2.7. Spherically symmetric PDE

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

  0%|          | 0/0.1 [00:00<?, ?it/s]
Initializing:   0%|          | 0/0.1 [00:00<?, ?it/s]
  0%|          | 0/0.1 [00:03<?, ?it/s]
  6%|6         | 0.006/0.1 [00:03<00:57, 611.47s/it]
 14%|#4        | 0.014/0.1 [00:04<00:26, 305.39s/it]
 24%|##4       | 0.024/0.1 [00:04<00:13, 178.16s/it]
 24%|##4       | 0.024/0.1 [00:04<00:13, 178.18s/it]
100%|##########| 0.1/0.1 [00:04<00:00, 42.76s/it]
100%|##########| 0.1/0.1 [00:04<00:00, 42.77s/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")