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 [00:12<?, ?it/s]
  0%|          | 0.00316/10.0 [00:12<11:18:51, 4074.39s/it]
  0%|          | 0.04931/10.0 [00:12<43:19, 261.21s/it]
  7%|6         | 0.68031/10.0 [00:12<02:56, 18.94s/it]
  7%|6         | 0.68031/10.0 [00:12<02:56, 18.96s/it]
100%|##########| 10.0/10.0 [00:12<00:00,  1.29s/it]
100%|##########| 10.0/10.0 [00:12<00:00,  1.29s/it]

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()