def setUp(self):
grid_size = 200
self.grid = grids.Grid(grid_size, grid_size, 2 * np.pi / grid_size)
self.finite_vol_eq = (
advection_equations.FiniteVolumeAdvectionDiffusion(0.05))
self.finite_diff_eq = (
advection_equations.FiniteDifferenceAdvectionDiffusion(0.05))
self.upwind_eq = (advection_equations.UpwindAdvectionDiffusion(0.05))
self.base_vol_model = models.FiniteDifferenceModel(
self.finite_vol_eq, self.grid)
self.base_diff_model = models.FiniteDifferenceModel(
self.finite_diff_eq, self.grid)
self.base_upwind_model = models.FiniteDifferenceModel(
self.upwind_eq, self.grid)
def test_integration_in_constant_velocity_field(self, equation, atol):
grid = grids.Grid.from_period(100, length=100)
model = models.FiniteDifferenceModel(equation, grid)
initial_concentration = equations.symmetrized_gaussian(
grid, 50, 50, gaussian_width=20)
self.assertGreaterEqual(initial_concentration.min(), 0.0)
self.assertLessEqual(initial_concentration.max(), 1.0 + 1e-7)
initial_state = {
'concentration': initial_concentration.astype(np.float32),
'x_velocity': np.ones(grid.shape, np.float32),
'y_velocity': np.zeros(grid.shape, np.float32)
}
steps = round(1 / equation.cfl_safety_factor) * np.arange(10)
integrated = integrate.integrate_steps(model, initial_state, steps)
actual = integrated['concentration'].numpy()
expected = np.stack(
[np.roll(initial_concentration, i, axis=0) for i in range(10)])
np.testing.assert_allclose(actual, expected, atol=atol)
if equation.METHOD is polynomials.Method.FINITE_VOLUME:
np.testing.assert_allclose(actual[-1].sum(),
actual[0].sum(),
rtol=1e-7)
else:
np.testing.assert_allclose(actual[-1].sum(),
actual[0].sum(),
rtol=1e-3)
if equation.MONOTONIC:
self.assertGreaterEqual(actual[-1].min(), 0.0)
self.assertLessEqual(actual[-1].max(), 1.0)
def coarse_model(self):
return models.FiniteDifferenceModel(self.equation, self.output_grid)
def model(self):
return models.FiniteDifferenceModel(self.equation,
self.simulation_grid)