2.7. Spherically symmetric PDE

This example illustrates how to solve a PDE in a spherically symmetric geometry.

Out:

  0%|          | 0/0.1 [00:00<?, ?it/s]
Initializing:   0%|          | 0/0.1 [00:00<?, ?it/s]
  0%|          | 0/0.1 [00:02<?, ?it/s]
  6%|6         | 0.006/0.1 [00:03<00:51, 548.00s/it]
 15%|#5        | 0.015/0.1 [00:03<00:20, 246.90s/it]
 29%|##9       | 0.029/0.1 [00:03<00:09, 127.72s/it]
 29%|##9       | 0.029/0.1 [00:03<00:09, 127.73s/it]
100%|##########| 0.1/0.1 [00:03<00:00, 37.04s/it]
100%|##########| 0.1/0.1 [00:03<00:00, 37.05s/it]

from pde import DiffusionPDE, ScalarField, SphericalSymGrid

grid = SphericalSymGrid(radius=[1, 5], shape=128)  # generate grid
state = ScalarField.random_uniform(grid)  # generate initial condition

eq = DiffusionPDE(0.1)  # define the PDE
result = eq.solve(state, t_range=0.1, dt=0.001)

result.plot(kind="image")