1 | import os |
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2 | from math import sqrt, pi |
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3 | from shallow_water_domain 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 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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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 | |
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26 | if ( x[i] <= -t*sqrt(g*h1) ): |
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27 | u[i] = 0.0 |
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28 | h[i] = h1 |
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29 | elif ( x[i] <= 2.0*t*sqrt(g*h1) ): |
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30 | u[i] = u3 |
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31 | h[i] = h3 |
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32 | else: |
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33 | u[i] = 0.0 |
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34 | h[i] = h0 |
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35 | |
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36 | return h , u*h |
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37 | |
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38 | #def newLinePlot(title='Simple Plot'): |
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39 | # import Gnuplot |
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40 | # gg = Gnuplot.Gnuplot(persist=0) |
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41 | # gg.terminal(postscript) |
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42 | # gg.title(title) |
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43 | # gg('set data style linespoints') |
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44 | # gg.xlabel('x') |
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45 | # gg.ylabel('y') |
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46 | # return gg |
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47 | |
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48 | #def linePlot(gg,x1,y1,x2,y2): |
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49 | # import Gnuplot |
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50 | # plot1 = Gnuplot.PlotItems.Data(x1.flat,y1.flat,with="linespoints") |
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51 | # plot2 = Gnuplot.PlotItems.Data(x2.flat,y2.flat, with="lines 3") |
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52 | # g.plot(plot1,plot2) |
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53 | |
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54 | |
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55 | |
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56 | print "TEST 1D-SOLUTION III -- DRY BED" |
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57 | |
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58 | L = 2000.0 # Length of channel (m) |
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59 | N = 200 # Number of compuational cells |
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60 | cell_len = L/N # Origin = 0.0 |
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61 | |
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62 | points = zeros(N+1,Float) |
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63 | for i in range(N+1): |
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64 | points[i] = i*cell_len |
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65 | |
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66 | domain = Domain(points) |
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67 | |
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68 | def stage(x): |
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69 | h1 = 10.0 |
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70 | h0 = 0.0 |
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71 | y = zeros(len(x),Float) |
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72 | for i in range(len(x)): |
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73 | if x[i]<=L/4.0: |
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74 | y[i] = h0 |
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75 | elif x[i]<=3*L/4.0: |
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76 | y[i] = h1 |
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77 | else: |
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78 | y[i] = h0 |
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79 | return y |
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80 | |
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81 | |
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82 | import time |
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83 | |
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84 | finaltime = 20.0 |
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85 | yieldstep = 1.0 |
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86 | L = 2000.0 # Length of channel (m) |
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87 | k = 0 |
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88 | |
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89 | print "Evaluating domain with %d cells" %N |
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90 | cell_len = L/N # Origin = 0.0 |
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91 | points = zeros(N+1,Float) |
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92 | for j in range(N+1): |
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93 | points[j] = j*cell_len |
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94 | |
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95 | domain = Domain(points) |
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96 | |
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97 | domain.set_quantity('stage', stage) |
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98 | domain.set_boundary({'exterior': Reflective_boundary(domain)}) |
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99 | domain.default_order = 2 |
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100 | domain.default_time_order = 1 |
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101 | domain.cfl = 1.0 |
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102 | domain.limiter = "vanleer" |
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103 | |
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104 | t0 = time.time() |
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105 | |
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106 | s = 'for t in domain.evolve(yieldstep = yieldstep, finaltime = finaltime): domain.write_time()' |
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107 | |
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108 | import profile, pstats |
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109 | FN = 'profile.dat' |
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110 | |
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111 | profile.run(s, FN) |
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112 | |
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113 | #print 'That took %.2f seconds' %(time.time()-t0) |
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114 | |
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115 | S = pstats.Stats(FN) |
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116 | s = S.sort_stats('cumulative').print_stats(30) |
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117 | |
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118 | print s |
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119 | |
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120 | N = float(N) |
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121 | StageC = domain.quantities['stage'].centroid_values |
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122 | XmomC = domain.quantities['xmomentum'].centroid_values |
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123 | C = domain.centroids |
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124 | h, uh = analytical_sol(C,domain.time) |
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125 | h_error = 1.0/(N)*sum(abs(h-StageC)) |
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126 | uh_error = 1.0/(N)*sum(abs(uh-XmomC)) |
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127 | print "h_error %.10f" %(h_error) |
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128 | print "uh_error %.10f"% (uh_error) |
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129 | |
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130 | print 'That took %.2f seconds' %(time.time()-t0) |
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131 | |
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