77 lines
1.4 KiB
Python
Executable File
77 lines
1.4 KiB
Python
Executable File
#!/usr/bin/python
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# Boundary layer flow
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from numpy import zeros, linspace, exp, cos, cosh, sqrt, tanh
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import matplotlib.pyplot as plt
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# import matplotlib.animation as animation
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def K(t): # Forcing function
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return (1-exp(-0.1*t))*cos(t)
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s = 10
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# Define domain
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n = 50 # Number of gridpoints
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y = linspace(-1, 1, n)
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dy = y[1]-y[0]
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dt = 0.0005
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l = (dt/(s**2*dy**2))
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hnu = cosh(sqrt(1j)*s*y)/cosh(sqrt(1j)*s)
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fnu = tanh(sqrt(1j)*s)/(sqrt(1j)*s)
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def u_ex(tn):
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return (((1-hnu)/(1-fnu))*exp(1j*(tn))/1j).real
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def u_np1(un, tn, dt):
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Kn = K(tn)
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unp1 = un
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unp1[0] = 0 # Velocity zero ver here
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unp1[1:-1] = un[1:-1]+dt*Kn+l*(un[0:-2]-2*un[1:-1]+un[2:])
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unp1[-1] = 0 # Boundary other side
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return unp1
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un0 = zeros(n, float)
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t = 0
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un = un0
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f = plt.figure(1, figsize=(12, 6))
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linefd, = plt.plot(un0, y)
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linee, = plt.plot(un0, y)
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plt.legend(('Finite difference', 'Periodic exact'),
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loc='lower right')
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plt.ylim(-1, 1)
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plt.xlim(-1.5, 1.5)
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plt.ylabel('y [m]')
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plt.xlabel('Velocity [m/s]')
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plt.grid(True)
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plt.show(block=False)
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i = 0
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uold = un
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try:
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while(True):
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t += dt
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uold = un
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un = u_np1(uold, t, dt)
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if(i % 25 == 0):
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linefd.set_xdata(un)
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linee.set_xdata(u_ex(t))
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f.canvas.draw_idle()
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plt.pause(.000005)
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if not plt.fignum_exists(1):
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break
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i += 1
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except Exception:
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pass
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exit(0)
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