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 [00:06<?, ?it/s]
  0%|          | 0.00379/10.0 [00:06<5:06:39, 1840.63s/it]
  1%|          | 0.07613/10.0 [00:06<15:10, 91.73s/it]
  9%|9         | 0.92535/10.0 [00:06<01:08,  7.55s/it]
  9%|9         | 0.92535/10.0 [00:06<01:08,  7.56s/it]
100%|##########| 10.0/10.0 [00:06<00:00,  1.43it/s]
100%|##########| 10.0/10.0 [00:06<00:00,  1.43it/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()