[7910] | 1 | """ |
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| 2 | This module contains various auxiliary function used by pyvolution. |
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| 3 | """ |
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| 4 | |
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| 5 | def mean(x): |
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| 6 | from Numeric import sum |
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| 7 | return sum(x)/len(x) |
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| 8 | |
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| 9 | |
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| 10 | def gradient(x0, x1, q0, q1): |
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| 11 | |
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| 12 | if q1-q0 != 0: |
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| 13 | a = (q1-q0)/(x1-x0) |
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| 14 | else: |
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| 15 | a = 0 |
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| 16 | |
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| 17 | return a |
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| 18 | |
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| 19 | def minmod(beta_p,beta_m): |
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| 20 | if (abs(beta_p) <= abs(beta_m)) & (beta_p*beta_m > 0.0): |
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| 21 | phi = beta_p |
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| 22 | elif (abs(beta_m) < abs(beta_p)) & (beta_p*beta_m > 0.0): |
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| 23 | phi = beta_m |
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| 24 | else: |
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| 25 | phi = 0.0 |
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| 26 | return phi |
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| 27 | |
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| 28 | def minmod_kurganov(a,b,c): |
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| 29 | from Numeric import sign |
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| 30 | if sign(a)==sign(b)==sign(c): |
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| 31 | return sign(a)*min(abs(a),abs(b),abs(c)) |
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| 32 | else: |
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| 33 | return 0.0 |
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| 34 | |
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| 35 | def maxmod(a,b): |
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| 36 | if (abs(a) >= abs(b)) & (a*b > 0.0): |
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| 37 | phi = a |
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| 38 | elif (abs(b) > abs(a)) & (a*b > 0.0): |
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| 39 | phi = b |
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| 40 | else: |
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| 41 | phi = 0.0 |
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| 42 | return phi |
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| 43 | |
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| 44 | def vanleer(a,b): |
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| 45 | if abs(a)+abs(b) > 1e-12: |
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| 46 | return (a*abs(b)+abs(a)*b)/(abs(a)+abs(b)) |
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| 47 | else: |
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| 48 | return 0.0 |
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| 49 | |
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| 50 | def vanalbada(a,b): |
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| 51 | if a*a+b*b > 1e-12: |
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| 52 | return (a*a*b+a*b*b)/(a*a+b*b) |
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| 53 | else: |
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| 54 | return 0.0 |
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| 55 | |
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| 56 | def calculate_wetted_area(x1,x2,z1,z2,w1,w2): |
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| 57 | if (w1 > z1) & (w2 < z2) & (z1 <= z2): |
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| 58 | x = ((w2-z1)*(x2-x1)+x1*(z2-z1)-x2*(w2-w1))/(z2-z1+w1-w2) |
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| 59 | A = 0.5*(w1-z1)*(x-x1) |
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| 60 | L = x-x1 |
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| 61 | elif (w1 < z1) & (w2 > z2) & (z1 < z2): |
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| 62 | x = ((w2-z1)*(x2-x1)+x1*(z2-z1)-x2*(w2-w1))/(z2-z1+w1-w2) |
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| 63 | A = 0.5*(w2-z2)*(x2-x) |
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| 64 | L = x2-x |
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| 65 | elif (w1 < z1) & (w2 > z2) & (z1 >= z2): |
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| 66 | x = ((w1-z2)*(x2-x1)+x2*(z2-z1)-x1*(w2-w1))/(z2-z1+w1-w2) |
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| 67 | A = 0.5*(w2-z2)*(x2-x) |
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| 68 | L = x2-x |
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| 69 | elif (w1 > z1) & (w2 < z2) & (z1 > z2): |
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| 70 | x = ((w1-z2)*(x2-x1)+x2*(z2-z1)-x1*(w2-w1))/(z2-z1+w1-w2) |
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| 71 | A = 0.5*(w1-z1)*(x-x1) |
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| 72 | L = x-x1 |
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| 73 | elif (w1 <= z1) & (w2 <= z2): |
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| 74 | A = 0.0 |
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| 75 | elif (w1 == z1) & (w2 > z2) & (z2 < z1): |
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| 76 | A = 0.5*(x2-x1)*(w2-z2) |
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| 77 | elif (w2 == z2) & (w1 > z1) & (z1 < z2): |
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| 78 | A = 0.5*(x2-x1)*(w1-z1) |
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| 79 | return A |
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| 80 | |
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| 81 | |
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| 82 | def calculate_new_wet_area(x1,x2,z1,z2,A): |
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| 83 | from Numeric import sqrt |
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| 84 | min_centroid_height = 1.0e-3 |
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| 85 | # Assumes reconstructed stage flat in a wetted cell |
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| 86 | M = (z2-z1)/(x2-x1) |
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| 87 | L = (x2-x1) |
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| 88 | min_area = min_centroid_height*L |
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| 89 | max_area = 0.5*(x2-x1)*abs(z2-z1) |
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| 90 | if A < max_area: |
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| 91 | if (z1 < z2): |
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| 92 | x = sqrt(2*A/M)+x1 |
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| 93 | wet_len = x-x1 |
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| 94 | wc = z1 + sqrt(M*2*A) |
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| 95 | elif (z2 < z1): |
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| 96 | x = -sqrt(-2*A/M)+x2 |
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| 97 | wet_len = x2-x |
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| 98 | wc = z2+sqrt(-M*2*A) |
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| 99 | else: |
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| 100 | wc = A/L+0.5*(z1+z2) |
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| 101 | wet_len = x2-x1 |
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| 102 | else: |
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| 103 | wc = 0.5*(z1+z2)+A/L |
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| 104 | wet_len = x2-x1 |
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| 105 | |
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| 106 | return wc,wet_len |
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| 107 | |
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| 108 | def calculate_new_wet_area_analytic(x1,x2,z1,z2,A,t): |
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| 109 | min_centroid_height = 1.0e-3 |
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| 110 | # Assumes reconstructed stage flat in a wetted cell |
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| 111 | M = (z2-z1)/(x2-x1) |
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| 112 | L = (x2-x1) |
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| 113 | min_area = min_centroid_height*L |
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| 114 | max_area = 0.5*(x2-x1)*abs(z2-z1) |
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| 115 | w1,uh1 = analytic_cannal(x1,t) |
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| 116 | w2,uh2 = analytic_cannal(x2,t) |
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| 117 | if (w1 > z1) & (w2 < z2) & (z1 <= z2): |
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| 118 | print "test1" |
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| 119 | x = ((w2-z1)*(x2-x1)+x1*(z2-z1)-x2*(w2-w1))/(z2-z1+w1-w2) |
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| 120 | wet_len = x-x1 |
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| 121 | elif (w1 < z1) & (w2 > z2) & (z1 < z2): |
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| 122 | print "test2" |
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| 123 | x = ((w2-z1)*(x2-x1)+x1*(z2-z1)-x2*(w2-w1))/(z2-z1+w1-w2) |
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| 124 | wet_len = x2-x |
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| 125 | elif (w1 < z1) & (w2 > z2) & (z1 >= z2): |
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| 126 | print "test3" |
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| 127 | x = ((w1-z2)*(x2-x1)+x2*(z2-z1)-x1*(w2-w1))/(z2-z1+w1-w2) |
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| 128 | wet_len = x2-x |
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| 129 | elif (w1 > z1) & (w2 < z2) & (z1 > z2): |
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| 130 | print "test4" |
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| 131 | x = ((w1-z2)*(x2-x1)+x2*(z2-z1)-x1*(w2-w1))/(z2-z1+w1-w2) |
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| 132 | wet_len = x-x1 |
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| 133 | elif (w1 >= z1) & (w2 >= z2): |
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| 134 | print "test5" |
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| 135 | wet_len = x2-x1 |
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| 136 | else: #(w1 <= z1) & (w2 <= z2) |
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| 137 | print "test5" |
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| 138 | if (w1 > z1) | (w2 > z2): |
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| 139 | print "ERROR" |
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| 140 | wet_len = x2-x1 |
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| 141 | return w1,w2,wet_len,uh1,uh2 |
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| 142 | |
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| 143 | def analytic_cannal(C,t): |
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| 144 | from Numeric import Float,sqrt,sin,cos |
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| 145 | from numpy import zeros |
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| 146 | |
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| 147 | |
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| 148 | #N = len(C) |
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| 149 | #u = zeros(N,Float) ## water velocity |
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| 150 | #h = zeros(N,Float) ## water depth |
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| 151 | x = C |
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| 152 | g = 9.81 |
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| 153 | |
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| 154 | |
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| 155 | ## Define Basin Bathymetry |
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| 156 | #z_b = zeros(N,Float) ## elevation of basin |
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| 157 | #z = zeros(N,Float) ## elevation of water surface |
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| 158 | z_infty = 10.0 ## max equilibrium water depth at lowest point. |
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| 159 | L_x = 2500.0 ## width of channel |
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| 160 | |
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| 161 | A0 = 0.5*L_x ## determines amplitudes of oscillations |
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| 162 | omega = sqrt(2*g*z_infty)/L_x ## angular frequency of osccilation |
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| 163 | |
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| 164 | x1 = A0*cos(omega*t)-L_x # left shoreline |
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| 165 | x2 = A0*cos(omega*t)+L_x # right shoreline |
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| 166 | if (x >=x1) & (x <= x2): |
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| 167 | z_b = z_infty*(x**2/L_x**2) ## or A0*cos(omega*t)\pmL_x |
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| 168 | u = -A0*omega*sin(omega*t) |
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| 169 | z = z_infty+2*A0*z_infty/L_x*cos(omega*t)*(x/L_x-0.5*A0/(L_x)*cos(omega*t)) |
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| 170 | else: |
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| 171 | z_b = z_infty*(x**2/L_x**2) |
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| 172 | u=0.0 |
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| 173 | z = z_b |
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| 174 | h = z-z_b |
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| 175 | return z,u*h |
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