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<7:03:05, 2539.59s/it]
  0%|          | 0.018/10.0 [00:10<1:33:53, 564.39s/it]
  6%|6         | 0.619/10.0 [00:10<02:34, 16.43s/it]
 64%|######4   | 6.408/10.0 [00:10<00:05,  1.60s/it]
 64%|######4   | 6.408/10.0 [00:10<00:05,  1.61s/it]
100%|##########| 10.0/10.0 [00:10<00:00,  1.03s/it]
100%|##########| 10.0/10.0 [00:10<00:00,  1.03s/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()