52 lines
1.5 KiB
Python
52 lines
1.5 KiB
Python
import numpy as np
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import matplotlib.pyplot as plt
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import time, sys
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"""
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Simulation comments :
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Since we doing diffusion, which is a isotropic phenomena, we add the central differences scheme to have a isotropic scheme.
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"""
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# Physical parameters.
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vis = 0.3
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# Spatial parameters.
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nx = 41 # Number of grid points.
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dx = 2 / (nx-1) # Distance between any pair of adjacent grid points.
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#Time parameters.
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nt = 40 # Number of timesteps we want to calculate.
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sigma = 0.3 # Sigma is a parameter defined later, but the resolution uses it.
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#dt = 0.01 # Amount of time each timesteps covers (delta t)
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dt = sigma * dx**2 / vis # dt is defined using sigma, see later lessons for the definition.
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tT = dt*nt
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print('Total time : ' + str(tT))
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print(dx)
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# Boundary conditions.
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# Starting all values as 1 m/s.
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u = np.ones(nx)
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# Setting u = 2 between 0.5 and 1 as per out initial conditions.
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u[int(0.5 / dx):int(1 / dx + 1)] = 2
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# PLot initial conditions.
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fig, ax = plt.subplots(nrows=1, ncols =2, sharey=True)
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ax[0].plot(np.linspace(0,2,nx),u)
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# Temporary array for the solutions.
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un = np.ones(nx)
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for n in range(nt): # Loop for values of n from 0 to nt.
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un = u.copy() # Copy the existing values of u into un.
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print('This is time step : ' + str(n))
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print(un)
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for i in range(1, nx-1): # Loop for values in u from 1 to nx -1
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u[i] = un[i] + vis * dt / (dx)**2 * (un[i+1]-2*un[i] + un[i-1])
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# PLot the solution at t = t_final.
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ax[1].plot(np.linspace(0,2,nx), u)
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plt.show()
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