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rayleigh_benard_onset.py
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rayleigh_benard_onset.py
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"""
Dedalus script for 2D Rayleigh-Benard convection.
This script uses a Fourier basis in the x direction with periodic boundary
conditions. The equations are scaled in units of the buoyancy time (Fr = 1).
Usage:
rayleigh_benard_onset.py [options]
Options:
--Rayleigh=<Rayleigh> Rayleigh number [default: 1e6]
--Prandtl=<Prandtl> Prandtl number = nu/kappa [default: 1]
--nz=<nz> Vertical resolution (8 yields single precision, 16 yields near double precision) [default: 8]
--nx=<nx> Horizontal resolution [default: 128]
--multiplier=<multiplier> How much higher resolution is the verification run [default: 1.5]
--aspect=<aspect> Aspect ratio of problem [default: 64]
--restart=<restart_file> Restart from checkpoint
--label=<label> Optional additional case name label
--no_slip Use no-slip boundary conditions
--stress_free Use stress-free boundary conditions
--no_lid Use no-slip/stress-free boundary conditions
"""
import logging
logger = logging.getLogger(__name__)
import numpy as np
import time
from dedalus import public as de
def Rayleigh_Benard_onset(Prandtl=1, nz=32, nx=128, aspect=64, data_dir='./',
multiplier=1.5,
no_slip=False, stress_free=False, no_lid=False):
if not no_slip and not stress_free and not no_lid:
no_slip = True
# input parameters
logger.info(" Pr = {}".format(Prandtl))
# Parameters
Lz = 1.
Lx = aspect*Lz
logger.info("resolution: [{}x{}]".format(nx, nz))
# Create bases and domain
x_basis = de.Fourier('x', nx, interval=(0, Lx), dealias=3/2)
z_basis_set = []
nz_set = [nz, int(nz*multiplier)]
for nz_solve in nz_set:
z_basis_set.append(de.Chebyshev('z', nz_solve, interval=(0, Lz), dealias=3/2))
domain_set = []
for z_basis in z_basis_set:
domain_set.append(de.Domain([x_basis, z_basis], grid_dtype=np.float64))
solver_set = []
# 2D Boussinesq hydrodynamics
for domain in domain_set:
problem = de.EVP(domain, variables=['p','b','u','w','bz','uz','wz'], eigenvalue='Ra')
problem.meta['p','b','u','w']['z']['dirichlet'] = True
problem.parameters['F'] = F = 1
problem.parameters['Pr'] = np.sqrt(Prandtl)
problem.parameters['Lx'] = Lx
problem.parameters['Lz'] = Lz
problem.substitutions['plane_avg(A)'] = 'integ(A, "x")/Lx'
problem.substitutions['vol_avg(A)'] = 'integ(A)/Lx/Lz'
# for eq_type_1 = False; not working
problem.substitutions['dt(f)'] = '(0*f)'
problem.substitutions['P'] = '(1/sqrt(Ra)*1/sqrt(Pr))'
problem.substitutions['R'] = '(1/sqrt(Ra)*sqrt(Pr))'
#problem.substitutions['scale'] = 'sqrt(Ra)'
eq_type_1 = True
problem.add_equation("dx(u) + wz = 0")
if eq_type_1:
problem.add_equation(" - (dx(dx(b)) + dz(bz)) - F*w = 0")
problem.add_equation(" - (dx(dx(u)) + dz(uz)) + dx(p) = 0")
problem.add_equation(" - (dx(dx(w)) + dz(wz)) + dz(p) - Ra*b = 0")
else:
# not working
problem.add_equation("(dt(b) - P*(dx(dx(b)) + dz(bz)) - F*w ) = -(u*dx(b) + w*bz)")
problem.add_equation("(dt(u) - R*(dx(dx(u)) + dz(uz)) + dx(p) ) = -(u*dx(u) + w*uz)")
problem.add_equation("(dt(w) - R*(dx(dx(w)) + dz(wz)) + dz(p) - b ) = -(u*dx(w) + w*wz)")
problem.add_equation("bz - dz(b) = 0")
problem.add_equation("uz - dz(u) = 0")
problem.add_equation("wz - dz(w) = 0")
problem.add_bc("left(b) = 0")
if no_slip:
problem.add_bc("left(u) = 0")
problem.add_bc("right(u) = 0")
logger.info("using no_slip BCs")
elif stress_free:
problem.add_bc("left(uz) = 0")
problem.add_bc("right(uz) = 0")
logger.info("using stress_free BCs")
elif no_lid:
problem.add_bc("left(u) = 0")
problem.add_bc("right(uz) = 0")
logger.info("using stress_free BCs")
problem.add_bc("left(w) = 0")
problem.add_bc("right(b) = 0")
problem.add_bc("right(w) = 0", condition="(nx != 0)")
problem.add_bc("integ(p, 'z') = 0", condition="(nx == 0)")
solver_set.append(problem.build_solver())
logger.info('Solver built')
# Main loop
try:
logger.info('Starting loop')
start_time = time.time()
crit_Ra_set = []
min_wavenumber = 1
max_wavenumber = int(nx/2)
first_output = True
for wave in np.arange(min_wavenumber, max_wavenumber):
low_e_val_set = []
for solver in solver_set:
solver.solve(solver.pencils[wave])
eigenvalue_indices = np.argsort(np.abs(solver.eigenvalues))
eigenvalues = np.copy(solver.eigenvalues[eigenvalue_indices])
low_e_val_set.append(eigenvalues[0])
x_grid = solver.domain.grid(0)
if np.isfinite(low_e_val_set[0]):
if first_output:
print("k_h Ra_1 Ra_2 relative error")
print(" (nz={:4d}) (nz={:4d}) |Ra_1 - Ra_2|/|Ra_1|".format(nz_set[0], nz_set[1]))
first_output = False
print("{:4d}:{:12.4g} {:>12.4g} {:>12.4g} {:8.3g}".format(wave, wave/Lx, low_e_val_set[0], low_e_val_set[1],
np.abs(np.abs(low_e_val_set[0]-low_e_val_set[1])/low_e_val_set[0])))
crit_Ra_set.append(low_e_val_set[1])
else:
print(wave, "no finite values")
except:
logger.error('Exception raised, triggering end of main loop.')
raise
finally:
i_min_Ra = np.argmin(crit_Ra_set)
logger.info("Minimum Ra = {:g} at wavenumber={:g} (# {:d})".format(crit_Ra_set[i_min_Ra], (i_min_Ra + min_wavenumber)/Lx, i_min_Ra + min_wavenumber))
end_time = time.time()
logger.info('Run time: %.2f sec' %(end_time-start_time))
#logger.info('Run time: %f cpu-hr' %((end_time-start_time)/60/60*domain.dist.comm_cart.size))
if __name__ == "__main__":
from docopt import docopt
args = docopt(__doc__)
import sys
# save data in directory named after script
data_dir = sys.argv[0].split('.py')[0]
data_dir += "_Ra{}_Pr{}_a{}".format(args['--Rayleigh'], args['--Prandtl'], args['--aspect'])
if args['--label'] is not None:
data_dir += "_{}".format(args['--label'])
data_dir += '/'
#logger.info("saving run in: {}".format(data_dir))
if args['--nx'] is not None:
nx = int(args['--nx'])
else:
nx = None
Rayleigh_Benard_onset(
Prandtl=float(args['--Prandtl']),
aspect=int(args['--aspect']),
nz=int(args['--nz']),
nx=nx,
data_dir=data_dir,
multiplier=float(args['--multiplier']),
no_slip=args['--no_slip'],
stress_free=args['--stress_free'],
no_lid=args['--no_lid'])