64 lines
2.0 KiB
Python
64 lines
2.0 KiB
Python
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# Task 1.1, 1.2
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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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# report stability
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if d > 0.5:
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print("NOT Stable")
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else:
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print("Stable")
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# explicit scheme integration for `u_t - D u_xx = 0` with boundary conditions
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# enforced by `set_bounds` and initial conditions `initial`.
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def integrate(*, name: str, initial: np.array, set_bounds: Callable[[np.array], None]) -> None:
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C = initial
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# Setup boundary conditions
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set_bounds(C)
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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/{name}_{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[1:-1] += d * (C[2:] - 2 * C[1:-1] + C[:-2])
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# update right Neumann BC
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set_bounds(C)
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# Subtask 1 boundary conditions (Dirichlet and Neumann)
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def bounds_1(C):
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C[0] = 1
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C[-1] = C[-2]
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# Subtask 2 boundary conditions (two Dirichlet)
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def bounds_2(C):
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C[0] = 1
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C[-1] = 0
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# run simulations
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integrate(name = 'task01_1', initial = np.zeros(nx), set_bounds = bounds_1)
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integrate(name = 'task01_2', initial = np.zeros(nx), set_bounds = bounds_2)
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# to convert generated image sequence to video use:
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# $> ffmpeg -r 60 -i plots/task01_1_%05d.png -pix_fmt yuv420p video_1_1.mp4
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# $> ffmpeg -r 60 -i plots/task01_2_%05d.png -pix_fmt yuv420p video_1_2.mp4
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