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 [00:10<?, ?it/s]
  0%|          | 0.004/10.0 [00:10<7:37:28, 2745.90s/it]
  0%|          | 0.018/10.0 [00:10<1:41:31, 610.24s/it]
  6%|5         | 0.584/10.0 [00:10<02:57, 18.83s/it]
 55%|#####4    | 5.469/10.0 [00:11<00:09,  2.03s/it]
 55%|#####4    | 5.469/10.0 [00:11<00:09,  2.05s/it]
100%|##########| 10.0/10.0 [00:11<00:00,  1.12s/it]
100%|##########| 10.0/10.0 [00:11<00:00,  1.12s/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()