2.5. Simple diffusion equation

This example solves a simple diffusion equation in two dimensions.

  0%|          | 0/10.0 [00:00<?, ?it/s]
Initializing:   0%|          | 0/10.0 [00:00<?, ?it/s]
  0%|          | 0/10.0 [00:06<?, ?it/s]
  0%|          | 0.00383/10.0 [00:06<4:56:05, 1777.22s/it]
  1%|          | 0.08076/10.0 [00:06<13:56, 84.36s/it]
 10%|#         | 1.04027/10.0 [00:06<00:58,  6.55s/it]
 10%|#         | 1.04027/10.0 [00:06<00:58,  6.56s/it]
100%|##########| 10.0/10.0 [00:06<00:00,  1.46it/s]
100%|##########| 10.0/10.0 [00:06<00:00,  1.46it/s]

from pde import DiffusionPDE, ScalarField, UnitGrid

grid = UnitGrid([64, 64])  # generate grid
state = ScalarField.random_uniform(grid, 0.2, 0.3)  # generate initial condition

eq = DiffusionPDE(diffusivity=0.1)  # define the pde
result = eq.solve(state, t_range=10)
result.plot()