12.0 |
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87 | return y |
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88 | |
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89 | def elevation(x): |
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90 | N = len(x) |
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91 | z_infty = 10.0 |
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92 | z = zeros(N,Float) |
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93 | L_x = 2500.0 |
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94 | A0 = 0.5*L_x |
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95 | omega = sqrt(2*g*z_infty)/L_x |
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96 | for i in range(N): |
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97 | z[i] = z_infty*(x[i]**2/L_x**2) |
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98 | return z |
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99 | |
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100 | def height(x): |
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101 | z_infty = 10.0 ## max equilibrium water depth at lowest point. |
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102 | L_x = 2500.0 ## width of channel |
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103 | A0 = 0.5*L_x ## determines amplitudes of oscillations |
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104 | omega = sqrt(2*g*z_infty)/L_x ## angular frequency of osccilation |
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105 | t=0.0 |
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106 | y = zeros(len(x),Float) |
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107 | for i in range(len(x)): |
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108 | 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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109 | return y |
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110 | |
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111 | |
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112 | domain.set_quantity('stage', stage) |
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113 | domain.set_quantity('elevation',elevation) |
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114 | #domain.set_quantity('height',height) |
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115 | |
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116 | domain.set_boundary({'exterior': Reflective_boundary(domain)}) |
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117 | |
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118 | import time |
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119 | t0 = time.time() |
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120 | finaltime = 1122.0*0.75 |
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121 | yieldstep = finaltime |
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122 | yieldstep = 10.0 |
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123 | plot1 = newLinePlot("Stage") |
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124 | plot2 = newLinePlot("Xmomentum") |
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125 | C = domain.centroids |
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126 | X = domain.vertices |
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127 | StageQ = domain.quantities['stage'].vertex_values |
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128 | XmomQ = domain.quantities['xmomentum'].vertex_values |
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129 | import time |
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130 | t0 = time.time() |
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131 | for t in domain.evolve(yieldstep = yieldstep, finaltime = finaltime): |
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132 | #pass |
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133 | domain.write_time() |
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134 | u,h,z,z_b = analytic_cannal(X.flat,t) |
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135 | linePlot(plot1,X,z,X,z_b,X,StageQ) |
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136 | linePlot(plot2,X,u*h,X,u*h,X,XmomQ) |
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137 | HeightQ = domain.quantities['stage'].centroid_values-domain.quantities['elevation'].centroid_values |
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138 | u,hc,z,z_b = analytic_cannal(C,t) |
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139 | #for k in range(N): |
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140 | # if hc[k] < 0.0: |
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141 | # hc[k] = 0.0 |
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142 | error = 1.0/(N)*sum(abs(hc-HeightQ)) |
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143 | print 'Error measured at centroids', error |
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144 | #raw_input() |
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145 | |
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146 | #from Gnuplot import plot,title,xlabel,ylabel,legend,savefig,show,hold,subplot |
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147 | from pylab import plot,title,xlabel,ylabel,legend,savefig,show,hold,subplot |
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148 | #import Gnuplot |
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149 | X = domain.vertices |
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150 | u,h,z,z_b = analytic_cannal(X.flat,domain.time) |
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151 | StageQ = domain.quantities['stage'].vertex_values |
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152 | XmomQ = domain.quantities['xmomentum'].vertex_values |
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153 | hold(False) |
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154 | plot1 = subplot(211) |
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155 | plot(X,h,X,StageQ) |
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156 | #plot1.set_ylim([4,11]) |
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157 | #title('Free Surface Elevation of a Dry Dam-Break') |
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158 | xlabel('Position') |
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159 | ylabel('Stage') |
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160 | legend(('Analytical Solution', 'Numerical Solution'), |
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161 | 'upper right', shadow=True) |
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162 | plot2 = subplot(212) |
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163 | plot(X,u*h,X,XmomQ) |
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164 | #plot2.set_ylim([-1,25]) |
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165 | #title('Xmomentum Profile of a Dry Dam-Break') |
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166 | xlabel('Position') |
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167 | ylabel('Xmomentum') |
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168 | show() |
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