51 lines
1.5 KiB
Python
51 lines
1.5 KiB
Python
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# Task 1.3
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import numpy as np
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from typing import Callable
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from matplotlib import pyplot as plt
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# Config
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D = 1e-6 # diffusion coefficient
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h = 1 # space domain (max x size)
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T = 2e6 # solution end time
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nx = 50 # nr of space discretization points
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nt = 20000 # nr of time discretization points
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# derived constants
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dx = h / (nx - 1) # space step size
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dt = T / (nt - 1) # time step size
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d = dt * D / dx**2 # stability/stepsize coefficient
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# Setup implicit scheme equation matrix
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T = (1 + 2 * d) * np.eye(nx) - d * np.eye(nx, k = 1) - d * np.eye(nx, k = -1)
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# fix boundary condition equations
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T[0, 0] = 1 # Left Dirichlet BC
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T[0, 1] = 0
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T[-1, -2] = 1 # Right Neumann BC
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T[-1, -1] = 0
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# Set initial solution
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C = np.zeros(nx)
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C[0] = 1
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C[-1] = C[-2] # (0 = 0)
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i = 0 # index for plot generation
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plt.figure(figsize = (8, 6), dpi = 100)
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for t in range(nt):
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# every 400'th time step save a plot
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if t % (nt // 400) == 0:
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plt.clf()
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plt.plot(np.linspace(0, h, nx), C)
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plt.xlim([0, h])
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plt.ylim([0, 1.2])
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plt.savefig(f"plots/task01_3_{i:0>5}.png")
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i += 1
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# update solution using the explicit schema
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C = np.linalg.solve(T, C)
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# fix BC conditions (theoretically, they are set by the update but for
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# stability reasons (numerical) we enforce the correct values)
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C[0] = 1
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C[-1] = C[-2]
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# to convert generated image sequence to video use:
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# $> ffmpeg -r 60 -i plots/task01_3_%05d.png -pix_fmt yuv420p video_1_3.mp4
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