2.2.3 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 [00:05<?, ?it/s]
  0%|          | 0.00429/10.0 [00:05<3:31:00, 1266.63s/it]
  3%|▎         | 0.27611/10.0 [00:05<03:11, 19.68s/it]
  3%|▎         | 0.27611/10.0 [00:05<03:11, 19.69s/it]
100%|██████████| 10.0/10.0 [00:05<00:00,  1.84it/s]
100%|██████████| 10.0/10.0 [00:05<00:00,  1.84it/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()