def main():
PARAMS = {
"nx": 2**11,
"nz": 2**10,
"lx": 16.0 / 9.0,
"lz": 1.0,
"Re": 1e5,
"integrator_order": 2,
"max_time": 3.0,
"final_time": 10,
"save_cadence": 0.003,
"precision": "single",
"spatial_derivative_order": 2,
"integrator_order": 2,
"integrator": "semi-implicit",
"cfl_cutoff": 0.5,
}
PARAMS["initial_dt"] = 0.05 * PARAMS["lx"] / PARAMS["nx"]
params = Parameters(PARAMS)
params.save()
simulation = Simulation(params, xp)
basis_fns = [BasisFunctions.COMPLEX_EXP, BasisFunctions.COMPLEX_EXP]
# Simulation variables
w = simulation.make_variable("w", basis_fns)
ink = simulation.make_variable("ink", basis_fns)
dw = simulation.make_derivative("dw")
dink = simulation.make_derivative("dink")
psi = simulation.make_variable("psi", basis_fns)
ux = simulation.make_variable("ux", basis_fns)
uz = simulation.make_variable("uz", basis_fns)
simulation.init_laplacian_solver(basis_fns)
simulation.config_dump([w, ink], [dw, dink])
simulation.config_save([w])
simulation.config_cfl(ux, uz)
simulation.config_scalar_trackers({
"kinetic_energy.npz":
partial(calc_kinetic_energy, ux, uz, xp, params),
})
# Load initial conditions
if params.load_from is not None:
simulation.load(params.load_from)
else:
load_initial_conditions(params, w, ink)
total_start = time.time()
# Main loop
while simulation.is_running():
# SOLVER STARTS HERE
calc_velocity_from_vorticity(w, psi, ux, uz,
simulation.get_laplacian_solver())
lin_op = 1.0 / params.Re * w.lap()
dw[:] = -w.vec_dot_nabla(ux.getp(), uz.getp())
simulation._integrator.integrate(w, dw, lin_op)
# lin_op = 1.0/params.Re * ink.lap()
# dink[:] = (
# -ink.vec_dot_nabla(ux.getp(), uz.getp())
# )
# simulation._integrator.integrate(ink, dink, lin_op)
simulation.end_loop()
total_end = time.time() - total_start
print(f"Total time: {total_end/3600:.2f} hr")
print(f"Total time: {total_end:.2f} s")
def main():
PARAMS = {
"nx": 2**10,
"nz": 2**10,
"lx": 2 * np.pi,
"lz": 2 * np.pi,
"nu": 0.25,
"initial_dt": 1e-3,
"precision": "single",
"spatial_derivative_order": 2,
"integrator_order": 2,
"integrator": "semi-implicit",
"cfl_cutoff": 0.5,
}
PARAMS["final_time"] = 1000 * PARAMS["initial_dt"]
params = Parameters(PARAMS)
params.save()
simulation = Simulation(params, xp)
basis_fns = [BasisFunctions.COMPLEX_EXP, BasisFunctions.COMPLEX_EXP]
# Simulation variables
w = simulation.make_variable("w", basis_fns)
dw = simulation.make_derivative("dw")
psi = simulation.make_variable("psi", basis_fns)
ux = simulation.make_variable("ux", basis_fns)
uz = simulation.make_variable("uz", basis_fns)
simulation.init_laplacian_solver(basis_fns)
simulation.config_dump([w], [dw])
simulation.config_save([w])
simulation.config_cfl(ux, uz)
simulation.config_scalar_trackers({
"kinetic_energy.npz":
partial(calc_kinetic_energy, ux, uz, xp, params),
})
# Load initial conditions
if params.load_from is not None:
simulation.load(params.load_from)
else:
load_initial_conditions(params, w)
total_start = time.time()
# Main loop
while simulation.is_running():
# SOLVER STARTS HERE
calc_velocity_from_vorticity(w, psi, ux, uz,
simulation.get_laplacian_solver())
lin_op = params.nu * w.lap()
dw[:] = -w.vec_dot_nabla(ux.getp(), uz.getp())
simulation._integrator.integrate(w, dw, lin_op)
simulation.end_loop()
final_ke = calc_kinetic_energy(ux, uz, xp, params)
initial_ke = simulation._trackers[0]._values[0]
viscous_factor = final_ke / initial_ke
true_factor = np.exp(-simulation._t)
print("abs error = ", abs(viscous_factor - true_factor))
print(
"rel error = ",
abs(viscous_factor - true_factor) / true_factor * 100,
"%",
)
total_end = time.time() - total_start
print(f"Total time: {total_end/3600:.2f} hr")
print(f"Total time: {total_end:.2f} s")
def main():
PARAMS = {
"nx": 2**12,
"nz": 2**11,
"lx": 16.0 / 9,
"lz": 1.0,
"initial_dt": 1e-4,
"cfl_cutoff": 0.5,
"Re": 1e6,
"S": 1e6,
"final_time": 1,
"spatial_derivative_order": 2,
"integrator_order": 2,
"integrator": "semi-implicit",
"save_cadence": 0.003,
"dump_cadence": 0.1,
"precision": "single",
}
params = Parameters(PARAMS)
params.save()
simulation = Simulation(params, xp)
basis_fns = [BasisFunctions.COMPLEX_EXP, BasisFunctions.COMPLEX_EXP]
# Simulation variables
w = simulation.make_variable("w", basis_fns)
j = simulation.make_variable("j", basis_fns)
dw = simulation.make_derivative("dw")
dj = simulation.make_derivative("dj")
psi = simulation.make_variable("psi", basis_fns)
ux = simulation.make_variable("ux", basis_fns)
uz = simulation.make_variable("uz", basis_fns)
phi = simulation.make_variable("phi", basis_fns)
bx = simulation.make_variable("bx", basis_fns)
bz = simulation.make_variable("bz", basis_fns)
simulation.init_laplacian_solver(psi._basis_functions)
simulation.config_dump([w, j], [dw, dj])
simulation.config_save([j])
simulation.config_cfl(ux, uz)
simulation.config_scalar_trackers({
"kinetic_energy.npz":
partial(calc_kinetic_energy, ux, uz, xp, params),
})
# Load initial conditions
if params.load_from is not None:
simulation.load(params.load_from)
else:
load_initial_conditions(params, w, j)
total_start = time.time()
# Main loop
while simulation.is_running():
# SOLVER STARTS HERE
calc_velocity_from_vorticity(w, psi, ux, uz,
simulation.get_laplacian_solver())
# FIXME - this is not really velocity!! This should be refactored!
calc_velocity_from_vorticity(j, phi, bx, bz,
simulation.get_laplacian_solver())
lin_op = 1.0 / params.Re * w.lap()
dw[:] = -w.vec_dot_nabla(ux.getp(), uz.getp()) + j.vec_dot_nabla(
bx.getp(), bz.getp())
simulation._integrator.integrate(w, dw, lin_op)
lin_op = 1.0 / params.S * j.lap()
dj[:] = -j.vec_dot_nabla(ux.getp(), uz.getp()) + w.vec_dot_nabla(
bx.getp(), bz.getp())
simulation._integrator.integrate(j, dj, lin_op)
simulation.end_loop()
total_end = time.time() - total_start
print(f"Total time: {total_end/3600:.2f} hr")
print(f"Total time: {total_end:.2f} s")
def main():
PARAMS = {
"nx": 2 ** 7,
"nz": 2 ** 6,
"lx": 16.0 / 9,
"lz": 1.0,
"initial_dt": 1e-5,
"cfl_cutoff": 0.5,
"Pr": 1.0,
"Ra": 1e6,
"final_time": 1e-1,
"spatial_derivative_order": 2,
"integrator_order": 2,
"integrator": "explicit",
"save_cadence": 5e-5,
"dump_cadence": 1e-1,
"discretisation": ["spectral", "fdm"],
"precision": "single",
}
params = Parameters(PARAMS)
params.save()
simulation = Simulation(params, xp)
basis_fns = [BasisFunctions.COMPLEX_EXP, BasisFunctions.FDM]
# Simulation variables
w = simulation.make_variable("w", basis_fns)
tmp = simulation.make_variable("tmp", basis_fns)
dw = simulation.make_derivative("dw")
dtmp = simulation.make_derivative("dtmp")
psi = simulation.make_variable("psi", basis_fns)
ux = simulation.make_variable("ux", basis_fns)
uz = simulation.make_variable("uz", basis_fns)
simulation.init_laplacian_solver(psi._basis_functions)
simulation.config_dump([w, tmp], [dw, dtmp])
simulation.config_save([tmp])
simulation.config_cfl(ux, uz)
simulation.config_scalar_trackers(
{
"kinetic_energy.npz": partial(
calc_kinetic_energy, ux, uz, xp, params
),
}
)
# Load initial conditions
if params.load_from is not None:
simulation.load(params.load_from)
else:
load_initial_conditions(params, w, tmp)
total_start = time.time()
# Main loop
while simulation.is_running():
# SOLVER STARTS HERE
calc_velocity_from_vorticity(
w, psi, ux, uz, simulation.get_laplacian_solver()
)
diffusion_term = params.Pr * w.snabla2()
dw[:] = (
-w.vec_dot_nabla(ux.getp(), uz.getp())
- params.Pr * params.Ra * tmp.sddx()
)
simulation._integrator.integrate(w, dw, diffusion_term)
diffusion_term = tmp.snabla2()
dtmp[:] = -tmp.vec_dot_nabla(ux.getp(), uz.getp())
simulation._integrator.integrate(tmp, dtmp, diffusion_term)
w[1:, 0] = 0.0
w[1:, -1] = 0.0
psi[1:, 0] = 0.0
psi[1:, -1] = 0.0
psi[0, :] = 0.0
w[0, :] = 0.0
tmp[0, 0] = 1.0
tmp[0, -1] = 0.0
tmp[1:, 0] = 0.0
tmp[1:, -1] = 0.0
simulation.end_loop()
total_end = time.time() - total_start
print(f"Total time: {total_end/3600:.2f} hr")
print(f"Total time: {total_end:.2f} s")
def main():
factor = 0.25
LX = 335.0 * factor
LZ = 9.0 / 16 * LX
PARAMS = {
"nx": 2**9,
"nz": 2**8,
"lx": LX,
"lz": LZ,
"initial_dt": 1e-3,
"cfl_cutoff": 0.5,
"Pr": 7.0,
"R0": 1.1,
"tau": 1.0 / 3.0,
"final_time": 100,
"spatial_derivative_order": 2,
"integrator_order": 2,
"integrator": "semi-implicit",
"save_cadence": 0.05,
"dump_cadence": 10,
"precision": "single",
}
params = Parameters(PARAMS)
params.save()
simulation = Simulation(params, xp)
basis_fns = [BasisFunctions.COMPLEX_EXP, BasisFunctions.COMPLEX_EXP]
# Simulation variables
w = simulation.make_variable("w", basis_fns)
tmp = simulation.make_variable("tmp", basis_fns)
xi = simulation.make_variable("xi", basis_fns)
dw = simulation.make_derivative("dw")
dtmp = simulation.make_derivative("dtmp")
dxi = simulation.make_derivative("dxi")
psi = simulation.make_variable("psi", basis_fns)
ux = simulation.make_variable("ux", basis_fns)
uz = simulation.make_variable("uz", basis_fns)
simulation.init_laplacian_solver(psi._basis_functions)
simulation.config_dump([w, tmp, xi], [dw, dtmp, dxi])
simulation.config_save([tmp])
simulation.config_cfl(ux, uz)
simulation.config_scalar_trackers({
"kinetic_energy.npz":
partial(calc_kinetic_energy, ux, uz, xp, params),
"nusselt_number.npz":
partial(calc_nusselt_number, tmp, uz, xp, params),
})
# Load initial conditions
if params.load_from is not None:
simulation.load(params.load_from)
else:
load_initial_conditions(params, w, tmp, xi)
total_start = time.time()
# Main loop
while simulation.is_running():
# SOLVER STARTS HERE
calc_velocity_from_vorticity(w, psi, ux, uz,
simulation.get_laplacian_solver())
lin_op = params.Pr * w.lap()
dw[:] = (-w.vec_dot_nabla(ux.getp(), uz.getp()) +
params.Pr * xi.sddx() - params.Pr * tmp.sddx())
simulation._integrator.integrate(w, dw, lin_op)
lin_op = tmp.lap()
dtmp[:] = -tmp.vec_dot_nabla(ux.getp(), uz.getp()) - uz[:]
simulation._integrator.integrate(tmp, dtmp, lin_op)
lin_op = params.tau * xi.lap()
dxi[:] = -xi.vec_dot_nabla(ux.getp(), uz.getp()) - uz[:] / params.R0
simulation._integrator.integrate(xi, dxi, lin_op)
# Remove mean z variation
tmp[:, 0] = 0.0
xi[:, 0] = 0.0
simulation.end_loop()
total_end = time.time() - total_start
print(f"Total time: {total_end/3600:.2f} hr")
print(f"Total time: {total_end:.2f} s")