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"""Solve the wave equation using finite differences and the Euler method"""
import numpy as np
from scipy.ndimage import gaussian_filter
from vedo import Plotter, Grid, Text2D
N = 400 # grid resolution
A, B = 5, 4 # box sides
end = 5 # end time
nframes = 150
X, Y = np.mgrid[-A:A:N*1j, -B:B:N*1j]
dx = X[1,0] - X[0,0]
dt = 0.1 * dx
time = np.arange(0, end, dt)
m = int(len(time)/nframes)
# initial condition (a ring-like wave)
Z0 = np.ones_like(X)
Z0[X**2+Y**2 < 1] = 0
Z0[X**2+Y**2 > 2] = 0
Z0 = gaussian_filter(Z0, sigma=4)
Z1 = np.array(Z0)
grid = Grid(s=(X[:,0], Y[0])).linewidth(0).lighting('glossy')
txt = Text2D(font='Brachium', pos='bottom-left', bg='yellow5')
cam = dict(
pos=(5.715, -10.54, 12.72),
focal_point=(0.1380, -0.7437, -0.5408),
viewup=(-0.2242, 0.7363, 0.6384),
distance=17.40,
)
plt = Plotter(axes=1, size=(1000,700), interactive=False)
plt.show(grid, txt, __doc__, camera=cam)
for i in range(nframes):
# Integrate multiple internal steps per rendered frame.
for _ in range(m):
ZC = Z1.copy()
Z1[1:N-1, 1:N-1] = (
2*Z1[1:N-1, 1:N-1]
- Z0[1:N-1, 1:N-1]
+ (dt/dx)**2
* ( Z1[2:N, 1:N-1]
+ Z1[0:N-2, 1:N-1]
+ Z1[1:N-1, 0:N-2]
+ Z1[1:N-1, 2:N ]
- 4*Z1[1:N-1, 1:N-1] )
)
Z0[:] = ZC[:]
wave = Z1.ravel()
txt.text(f"frame: {i}/{nframes}, height_max = {wave.max()}")
grid.cmap("Blues", wave, vmin=-2, vmax=2)
newpts = grid.points
newpts[:,2] = wave
grid.points = newpts # update the z component
plt.render()
plt.interactive()
plt.close()
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