def test_Bates_analytical():
from landlab import RasterModelGrid
grid = RasterModelGrid((32, 240), xy_spacing=25)
grid.add_zeros("node", "surface_water__depth")
grid.add_zeros("node", "topographic__elevation")
grid.set_closed_boundaries_at_grid_edges(True, True, True, True)
bates = OverlandFlowBates(grid, mannings_n=0.01, h_init=0.001)
time = 0.0
bates.dt = 1.0
while time < 500:
bates.overland_flow(grid)
h_boundary = ((7. / 3.) * (0.01 ** 2) * (0.4 ** 3) * time) ** (3. / 7.)
grid.at_node["surface_water__depth"][grid.nodes[1:-1, 1]] = h_boundary
time += bates.dt
x = np.arange(0, ((grid.shape[1]) * grid.dx), grid.dx)
h_analytical = -(7. / 3.) * (0.01 ** 2) * (0.4 ** 2) * (x - (0.4 * 500))
h_analytical[np.where(h_analytical > 0)] = h_analytical[
np.where(h_analytical > 0)
] ** (3. / 7.)
h_analytical[np.where(h_analytical < 0)] = 0.0
hBates = bates.h.reshape(grid.shape)
hBates = hBates[1][1:]
hBates = np.append(hBates, [0])
np.testing.assert_almost_equal(h_analytical, hBates, decimal=1)
# Now we'll identify our leftmost, but interior, column and the IDs of those
# nodes. One column in to prevent issues with BC.
inside_left_edge = rmg.nodes[1: -1, 1]
# Initializing our class...
of = OverlandFlowBates(rmg, mannings_n=n, h_init=h_init)
# Let's see how long this run takes...
starttime = time()
while elapsed_time < run_time:
# Now, we generate overland flow.
of.overland_flow()
# Recalculate water depth at the boundary ...
# water depth at left side (m)
h_boundary = (seven_over_three * n * n * u * u * u *
elapsed_time) ** three_over_seven
# And now we input that water depth along the left-most interior column,
# in all rows that are not boundary rows.
rmg.at_node['water__depth'][inside_left_edge] = h_boundary
# Increased elapsed time
elapsed_time += of.dt
# End time...
endtime = time()
# Now we'll identify our leftmost, but interior, column and the IDs of those
# nodes. One column in to prevent issues with BC.
inside_left_edge = rmg.nodes[1: -1, 1]
# Initializing our class...
of = OverlandFlowBates(rmg, mannings_n=n, h_init=h_init)
# Let's see how long this run takes...
starttime = time()
while elapsed_time < run_time:
# Now, we generate overland flow.
of.overland_flow()
# Recalculate water depth at the boundary ...
# water depth at left side (m)
h_boundary = (seven_over_three * n * n * u * u * u *
elapsed_time) ** three_over_seven
# And now we input that water depth along the left-most interior column,
# in all rows that are not boundary rows.
rmg.at_node['surface_water__depth'][inside_left_edge] = h_boundary
# Increased elapsed time
elapsed_time += of.dt
# End time...
endtime = time()
# Now we'll identify our leftmost, but interior, column and the IDs of those
# nodes. One column in to prevent issues with BC.
inside_left_edge = rmg.nodes[1: -1, 1]
# Initializing our class...
of = OverlandFlowBates(rmg)
# Let's see how long this run takes...
starttime = time()
while elapsed_time < run_time:
# First, we calculate our time step.
dt = of.gear_time_step(rmg)
# Now, we generate overland flow.
of.overland_flow(rmg)
# Recalculate water depth at the boundary ...
# water depth at left side (m)
h_boundary = (seven_over_three * n * n * u * u * u *
elapsed_time) ** three_over_seven
# And now we input that water depth along the left-most interior column, in all rows that are not boundary rows.
rmg.at_node['water_depth'][inside_left_edge] = h_boundary
# Print time
#print(elapsed_time)
# Increased elapsed time
elapsed_time += dt
# Now we'll identify our leftmost, but interior, column and the IDs of those
# nodes. One column in to prevent issues with BC.
inside_left_edge = rmg.nodes[1: -1, 1]
# Initializing our class...
of = OverlandFlowBates(rmg)
dt = 1.0
# Let's see how long this run takes...
starttime = time()
while elapsed_time < run_time:
# Now, we generate overland flow.
of.overland_flow(rmg, dt)
# Recalculate water depth at the boundary ...
# water depth at left side (m)
h_boundary = (seven_over_three * n * n * u * u * u *
elapsed_time) ** three_over_seven
# And now we input that water depth along the left-most interior column,
# in all rows that are not boundary rows.
rmg.at_node['water_depth'][inside_left_edge] = h_boundary
# Print time
#print(elapsed_time)
dt = of.gear_time_step(rmg)
#print(elapsed_time)
rmg.add_zeros('water__discharge', at='active_link') # unit discharge (m2/s)
# Now we'll identify our leftmost, but interior, column and the IDs of those
# nodes. One column in to prevent issues with BC.
inside_left_edge = rmg.nodes[1:-1, 1]
# Initializing our class...
of = OverlandFlowBates(rmg, mannings_n=n, h_init=h_init)
# Let's see how long this run takes...
starttime = time()
while elapsed_time < run_time:
# Now, we generate overland flow.
of.overland_flow(rmg)
# Recalculate water depth at the boundary ...
# water depth at left side (m)
h_boundary = (seven_over_three * n * n * u * u * u *
elapsed_time)**three_over_seven
# And now we input that water depth along the left-most interior column,
# in all rows that are not boundary rows.
rmg.at_node['water__depth'][inside_left_edge] = h_boundary
# Increased elapsed time
elapsed_time += of.dt
# End time...
endtime = time()
