[5535] | 1 | import os |
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| 2 | from math import sqrt, pi |
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[5536] | 3 | from shallow_water_domain import * |
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[5535] | 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 analytical_sol(C,t): |
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| 8 | |
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| 9 | #t = 0.0 # time (s) |
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| 10 | g = 9.81 # gravity (m/s^2) |
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| 11 | h1 = 10.0 # depth upstream (m) |
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| 12 | h0 = 0.0 # depth downstream (m) |
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| 13 | L = 2000.0 # length of stream/domain (m) |
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| 14 | n = len(C) # number of cells |
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| 15 | |
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| 16 | u = zeros(n,Float) |
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| 17 | h = zeros(n,Float) |
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| 18 | x = C-3*L/4.0 |
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| 19 | |
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| 20 | |
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| 21 | for i in range(n): |
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| 22 | # Calculate Analytical Solution at time t > 0 |
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| 23 | u3 = 2.0/3.0*(sqrt(g*h1)+x[i]/t) |
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[5587] | 24 | h3 = 4.0/(9.0*g)*(sqrt(g*h1)-x[i]/(2.0*t))*(sqrt(g*h1)-x[i]/(2.0*t)) |
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| 25 | u3_ = 2.0/3.0*((x[i]+L/2.0)/t-sqrt(g*h1)) |
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| 26 | h3_ = 1.0/(9.0*g)*((x[i]+L/2.0)/t+2*sqrt(g*h1))*((x[i]+L/2.0)/t+2*sqrt(g*h1)) |
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[5535] | 27 | |
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[5587] | 28 | if ( x[i] <= -1*L/2.0+2*(-sqrt(g*h1)*t)): |
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| 29 | u[i] = 0.0 |
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| 30 | h[i] = h0 |
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| 31 | elif ( x[i] <= -1*L/2.0-(-sqrt(g*h1)*t)): |
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| 32 | u[i] = u3_ |
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| 33 | h[i] = h3_ |
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| 34 | |
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| 35 | elif ( x[i] <= -t*sqrt(g*h1) ): |
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[5535] | 36 | u[i] = 0.0 |
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| 37 | h[i] = h1 |
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| 38 | elif ( x[i] <= 2.0*t*sqrt(g*h1) ): |
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| 39 | u[i] = u3 |
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| 40 | h[i] = h3 |
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| 41 | else: |
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| 42 | u[i] = 0.0 |
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| 43 | h[i] = h0 |
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| 44 | |
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| 45 | return h , u*h |
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| 46 | |
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| 47 | #def newLinePlot(title='Simple Plot'): |
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| 48 | # import Gnuplot |
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| 49 | # gg = Gnuplot.Gnuplot(persist=0) |
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| 50 | # gg.terminal(postscript) |
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| 51 | # gg.title(title) |
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| 52 | # gg('set data style linespoints') |
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| 53 | # gg.xlabel('x') |
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| 54 | # gg.ylabel('y') |
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| 55 | # return gg |
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| 56 | |
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| 57 | #def linePlot(gg,x1,y1,x2,y2): |
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| 58 | # import Gnuplot |
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| 59 | # plot1 = Gnuplot.PlotItems.Data(x1.flat,y1.flat,with="linespoints") |
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| 60 | # plot2 = Gnuplot.PlotItems.Data(x2.flat,y2.flat, with="lines 3") |
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| 61 | # g.plot(plot1,plot2) |
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| 62 | |
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| 63 | |
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| 64 | |
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| 65 | print "TEST 1D-SOLUTION III -- DRY BED" |
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| 66 | |
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| 67 | L = 2000.0 # Length of channel (m) |
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[5587] | 68 | N = 800 # Number of computational cells |
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[5535] | 69 | cell_len = L/N # Origin = 0.0 |
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| 70 | |
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| 71 | points = zeros(N+1,Float) |
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| 72 | for i in range(N+1): |
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| 73 | points[i] = i*cell_len |
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| 74 | |
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| 75 | domain = Domain(points) |
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| 76 | |
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| 77 | def stage(x): |
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| 78 | h1 = 10.0 |
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| 79 | h0 = 0.0 |
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| 80 | y = zeros(len(x),Float) |
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| 81 | for i in range(len(x)): |
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| 82 | if x[i]<=L/4.0: |
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| 83 | y[i] = h0 |
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| 84 | elif x[i]<=3*L/4.0: |
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| 85 | y[i] = h1 |
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| 86 | else: |
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| 87 | y[i] = h0 |
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| 88 | return y |
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| 89 | |
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| 90 | |
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| 91 | import time |
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| 92 | |
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| 93 | finaltime = 20.0 |
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| 94 | yieldstep = 1.0 |
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| 95 | L = 2000.0 # Length of channel (m) |
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[5587] | 96 | number_of_cells = [200]#,200,500,1000,2000,5000,10000,20000] |
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[5535] | 97 | h_error = zeros(len(number_of_cells),Float) |
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| 98 | uh_error = zeros(len(number_of_cells),Float) |
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| 99 | k = 0 |
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| 100 | for i in range(len(number_of_cells)): |
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| 101 | N = int(number_of_cells[i]) |
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| 102 | print "Evaluating domain with %d cells" %N |
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| 103 | cell_len = L/N # Origin = 0.0 |
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| 104 | points = zeros(N+1,Float) |
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| 105 | for j in range(N+1): |
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| 106 | points[j] = j*cell_len |
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| 107 | |
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| 108 | domain = Domain(points) |
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| 109 | |
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| 110 | domain.set_quantity('stage', stage) |
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| 111 | domain.set_boundary({'exterior': Reflective_boundary(domain)}) |
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| 112 | domain.default_order = 2 |
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[5587] | 113 | domain.default_time_order = 2 |
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[5535] | 114 | domain.cfl = 1.0 |
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[5587] | 115 | domain.limiter = "minmod" |
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[5535] | 116 | |
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| 117 | t0 = time.time() |
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[5565] | 118 | |
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[5535] | 119 | for t in domain.evolve(yieldstep = yieldstep, finaltime = finaltime): |
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[5587] | 120 | domain.write_time() |
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[5565] | 121 | |
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[5535] | 122 | N = float(N) |
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| 123 | StageC = domain.quantities['stage'].centroid_values |
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| 124 | XmomC = domain.quantities['xmomentum'].centroid_values |
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| 125 | C = domain.centroids |
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| 126 | h, uh = analytical_sol(C,domain.time) |
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| 127 | h_error[k] = 1.0/(N)*sum(abs(h-StageC)) |
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| 128 | uh_error[k] = 1.0/(N)*sum(abs(uh-XmomC)) |
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| 129 | print "h_error %.10f" %(h_error[k]) |
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| 130 | print "uh_error %.10f"% (uh_error[k]) |
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| 131 | k = k+1 |
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| 132 | print 'That took %.2f seconds' %(time.time()-t0) |
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| 133 | X = domain.vertices |
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| 134 | StageQ = domain.quantities['stage'].vertex_values |
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| 135 | XmomQ = domain.quantities['xmomentum'].vertex_values |
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| 136 | h, uh = analytical_sol(X.flat,domain.time) |
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| 137 | x = X.flat |
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| 138 | |
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| 139 | from pylab import plot,title,xlabel,ylabel,legend,savefig,show,hold,subplot |
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| 140 | print 'test 2' |
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| 141 | hold(False) |
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| 142 | print 'test 3' |
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| 143 | plot1 = subplot(211) |
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| 144 | print 'test 4' |
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| 145 | plot(x,h,x,StageQ.flat) |
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| 146 | print 'test 5' |
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| 147 | plot1.set_ylim([-1,11]) |
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| 148 | xlabel('Position') |
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| 149 | ylabel('Stage') |
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| 150 | legend(('Analytical Solution', 'Numerical Solution'), |
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| 151 | 'upper right', shadow=True) |
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| 152 | plot2 = subplot(212) |
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| 153 | plot(x,uh,x,XmomQ.flat) |
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| 154 | plot2.set_ylim([-35,35]) |
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| 155 | |
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| 156 | xlabel('Position') |
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| 157 | ylabel('Xmomentum') |
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| 158 | |
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| 159 | file = "dry_bed_" |
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| 160 | file += str(number_of_cells[i]) |
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| 161 | file += ".eps" |
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| 162 | #savefig(file) |
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| 163 | show() |
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| 164 | |
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| 165 | print "Error in height", h_error |
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| 166 | print "Error in xmom", uh_error |
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