def checkpoint(): from firedrake_fluids.shallow_water import ShallowWater # Initialise the simulation from scratch. sw = ShallowWater(path=os.path.join(cwd, "checkpoint.swml")) solution = sw.run(checkpoint=None) ux_initial = solution.split()[0] h_initial = solution.split()[1] # Initialise the simulation using the data in checkpoint.npy for the initial conditions. sw = ShallowWater(path=os.path.join(cwd, "checkpoint.swml")) solution = sw.run(checkpoint=os.path.join(cwd, "checkpoint.npy")) ux_initial_from_checkpoint = solution.split()[0] h_initial_from_checkpoint = solution.split()[1] return ux_initial.vector().array(), h_initial.vector().array(), ux_initial_from_checkpoint.vector().array(), h_initial_from_checkpoint.vector().array()
def swe_mms_p2p1_quadratic_drag_divergence_free():
from firedrake_fluids.shallow_water import ShallowWater
configs = ["MMS_A", "MMS_B", "MMS_C"]
ux_norms = []
uy_norms = []
h_norms = []
for c in configs:
sw = ShallowWater(path=os.path.join(cwd, c + ".swml"))
solution = sw.run()
ux_old = solution.split()[0][0]
uy_old = solution.split()[0][1]
h_old = solution.split()[1]
fs_exact = FunctionSpace(sw.mesh, "CG", 3)
ux_exact = project(Expression("cos(x[1])*sin(x[0])"), fs_exact)
uy_exact = project(Expression("-cos(x[0])*sin(x[1])"), fs_exact)
h_exact = project(Expression("sin(x[0])*sin(x[1])"), fs_exact)
h_norms.append(sqrt(assemble(dot(h_old - h_exact, h_old - h_exact) * dx)))
ux_norms.append(sqrt(assemble(dot(ux_old - ux_exact, ux_old - ux_exact) * dx)))
uy_norms.append(sqrt(assemble(dot(uy_old - uy_exact, uy_old - uy_exact) * dx)))
return (h_norms, ux_norms, uy_norms)
def swe_mms_p2p1():
from firedrake_fluids.shallow_water import ShallowWater
configs = ["MMS_A", "MMS_B", "MMS_C"]
ux_norms = []
uy_norms = []
h_norms = []
for c in configs:
sw = ShallowWater(path=os.path.join(cwd, c + ".swml"))
solution = sw.run()
ux_old = solution.split()[0][0]
uy_old = solution.split()[0][1]
h_old = solution.split()[1]
fs_exact = FunctionSpace(sw.mesh, "CG", 3)
ux_exact = project(Expression("cos(x[0])*sin(x[1])"), fs_exact)
uy_exact = project(Expression("sin(x[0]*x[0]) + cos(x[1])"), fs_exact)
h_exact = project(Expression("sin(x[0])*sin(x[1])"), fs_exact)
h_norms.append(
sqrt(assemble(dot(h_old - h_exact, h_old - h_exact) * dx)))
ux_norms.append(
sqrt(assemble(dot(ux_old - ux_exact, ux_old - ux_exact) * dx)))
uy_norms.append(
sqrt(assemble(dot(uy_old - uy_exact, uy_old - uy_exact) * dx)))
return (h_norms, ux_norms, uy_norms)
def swe_tidal_flow_regular_bed(): from firedrake_fluids.shallow_water import ShallowWater from firedrake_adjoint import project sw = ShallowWater(path=os.path.join(cwd, "swe_tidal_flow_regular_bed.swml")) solution = sw.run() mesh = sw.mesh # Get the coordinates of each node coordinates = mesh.coordinates # For projecting to the same space as the coordinate field vfs = VectorFunctionSpace(mesh, "CG", 1) fs = FunctionSpace(mesh, "CG", 1) u = solution.split()[0] h = solution.split()[1] u = project(u, vfs, annotate=False) h = project(h, fs, annotate=False) print coordinates.vector().array() print u.vector().array() print h.vector().array() # Use [0::2] to select the even-numbered components of the vector's array (i.e. the x-component only). return coordinates.vector().array()[0::2], u.vector().array()[0::2], h.vector().array()
def swe_tidal_flow_regular_bed():
from firedrake_fluids.shallow_water import ShallowWater
from firedrake_adjoint import project
sw = ShallowWater(
path=os.path.join(cwd, "swe_tidal_flow_regular_bed.swml"))
solution = sw.run()
mesh = sw.mesh
# Get the coordinates of each node
coordinates = mesh.coordinates
# For projecting to the same space as the coordinate field
vfs = VectorFunctionSpace(mesh, "CG", 1)
fs = FunctionSpace(mesh, "CG", 1)
u = solution.split()[0]
h = solution.split()[1]
u = project(u, vfs, annotate=False)
h = project(h, fs, annotate=False)
print coordinates.vector().array()
print u.vector().array()
print h.vector().array()
# Use [0::2] to select the even-numbered components of the vector's array (i.e. the x-component only).
return coordinates.vector().array()[0::2], u.vector().array(
)[0::2], h.vector().array()
def swe_mms_p0p1():
from firedrake_fluids.shallow_water import ShallowWater
configs = ["MMS_A", "MMS_B", "MMS_C"]
ux_norms = []
uy_norms = []
h_norms = []
for c in configs:
sw = ShallowWater(path=os.path.join(cwd, c + ".swml"))
solution = sw.run()
ux_old = solution.split()[0][0]
uy_old = solution.split()[0][1]
h_old = solution.split()[1]
fs_exact_dg = FunctionSpace(sw.mesh, "DG", 3)
fs_exact_cg = FunctionSpace(sw.mesh, "CG", 3)
ux_exact = project(Expression("cos(x[0])*sin(x[1])"), fs_exact_dg, solver_parameters={'ksp_type': 'gmres', 'ksp_rtol': 1e-8, 'pc_type': 'sor'})
uy_exact = project(Expression("sin(x[0]*x[0]) + cos(x[1])"), fs_exact_dg, solver_parameters={'ksp_type': 'gmres', 'ksp_rtol': 1e-8, 'pc_type': 'sor'})
h_exact = project(Expression("sin(x[0])*sin(x[1])"), fs_exact_cg, solver_parameters={'ksp_type': 'gmres', 'ksp_rtol': 1e-8, 'pc_type': 'sor'})
h_norms.append(sqrt(assemble(dot(h_old - h_exact, h_old - h_exact) * dx)))
ux_norms.append(sqrt(assemble(dot(ux_old - ux_exact, ux_old - ux_exact) * dx)))
uy_norms.append(sqrt(assemble(dot(uy_old - uy_exact, uy_old - uy_exact) * dx)))
return (h_norms, ux_norms, uy_norms)
def swe_steady_state(): from firedrake_fluids.shallow_water import ShallowWater sw = ShallowWater(path=os.path.join(cwd, "swe_steady_state.swml")) solution = sw.run() u_old = solution.split()[0] h_old = solution.split()[1] return u_old.vector().array(), h_old.vector().array()
def swe_steady_flow_dirichlet(): from firedrake_fluids.shallow_water import ShallowWater sw = ShallowWater(path=os.path.join(cwd, "swe_steady_flow_dirichlet.swml")) solution = sw.run() u_old = solution.split()[0] h_old = solution.split()[1] return u_old.vector().array(), h_old.vector().array()
def checkpoint():
from firedrake_fluids.shallow_water import ShallowWater
# Initialise the simulation from scratch.
sw = ShallowWater(path=os.path.join(cwd, "checkpoint.swml"))
solution = sw.run(checkpoint=None)
ux_initial = solution.split()[0]
h_initial = solution.split()[1]
# Initialise the simulation using the data in checkpoint.npy for the initial conditions.
sw = ShallowWater(path=os.path.join(cwd, "checkpoint.swml"))
solution = sw.run(checkpoint=os.path.join(cwd, "checkpoint.npy"))
ux_initial_from_checkpoint = solution.split()[0]
h_initial_from_checkpoint = solution.split()[1]
return ux_initial.vector().array(), h_initial.vector().array(
), ux_initial_from_checkpoint.vector().array(
), h_initial_from_checkpoint.vector().array()
def swe_standing_wave():
from firedrake_fluids.shallow_water import ShallowWater
sw = ShallowWater(path=os.path.join(cwd, "swe_standing_wave.swml"))
solution = sw.run()
h = solution.split()[-1]
return h.vector().array()
def swe_standing_wave():
from firedrake_fluids.shallow_water import ShallowWater
sw = ShallowWater(path=os.path.join(cwd, "swe_standing_wave.swml"))
solution = sw.run()
h = solution.split()[-1]
return h.vector().array()
def swe_dam_break_1d():
from firedrake_fluids.shallow_water import ShallowWater
sw = ShallowWater(path=os.path.join(cwd, "swe_dam_break_1d.swml"))
solution = sw.run()
h = solution.split()[1]
u = solution.split()[0]
return h.vector().array(), u.vector().array()
def swe_dam_break_2d(): from firedrake_fluids.shallow_water import ShallowWater sw = ShallowWater(path=os.path.join(cwd, "swe_dam_break_2d.swml")) solution = sw.run() h = solution.split()[1] u = solution.split()[0] return h.vector().array(), u.vector().array()
def swe_wave_speed_1d():
from firedrake_fluids.shallow_water import ShallowWater
sw = ShallowWater(path=os.path.join(cwd, "swe_wave_speed_1d.swml"))
solution = sw.run()
h_old = solution.split()[-1]
return h_old.vector().array()
def swe_wave_speed_1d(): from firedrake_fluids.shallow_water import ShallowWater sw = ShallowWater(path=os.path.join(cwd, "swe_wave_speed_1d.swml")) solution = sw.run() h_old = solution.split()[-1] return h_old.vector().array()