NSSC/Exercise_03/task01_3.py

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 explicit 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