def test_bad_coef_at_link(diff):
grid = RasterModelGrid((5, 6))
value_at_node = np.full(grid.number_of_nodes, 1.0)
coef_at_link = np.full(grid.number_of_links + diff, 1.0)
with pytest.raises(ValueError):
get_core_node_matrix(grid, value_at_node, coef_at_link=coef_at_link)
def test_scalar_value_at_node(Grid):
grid = Grid((4, 5))
_, expected = get_core_node_matrix(grid, np.full(grid.number_of_nodes,
11.0))
_, actual = get_core_node_matrix(grid, 11.0)
assert_array_equal(expected, actual)
def test_scalar_coef_at_link(Grid):
grid = Grid((4, 5))
expected, _ = get_core_node_matrix(grid,
1.0,
coef_at_link=np.full(
grid.number_of_links, 11.0))
actual, _ = get_core_node_matrix(grid, 1.0, coef_at_link=11.0)
assert_array_equal(expected.toarray(), actual.toarray())
def test_coef_at_link(Grid):
grid = Grid((4, 5))
value_at_node = np.full(grid.number_of_nodes, 1.0)
coef_at_link = np.full(grid.number_of_links, 1.0)
mat, rhs = get_core_node_matrix(grid,
value_at_node,
coef_at_link=coef_at_link)
actual, actual_rhs = get_core_node_matrix(grid, value_at_node,
coef_at_link * 2.0)
assert_array_equal(mat.toarray(), actual.toarray() / 2.0)
assert_array_equal(rhs, actual_rhs)
def test_default_coef_is_one(Grid):
grid = Grid((4, 5))
grid.status_at_node[13] = grid.BC_NODE_IS_FIXED_VALUE
grid.status_at_node[2] = grid.BC_NODE_IS_CLOSED
value_at_node = np.arange(grid.number_of_nodes, dtype=float)
coef_at_link = np.full(grid.number_of_links, 1.0, dtype=float)
expected, _ = get_core_node_matrix(grid,
value_at_node,
coef_at_link=coef_at_link)
actual, _ = get_core_node_matrix(grid, value_at_node)
assert_array_equal(expected.toarray(), actual.toarray())
def test_small_grids():
grid = RasterModelGrid((3, 3))
value_at_node = np.full(grid.number_of_nodes, 1.0)
mat, rhs = get_core_node_matrix(grid, value_at_node)
assert_array_equal(mat.toarray(), [[-4.0]])
assert_array_equal(rhs, [[-4.0]])
grid = RasterModelGrid((4, 4))
value_at_node = np.full(grid.number_of_nodes, 1.0)
mat, rhs = get_core_node_matrix(grid, value_at_node)
assert_array_equal(
mat.toarray(),
[
[-4.0, 1.0, 1.0, 0.0],
[1.0, -4.0, 0.0, 1.0],
[1.0, 0.0, -4.0, 1.0],
[0.0, 1.0, 1.0, -4.0],
],
)
assert_array_equal(rhs, [[-2.0], [-2.0], [-2.0], [-2.0]])
def run_one_step(self):
"""Calculate the tidal flow field and water-surface elevation."""
# Tidal mean water depth and water surface elevation at nodes
# (Note: mean water surf elev only used for boundary conditions in
# matrix construction; should be mean sea level)
self._calc_effective_water_depth()
self._boundary_mean_water_surf_elev[:] = self._mean_sea_level
# Map water depth to links
map_min_of_link_nodes_to_link(self.grid,
self._water_depth,
out=self._water_depth_at_links)
# Calculate velocity and diffusion coefficients on links
velocity_coef = self._water_depth_at_links**_FOUR_THIRDS / (
(self.roughness**2) * self._scale_velocity)
self._diffusion_coef_at_links[:] = self._water_depth_at_links * velocity_coef
# Calculate inundation / drainage rate at nodes
tidal_inundation_rate = self.calc_tidal_inundation_rate()
# Set up right-hand-side (RHS) vector for both ebb and flood tides (only
# difference is in the sign)
cores = self.grid.core_nodes
# For flood tide, set up matrix and add boundary info to RHS vector
# mat, rhs = make_core_node_matrix_var_coef(
mat, rhs = get_core_node_matrix(
self.grid,
self._boundary_mean_water_surf_elev,
coef_at_link=self._diffusion_coef_at_links,
)
rhs[:, 0] += self._grid_multiplier * tidal_inundation_rate[cores]
# Solve for flood tide water-surface elevation
tidal_wse = np.zeros(self.grid.number_of_nodes)
tidal_wse[self.grid.core_nodes] = spsolve(mat, rhs)
# Calculate flood-tide water-surface gradient at links
tidal_wse_grad = np.zeros(self.grid.number_of_links)
self.grid.calc_grad_at_link(tidal_wse, out=tidal_wse_grad)
# Calculate flow velocity field at links for flood tide, and assign
# negative of the flood tide values to ebb tide
self._flood_tide_vel[self.grid.active_links] = (
-velocity_coef[self.grid.active_links] *
tidal_wse_grad[self.grid.active_links])
self._ebb_tide_vel[:] = -self._flood_tide_vel
def test_hex_grid():
grid = HexModelGrid((4, 3))
value_at_node = np.full(grid.number_of_nodes, 1.0)
coef_at_link = np.full(grid.number_of_links, 1.0)
mat, rhs = get_core_node_matrix(grid,
value_at_node,
coef_at_link=coef_at_link)
assert_array_equal(
mat.toarray(),
[
[-6.0, 1.0, 1.0, 1.0, 0.0],
[1.0, -6.0, 0.0, 1.0, 1.0],
[1.0, 0.0, -6.0, 1.0, 0.0],
[1.0, 1.0, 1.0, -6.0, 1.0],
[0.0, 1.0, 0.0, 1.0, -6.0],
],
)
assert_array_equal(rhs, [[-3.0], [-3.0], [-4.0], [-2.0], [-4.0]])
def test_default_bc():
grid = RasterModelGrid((5, 6))
value_at_node = np.full(grid.number_of_nodes, 1.0, dtype=float)
mat, rhs = get_core_node_matrix(grid, value_at_node)
assert_array_equal(
mat.toarray(),
[
[-4.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[1.0, -4.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 1.0, -4.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 1.0, -4.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0],
[1.0, 0.0, 0.0, 0.0, -4.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0],
[0.0, 1.0, 0.0, 0.0, 1.0, -4.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0],
[0.0, 0.0, 1.0, 0.0, 0.0, 1.0, -4.0, 1.0, 0.0, 0.0, 1.0, 0.0],
[0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, -4.0, 0.0, 0.0, 0.0, 1.0],
[0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, -4.0, 1.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, -4.0, 1.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, -4.0, 1.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, -4.0],
],
)
assert_array_equal(
rhs,
[
[-2.0],
[-1.0],
[-1.0],
[-2.0],
[-1.0],
[0.0],
[0.0],
[-1.0],
[-2.0],
[-1.0],
[-1.0],
[-2.0],
],
)
def test_with_fixed_value_bc():
grid = RasterModelGrid((4, 5))
grid.status_at_node[13] = grid.BC_NODE_IS_FIXED_VALUE
grid.status_at_node[2] = grid.BC_NODE_IS_CLOSED
value_at_node = np.arange(grid.number_of_nodes, dtype=float)
mat, rhs = get_core_node_matrix(grid, value_at_node)
assert_array_equal(
mat.toarray(),
[
[-4.0, 1.0, 0.0, 1.0, 0.0],
[1.0, -3.0, 1.0, 0.0, 1.0],
[0.0, 1.0, -4.0, 0.0, 0.0],
[1.0, 0.0, 0.0, -4.0, 1.0],
[0.0, 1.0, 0.0, 1.0, -4.0],
],
)
assert_array_equal(
rhs,
[[-6.0], [0.0], [-25.0], [-26.0], [-30.0]],
)
def test_with_coef():
grid = RasterModelGrid((4, 5))
grid.status_at_node[13] = grid.BC_NODE_IS_FIXED_VALUE
grid.status_at_node[2] = grid.BC_NODE_IS_CLOSED
value_at_node = np.arange(grid.number_of_nodes, dtype=float)
coef_at_link = np.arange(grid.number_of_links, dtype=np.double)
mat, rhs = get_core_node_matrix(grid,
value_at_node,
coef_at_link=coef_at_link)
assert_array_equal(
mat.toarray(),
[
[-38.0, 10.0, 0.0, 14.0, 0.0],
[10.0, -36.0, 11.0, 0.0, 15.0],
[0.0, 11.0, -46.0, 0.0, 0.0],
[14.0, 0.0, 0.0, -74.0, 19.0],
[0.0, 15.0, 0.0, 19.0, -78.0],
],
)
assert_array_equal(rhs, [[-6.0], [0.0], [-25.0], [-26.0], [-30.0]])