[7837] | 1 | import os |
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| 2 | from scipy.special import jn |
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| 3 | from scipy import sin, cos, sqrt, linspace, pi, zeros |
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| 4 | from rootsearch import * |
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[7933] | 5 | from bisect_function import * |
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[7922] | 6 | from Numeric import Float |
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| 7 | from numpy import zeros,dot |
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[7837] | 8 | from gaussPivot import * |
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| 9 | from config import g |
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| 10 | from analytical_prescription import * |
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| 11 | |
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| 12 | |
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| 13 | def j0(x): |
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| 14 | return jn(0.0, x) |
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| 15 | |
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| 16 | def j1(x): |
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| 17 | return jn(1.0, x) |
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| 18 | |
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| 19 | def j2(x): |
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| 20 | return jn(2.0, x) |
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| 21 | |
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| 22 | def j3(x): |
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| 23 | return jn(3.0, x) |
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| 24 | |
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| 25 | def jm1(x): |
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| 26 | return jn(-1.0, x) |
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| 27 | |
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| 28 | def jm2(x): |
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| 29 | return jn(-2.0, x) |
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| 30 | |
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| 31 | def bed(x): |
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| 32 | return x-1.0 |
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| 33 | |
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| 34 | |
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| 35 | def w_at_O(t): |
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| 36 | return eps*cos(2.0*pi*t/T) |
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| 37 | |
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| 38 | def u_at_O(t): |
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| 39 | a = -1.01#-1.0 |
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| 40 | b = 1.01#1.0 |
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| 41 | dx = 0.01 |
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| 42 | w = w_at_O(t) |
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| 43 | def fun(u): |
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| 44 | return u + A*j1(4.0*pi/T*(1.0+w)**0.5)*sin(2.0*pi/T*(t+u))/(1.0+w)**0.5 |
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| 45 | while 1: |
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| 46 | x1,x2 = rootsearch(fun,a,b,dx) |
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| 47 | if x1 != None: |
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| 48 | a = x2 |
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| 49 | root = bisect(fun,x1,x2,1) |
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| 50 | else: |
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| 51 | break |
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| 52 | return root |
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| 53 | |
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| 54 | """ |
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| 55 | ##==========================================================================## |
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| 56 | #DIMENSIONAL PARAMETERS |
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| 57 | L = 5e4 # Length of channel (m) |
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| 58 | h_0 = 5e2 # Height at origin when the water is still |
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| 59 | Tp = 15.0*60.0 # Period of oscillation |
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| 60 | a = 1.0 # Amplitude at origin |
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| 61 | ##=========================================================================## |
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| 62 | #DIMENSIONLESS PARAMETERS |
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| 63 | eps = a/h_0 |
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| 64 | T = Tp*sqrt(g*h_0)/L |
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| 65 | A = eps/j0(4.0*pi/T) |
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| 66 | """ |
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| 67 | |
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| 68 | |
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| 69 | Time = linspace(0.0,T,100) |
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| 70 | N_T = len(Time) |
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| 71 | |
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| 72 | |
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| 73 | Stage = zeros(N_T, Float) |
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| 74 | Veloc = zeros(N_T, Float) |
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| 75 | for i in range(N_T): |
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| 76 | t=Time[i] |
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| 77 | zet, vel = prescribe(0.0,t) |
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| 78 | Stage[i] = zet |
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| 79 | Veloc[i] = vel |
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| 80 | |
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| 81 | |
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| 82 | Stage_johns = zeros(N_T, Float) |
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| 83 | Veloc_johns = zeros(N_T, Float) |
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| 84 | for i in range(N_T): |
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| 85 | t=Time[i] |
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| 86 | Stage_johns[i] = w_at_O(t) |
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| 87 | Veloc_johns[i] = u_at_O(t) |
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| 88 | |
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| 89 | """ |
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| 90 | num=len(Stage) |
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| 91 | error_w=(1.0/num)*sum(abs(Stage-Stage_johns))*h_0 |
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| 92 | error_u=(1.0/num)*sum(abs(Veloc-Veloc_johns))*sqrt(g*h_0) |
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| 93 | print "error_w=", error_w |
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| 94 | print "error_u=", error_u |
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| 95 | |
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| 96 | """ |
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| 97 | |
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| 98 | from pylab import clf,plot,title,xlabel,ylabel,legend,savefig,show,hold,subplot |
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| 99 | |
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| 100 | hold(False) |
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| 101 | clf() |
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| 102 | plot1 = subplot(211) |
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| 103 | plot(Time/T,Stage*h_0,'b-', Time/T,Stage_johns*h_0,'k--') |
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| 104 | xlabel('t/T') |
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| 105 | ylabel('Stage') |
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| 106 | #plot1.set_xlim([0.000,0.030]) |
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| 107 | #plot1.set_ylim([0.980,1.005]) #([-9.0e-3,9.0e-3]) |
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| 108 | legend(('C-G', 'Johns'), |
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| 109 | 'lower left', shadow=False) |
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| 110 | |
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| 111 | plot2 = subplot(212) |
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| 112 | plot(Time/T,Veloc*sqrt(g*h_0),'b-', Time/T,Veloc_johns*sqrt(g*h_0),'k--') |
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| 113 | xlabel('t/T') |
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| 114 | ylabel('Velocity') |
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| 115 | #plot1.set_xlim([0.0,1.1]) |
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| 116 | #plot2.set_ylim([-0.05,0.05]) #([-1.0e-12,1.0e-12]) |
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| 117 | legend(('C-G', 'Johns'), |
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| 118 | 'upper right', shadow=False) |
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| 119 | |
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| 120 | |
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| 121 | #filename = "discrepancy-closer" |
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| 122 | #filename += str(i) |
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| 123 | #filename += ".eps" |
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| 124 | #savefig(filename) |
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| 125 | #show() |
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| 126 | |
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| 127 | #plot(Time,Vel_at_O) |
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| 128 | #show() |
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