1 | import os |
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2 | from math import sqrt, pi |
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3 | from shallow_water_domain_suggestion1 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 | from numpy import sin, cos, tan, arcsin, arccos, arctan |
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7 | |
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8 | def analytical_sol(C,t): |
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9 | h1 = 10.0 # depth upstream (m) |
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10 | L = 2000.0 # length of stream/domain (m) |
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11 | n = len(C) # number of cells |
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12 | b0 = -0.005 # bottom slope |
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13 | |
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14 | u = zeros(n,Float) |
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15 | h = zeros(n,Float) |
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16 | x_prime = C-L/2.0 |
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17 | x = x_prime/cos(arctan(b0)) |
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18 | |
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19 | for i in range(n): |
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20 | # Calculate Analytical Solution at time t > 0 |
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21 | u3 = 2.0/3.0*sqrt(g*h1)*(1.0+ b0*t*sqrt(g/h1)+x[i]/(t*sqrt(g*h1))) |
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22 | h3 = h1/9.0*(2.0+0.5*b0*t*sqrt(g/h1) - x[i]/(t*sqrt(g*h1)))**2 |
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23 | |
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24 | if x[i] <= -1*sqrt(g*h1)*t: |
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25 | u[i] = 0.0 |
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26 | h[i] = h1 |
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27 | elif x[i] <= t*sqrt(g*h1)*(2.0 + 0.5*b0*t*sqrt(g/h1)): |
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28 | u[i] = u3 |
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29 | h[i] = (0.005*x[i] + 0.025) + h3 |
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30 | else: |
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31 | u[i] = 0.0 |
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32 | h[i] = 0.005*x[i] + 0.025 |
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33 | return h , u*h, u |
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34 | |
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35 | #def newLinePlot(title='Simple Plot'): |
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36 | # import Gnuplot |
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37 | # gg = Gnuplot.Gnuplot(persist=0) |
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38 | # gg.terminal(postscript) |
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39 | # gg.title(title) |
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40 | # gg('set data style linespoints') |
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41 | # gg.xlabel('x') |
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42 | # gg.ylabel('y') |
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43 | # return gg |
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44 | |
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45 | #def linePlot(gg,x1,y1,x2,y2): |
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46 | # import Gnuplot |
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47 | # plot1 = Gnuplot.PlotItems.Data(x1.flat,y1.flat,with="linespoints") |
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48 | # plot2 = Gnuplot.PlotItems.Data(x2.flat,y2.flat, with="lines 3") |
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49 | # g.plot(plot1,plot2) |
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50 | |
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51 | |
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52 | |
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53 | print "TEST 1D-SOLUTION III -- DRY BED" |
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54 | |
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55 | def stage(x): |
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56 | h1 = 10.0 |
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57 | h0 = 0.0 |
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58 | y = zeros(len(x),Float) |
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59 | for i in range(len(x)): |
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60 | if x[i]<=L/2.0: |
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61 | y[i] = h1 |
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62 | else: |
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63 | y[i] = h0 |
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64 | return y |
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65 | |
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66 | def elevation(x): |
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67 | y=zeros(len(x), Float) |
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68 | for i in range(len(x)): |
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69 | y[i] = 0.005*x[i] - 5.0 |
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70 | return y |
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71 | |
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72 | |
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73 | import time |
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74 | finaltime = 10.0 |
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75 | yieldstep = 10.0 |
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76 | L = 2000.0 # Length of channel (m) |
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77 | number_of_cells = [810]#,200,500,1000,2000,5000,10000,20000] |
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78 | h_error = zeros(len(number_of_cells),Float) |
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79 | uh_error = zeros(len(number_of_cells),Float) |
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80 | k = 0 |
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81 | for i in range(len(number_of_cells)): |
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82 | N = int(number_of_cells[i]) |
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83 | print "Evaluating domain with %d cells" %N |
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84 | cell_len = L/N # Origin = 0.0 |
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85 | points = zeros(N+1,Float) |
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86 | for j in range(N+1): |
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87 | points[j] = j*cell_len |
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88 | |
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89 | domain = Domain(points) |
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90 | domain.set_quantity('stage', stage) |
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91 | domain.set_quantity('elevation', elevation) |
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92 | |
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93 | domain.set_boundary({'exterior': Reflective_boundary(domain)}) |
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94 | domain.order = 2 |
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95 | domain.set_timestepping_method('rk2') |
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96 | domain.cfl = 1.0 |
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97 | domain.limiter = "minmod" |
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98 | |
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99 | t0 = time.time() |
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100 | for t in domain.evolve(yieldstep = yieldstep, finaltime = finaltime): |
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101 | domain.write_time() |
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102 | |
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103 | N = float(N) |
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104 | StageC = domain.quantities['stage'].centroid_values |
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105 | XmomC = domain.quantities['xmomentum'].centroid_values |
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106 | C = domain.centroids |
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107 | h, uh, u = analytical_sol(C,domain.time) |
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108 | h_error[k] = 1.0/(N)*sum(abs(h-StageC)) |
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109 | uh_error[k] = 1.0/(N)*sum(abs(uh-XmomC)) |
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110 | print "h_error %.10f" %(h_error[k]) |
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111 | print "uh_error %.10f"% (uh_error[k]) |
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112 | k = k+1 |
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113 | print 'That took %.2f seconds' %(time.time()-t0) |
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114 | X = domain.vertices |
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115 | StageQ = domain.quantities['stage'].vertex_values |
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116 | XmomQ = domain.quantities['xmomentum'].vertex_values |
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117 | velQ = domain.quantities['velocity'].vertex_values |
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118 | bedQ =domain.quantities['elevation'].vertex_values |
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119 | |
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120 | h, uh, u = analytical_sol(X.flat,domain.time) |
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121 | x = X.flat |
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122 | |
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123 | from pylab import plot,title,xlabel,ylabel,legend,savefig,show,hold,subplot |
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124 | hold(False) |
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125 | plot1 = subplot(211) |
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126 | plot(x,h,'b-', x,StageQ.flat,'r-', x, bedQ,'g-') |
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127 | plot1.set_ylim([-1,11]) |
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128 | xlabel('Position') |
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129 | ylabel('Stage') |
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130 | legend(('Analytical Solution', 'Numerical Solution', 'Bottom elevation'), |
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131 | 'upper right', shadow=True) |
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132 | plot2 = subplot(212) |
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133 | plot(x,u,x,velQ.flat) |
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134 | plot2.set_ylim([-35,35]) |
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135 | |
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136 | xlabel('Position') |
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137 | ylabel('Velocity') |
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138 | |
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139 | file = "dry_bed_" |
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140 | file += str(number_of_cells[i]) |
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141 | file += ".eps" |
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142 | #savefig(file) |
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143 | show() |
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144 | |
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145 | print "Error in height", h_error |
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146 | print "Error in xmom", uh_error |
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