2.5. Simple diffusion equation

This example solves a simple diffusion equation in two dimensions.

Out:

  0%|          | 0/10.0 [00:00<?, ?it/s]
Initializing:   0%|          | 0/10.0 [00:00<?, ?it/s]
  0%|          | 0/10.0 [00:11<?, ?it/s]
  0%|          | 0.00316/10.0 [00:11<10:19:24, 3717.66s/it]
  1%|          | 0.05706/10.0 [00:11<34:08, 205.98s/it]
  8%|8         | 0.80203/10.0 [00:11<02:14, 14.66s/it]
  8%|8         | 0.80203/10.0 [00:11<02:14, 14.67s/it]
100%|##########| 10.0/10.0 [00:11<00:00,  1.18s/it]
100%|##########| 10.0/10.0 [00:11<00:00,  1.18s/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()