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