def test_findiff_cyl():
"""test operator for a simple cylindrical grid. Note that we only
really test the polar symmetry"""
grid = CylindricalGrid(1.5, [0, 1], (3, 2), periodic_z=True)
_, r1, r2 = grid.axes_coords[0]
np.testing.assert_array_equal(grid.discretization, np.full(2, 0.5))
s = ScalarField(grid, [[1, 1], [2, 2], [4, 4]])
v = VectorField(grid,
[[[1, 1], [2, 2], [4, 4]], [[0, 0]] * 3, [[0, 0]] * 3])
# test gradient
grad = s.gradient(bc=["value", "periodic"])
np.testing.assert_allclose(grad.data[0], [[1, 1], [3, 3], [-6, -6]])
grad = s.gradient(bc=["derivative", "periodic"])
np.testing.assert_allclose(grad.data[0], [[1, 1], [3, 3], [2, 2]])
# test divergence
div = v.divergence(bc=["value", "periodic"])
y1 = 3 + 2 / r1
y2 = -6 + 4 / r2
np.testing.assert_allclose(div.data, [[5, 5], [y1, y1], [y2, y2]])
div = v.divergence(bc=["derivative", "periodic"])
y2 = 2 + 4 / r2
np.testing.assert_allclose(div.data, [[5, 5], [y1, y1], [y2, y2]])
# test laplace
lap = s.laplace(bc=[{"type": "value", "value": 3}, "periodic"])
y1 = 4 + 3 / r1
y2 = -16
np.testing.assert_allclose(lap.data, [[8, 8], [y1, y1], [y2, y2]])
lap = s.laplace(bc=[{"type": "derivative", "value": 3}, "periodic"])
y2 = -2 + 3.5 / r2
np.testing.assert_allclose(lap.data, [[8, 8], [y1, y1], [y2, y2]])
def test_divergence():
"""test the divergence operator"""
grid = CartesianGrid([[0, 2 * np.pi], [0, 2 * np.pi]], [16, 16],
periodic=True)
x, y = grid.cell_coords[..., 0], grid.cell_coords[..., 1]
data = [np.cos(x) + y, np.sin(y) - x]
v = VectorField(grid, data)
s1 = v.divergence("auto_periodic_neumann")
assert s1.data.shape == (16, 16)
div = np.cos(y) - np.sin(x)
np.testing.assert_allclose(s1.data, div, rtol=0.1, atol=0.1)
v.divergence("auto_periodic_neumann", out=s1)
assert s1.data.shape == (16, 16)
np.testing.assert_allclose(s1.data, div, rtol=0.1, atol=0.1)
def test_findiff_sph():
"""test operator for a simple spherical grid"""
grid = SphericalSymGrid(1.5, 3)
_, r1, r2 = grid.axes_coords[0]
assert grid.discretization == (0.5, )
s = ScalarField(grid, [1, 2, 4])
v = VectorField(grid, [[1, 2, 4], [0] * 3, [0] * 3])
# test gradient
grad = s.gradient(bc="value")
np.testing.assert_allclose(grad.data[0, :], [1, 3, -6])
grad = s.gradient(bc="derivative")
np.testing.assert_allclose(grad.data[0, :], [1, 3, 2])
# test divergence
div = v.divergence(bc="value", conservative=False)
np.testing.assert_allclose(div.data, [9, 3 + 4 / r1, -6 + 8 / r2])
div = v.divergence(bc="derivative", conservative=False)
np.testing.assert_allclose(div.data, [9, 3 + 4 / r1, 2 + 8 / r2])
def test_findiff():
""" test operator for a simple polar grid """
grid = PolarGrid(1.5, 3)
_, _, r2 = grid.axes_coords[0]
assert grid.discretization == (0.5, )
s = ScalarField(grid, [1, 2, 4])
v = VectorField(grid, [[1, 2, 4], [0] * 3])
# test gradient
grad = s.gradient(bc="value")
np.testing.assert_allclose(grad.data[0, :], [1, 3, -6])
grad = s.gradient(bc="derivative")
np.testing.assert_allclose(grad.data[0, :], [1, 3, 2])
# test divergence
div = v.divergence(bc="value")
np.testing.assert_allclose(div.data, [5, 17 / 3, -6 + 4 / r2])
div = v.divergence(bc="derivative")
np.testing.assert_allclose(div.data, [5, 17 / 3, 2 + 4 / r2])
def test_divergence_field_cyl():
""" test the divergence operator """
grid = CylindricalGrid(2 * np.pi, [0, 2 * np.pi], [8, 16], periodic_z=True)
r, z = grid.cell_coords[..., 0], grid.cell_coords[..., 1]
data = [
np.cos(r) + np.sin(z)**2,
np.cos(r)**2 + np.sin(z),
np.zeros_like(r)
]
v = VectorField(grid, data=data)
s = v.divergence(bc="natural")
assert s.data.shape == (8, 16)
res = np.cos(z) - np.sin(r) + (np.cos(r) + np.sin(z)**2) / r
np.testing.assert_allclose(s.data, res, rtol=0.1, atol=0.1)
