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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5 | from bisect import * |
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6 | from Numeric import zeros,Float,dot |
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7 | from gaussPivot import * |
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8 | from config import g |
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9 | |
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10 | def newtonRaphson2(f,q,tol=1.0e-15): ##1.0e-9 may be too large. |
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11 | for i in range(30): |
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12 | h = 1.0e-15 ##1.0e-4 may be too large. |
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13 | n = len(q) |
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14 | jac = zeros((n,n),Float) |
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15 | if 1.0+q[0]-x<0.0: |
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16 | temp1 = 1.0+q[0]-x |
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17 | q[0] = q[0]-temp1 |
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18 | q[1] = v |
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19 | return q |
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20 | f0 = f(q) |
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21 | for i in range(n): |
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22 | temp = q[i] |
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23 | q[i] = temp + h |
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24 | f1 = f(q) |
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25 | q[i] = temp |
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26 | jac[:,i] = (f1 - f0)/h |
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27 | if sqrt(dot(f0,f0)/len(q)) < tol: return q |
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28 | dq = gaussPivot(jac,-f0) |
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29 | q = q + dq |
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30 | if sqrt(dot(dq,dq)) < tol*max(max(abs(q)),1.0): return q |
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31 | print 'Too many iterations' |
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32 | |
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33 | |
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34 | def j0(x): |
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35 | return jn(0.0, x) |
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36 | |
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37 | def j1(x): |
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38 | return jn(1.0, x) |
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39 | |
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40 | def j2(x): |
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41 | return jn(2.0, x) |
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42 | |
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43 | def j3(x): |
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44 | return jn(3.0, x) |
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45 | |
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46 | def jm1(x): |
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47 | return jn(-1.0, x) |
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48 | |
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49 | def jm2(x): |
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50 | return jn(-2.0, x) |
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51 | |
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52 | def bed(x): |
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53 | return x-1.0 |
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54 | |
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55 | def prescribe(x,t): |
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56 | q = zeros(2, Float) |
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57 | def fun(q): #Here q=(z, u) |
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58 | f = zeros(2,Float) |
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59 | f[0] = q[0] + 0.5*q[1]**2.0 - A*j0(4.0*pi/T*(1.0+q[0]-x)**0.5)*cos(2.0*pi/T*(t+q[1])) |
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60 | f[1] = q[1] + A*j1(4.0*pi/T*(1.0+q[0]-x)**0.5)*sin(2.0*pi/T*(t+q[1]))/(1+q[0]-x)**0.5 |
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61 | return f |
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62 | def newtonRaphson2(f,q,tol=1.0e-15): ##1.0e-9 may be too large. |
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63 | for i in range(30): |
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64 | h = 1.0e-15 ##1.0e-4 may be too large. |
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65 | n = len(q) |
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66 | jac = zeros((n,n),Float) |
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67 | if 1.0+q[0]-x<0.0: |
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68 | temp1 = 1.0+q[0]-x |
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69 | q[0] = q[0]-temp1 |
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70 | q[1] = v |
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71 | return q |
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72 | f0 = f(q) |
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73 | for i in range(n): |
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74 | temp = q[i] |
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75 | q[i] = temp + h |
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76 | f1 = f(q) |
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77 | q[i] = temp |
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78 | jac[:,i] = (f1 - f0)/h |
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79 | if sqrt(dot(f0,f0)/len(q)) < tol: return q |
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80 | dq = gaussPivot(jac,-f0) |
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81 | q = q + dq |
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82 | if sqrt(dot(dq,dq)) < tol*max(max(abs(q)),1.0): return q |
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83 | print 'Too many iterations' |
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84 | q = newtonRaphson2(fun,q) |
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85 | return q[0], q[1] |
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86 | |
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87 | |
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88 | def root_g(a,b,t): |
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89 | dx = 0.01 |
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90 | def g(u): |
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91 | #It was u + 8.0*A*pi/T*sin(2.0*pi/T*(t+u)). See equation (10) in Johns. Use L'Hospital rule. |
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92 | #Note that there is misprint in equation (10) in Johns. |
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93 | return u + 2.0*A*pi/T*sin(2.0*pi/T*(t+u)) |
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94 | while 1: |
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95 | x1,x2 = rootsearch(g,a,b,dx) |
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96 | if x1 != None: |
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97 | a = x2 |
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98 | root = bisect(g,x1,x2,1) |
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99 | else: |
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100 | break |
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101 | return root |
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102 | |
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103 | |
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104 | def shore(t): |
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105 | a = -0.2#-1.0 |
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106 | b = 0.2#1.0 |
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107 | #dx = 0.01 |
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108 | u = root_g(a,b,t) |
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109 | xi = -0.5*u*u + A*cos(2.0*pi/T*(t+u)) |
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110 | position = 1.0 + xi |
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111 | return position, u |
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112 | |
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113 | |
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114 | def w_at_O(t): |
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115 | return eps*cos(2.0*pi*t/T) |
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116 | |
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117 | def u_at_O(t): |
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118 | a = -1.01#-1.0 |
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119 | b = 1.01#1.0 |
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120 | dx = 0.01 |
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121 | w = w_at_O(t) |
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122 | def fun(u): |
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123 | return u + A*j1(4.0*pi/T*(1.0+w)**0.5)*sin(2.0*pi/T*(t+u))/(1+w)**0.5 |
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124 | while 1: |
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125 | x1,x2 = rootsearch(fun,a,b,dx) |
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126 | if x1 != None: |
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127 | a = x2 |
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128 | root = bisect(fun,x1,x2,1) |
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129 | else: |
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130 | break |
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131 | return root |
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132 | |
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133 | |
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134 | ##==========================================================================## |
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135 | #DIMENSIONAL PARAMETERS |
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136 | L = 5e4 # Length of channel (m) |
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137 | h_0 = 5e2 # Height at origin when the water is still |
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138 | #N = 100#400 # Number of computational cells |
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139 | #cell_len = 1.1*L/N # Origin = 0.0 |
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140 | Tp = 15.0*60.0 # Period of oscillation |
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141 | a = 1.0 # Amplitude at origin |
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142 | #X_dimensionless = linspace(0.0, 1.1*L, N) # Discretized spatial domain |
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143 | ##=========================================================================## |
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144 | #DIMENSIONLESS PARAMETERS |
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145 | eps = a/h_0 |
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146 | T = Tp*sqrt(g*h_0)/L |
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147 | A = eps/j0(4.0*pi/T) |
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148 | Time = linspace(0.0,T,1000) |
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149 | #X = X_dimensionless/L |
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150 | #Z = bed(X) |
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151 | #N_X = len(X) |
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152 | N_T = len(Time) |
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153 | |
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154 | |
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155 | Stage = zeros(N_T, Float) |
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156 | Veloc = zeros(N_T, Float) |
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157 | for i in range(N_T): |
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158 | t=Time[i] |
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159 | zet, vel = prescribe(0.0,t) |
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160 | Stage[i] = zet |
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161 | Veloc[i] = vel |
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162 | |
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163 | |
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164 | Stage_johns = zeros(N_T, Float) |
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165 | Veloc_johns = zeros(N_T, Float) |
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166 | for i in range(N_T): |
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167 | t=Time[i] |
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168 | Stage_johns[i] = w_at_O(t) |
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169 | Veloc_johns[i] = u_at_O(t) |
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170 | |
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171 | |
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172 | num=len(Stage) |
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173 | error_w=(1.0/num)*sum(abs(Stage-Stage_johns))*h_0 |
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174 | error_u=(1.0/num)*sum(abs(Veloc-Veloc_johns))*sqrt(g*h_0) |
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175 | print "error_w=", error_w |
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176 | print "error_u=", error_u |
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177 | |
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178 | """ |
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179 | |
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180 | from pylab import clf,plot,title,xlabel,ylabel,legend,savefig,show,hold,subplot |
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181 | |
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182 | hold(False) |
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183 | clf() |
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184 | plot1 = subplot(111) |
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185 | plot(Time/T,Stage*h_0,'b-', Time/T,Stage_johns*h_0,'k--') |
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186 | xlabel('t/T') |
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187 | ylabel('Stage') |
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188 | plot1.set_xlim([0.000,0.030]) |
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189 | plot1.set_ylim([0.980,1.005]) #([-9.0e-3,9.0e-3]) |
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190 | legend(('C-G', 'Johns'), |
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191 | 'lower left', shadow=False) |
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192 | |
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193 | plot2 = subplot(212) |
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194 | plot(Time/T,Veloc*sqrt(g*h_0),'b-', Time/T,Veloc_johns*sqrt(g*h_0),'k--') |
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195 | xlabel('t/T') |
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196 | ylabel('Velocity') |
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197 | #plot1.set_xlim([0.0,1.1]) |
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198 | #plot2.set_ylim([-0.05,0.05]) #([-1.0e-12,1.0e-12]) |
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199 | legend(('C-G', 'Johns'), |
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200 | 'upper right', shadow=False) |
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201 | |
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202 | |
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203 | filename = "discrepancy-closer" |
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204 | #filename += str(i) |
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205 | filename += ".eps" |
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206 | savefig(filename) |
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207 | #show() |
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208 | |
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209 | #plot(Time,Vel_at_O) |
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210 | #show() |
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211 | """ |
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