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incompressible_NS_TG.py
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incompressible_NS_TG.py
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"""
Dedalus script for solution of 3D Navier-Stokes spin down.
This script uses a Fourier basis in the x and z directions with periodic boundary
conditions.
Usage:
incompressible_NS_TG.py [options]
Options:
--mesh=<mesh> Processor mesh if distributing in 2-D
--nz=<nz> Chebyshev resolution [default: 128]
--nx=<nx> Fourier resolution [default: 128]
--ny=<ny> Fourier resolution [default: 128]
--niter=<niter> Iterations to run scaling test for (+1 automatically added to account for startup) [default: 100]
--IO Do analysis IO
--verbose Make sparsity plots
"""
from docopt import docopt
args = docopt(__doc__)
import numpy as np
from mpi4py import MPI
import time
from dedalus import public as de
from dedalus.extras import flow_tools
import logging
logger = logging.getLogger(__name__)
verbose = args['--verbose']
niter = int(float(args['--niter']))+1
mesh = args['--mesh']
if mesh is not None:
mesh = mesh.split(',')
mesh = [int(mesh[0]), int(mesh[1])]
initial_time = time.time()
# Parameters
Lx, Ly, Lz = (1., 1., 1.)
nx, ny, nz = (int(args['--nx']),int(args['--ny']),int(args['--nz'])) # grid resolution is 3/2 higher
Reynolds = 1
v0, k0 = (1,4) # Amplitude and wavenumber of the initial conditions
# Create bases and domain
x_basis = de.Fourier('x', nx, interval=(0, Lx), dealias=3/2)
y_basis = de.Fourier('y', ny, interval=(0, Ly), dealias=3/2)
z_basis = de.Fourier('z', nz, interval=(0, Lz), dealias=3/2)
domain = de.Domain([x_basis, y_basis, z_basis], grid_dtype=np.float64, mesh=mesh)
# Implementation of Navier-Stokes equation system
problem = de.IVP(domain, variables=['p','u','v','w'])
problem.parameters['nu'] = 1 / Reynolds
problem.substitutions["L(thing)"] = 'nu*(d(thing,x=2) + d(thing,y=2) + d(thing,z=2))'
problem.substitutions["N(thing)"] = '-(u*dx(thing) + v*dy(thing) + w*dz(thing))'
problem.add_equation("u=0", condition="(nx==0) and (ny==0) and (nz==0)")
problem.add_equation("v=0", condition="(nx==0) and (ny==0) and (nz==0)")
problem.add_equation("w=0", condition="(nx==0) and (ny==0) and (nz==0)")
problem.add_equation("p=0", condition="(nx==0) and (ny==0) and (nz==0)")
problem.add_equation("dt(u) - L(u) + dx(p) = N(u) ", condition="(nx!=0) or (ny!=0) or (nz!=0)")
problem.add_equation("dt(v) - L(v) + dy(p) = N(v) ", condition="(nx!=0) or (ny!=0) or (nz!=0)")
problem.add_equation("dt(w) - L(w) + dz(p) = N(w) ", condition="(nx!=0) or (ny!=0) or (nz!=0)")
problem.add_equation("dx(u) + dy(v) + dz(w) = 0", condition="(nx!=0) or (ny!=0) or (nz!=0)")
# Build solver
solver = problem.build_solver(de.timesteppers.RK222)
logger.info('Solver built')
# Initial conditions : Taylor-Green forcing
u = solver.state['u']
v = solver.state['v']
w = solver.state['w']
x = domain.grid(0)
y = domain.grid(1)
z = domain.grid(2)
u['g'] = v0*np.sin(k0*x)*np.cos(k0*y)*np.cos(k0*z)
v['g'] = -v0*np.cos(k0*x)*np.sin(k0*y)*np.cos(k0*z)
w['g'] = 0
# Initial timestep
dt = 0.125
# Integration parameters
solver.stop_sim_time = 25
solver.stop_wall_time = 30 * 60.
solver.stop_iteration = niter
if args['--IO']:
# Analysis
snapshots = solver.evaluator.add_file_handler('snapshots', max_writes=50, sim_dt=0.125)
snapshots.add_system(solver.state)
snapshots.add_task('(dy(w)-dz(v))**2 + (dz(u)-dx(w))**2 + (dx(v)-dy(u))**2',name='enstrophy')
snapshots.add_task('integ((dy(w)-dz(v))**2 + (dz(u)-dx(w))**2 + (dx(v)-dy(u))**2)',name='enstrophy_tot')
snapshots.add_task('integ(u**2+v**2+w**2)',name='KE')
# CFL
CFL = flow_tools.CFL(solver, initial_dt=dt, cadence=10, safety=1,
max_change=1.5, min_change=0.5, max_dt=0.125, threshold=0.05)
CFL.add_velocities(('u', 'v', 'w'))
# Main loop
try:
logger.info('Starting loop')
first_loop = True
while solver.ok:
dt = CFL.compute_dt()
dt = solver.step(dt)
if (solver.iteration-1) % 1 == 0:
logger.info('Iteration: %i, Time: %e, dt: %e' %(solver.iteration, solver.sim_time, dt))
if first_loop:
if verbose:
data_dir='./'
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(1,1,1)
ax.spy(solver.pencils[0].L, markersize=1, markeredgewidth=0.0)
fig.savefig(data_dir+"sparsity_pattern.png", dpi=1200)
import scipy.sparse.linalg as sla
perm_spec_set = ['NATURAL', 'COLAMD', 'MMD_ATA', 'MMD_AT_plus_A']
for perm_spec in perm_spec_set:
LU = sla.splu(solver.pencils[0].LHS.tocsc(), permc_spec=perm_spec)
fig = plt.figure()
ax = fig.add_subplot(1,2,1)
ax.spy(LU.L.A, markersize=1, markeredgewidth=0.0)
ax = fig.add_subplot(1,2,2)
ax.spy(LU.U.A, markersize=1, markeredgewidth=0.0)
fig.savefig(data_dir+"sparsity_pattern_LU_{}.png".format(perm_spec), dpi=1200)
logger.info("------- {} -------".format(perm_spec))
logger.info("{} nonzero entries in LU".format(LU.nnz))
logger.info("{} nonzero entries in LHS".format(solver.pencils[0].LHS.tocsc().nnz))
logger.info("{} fill in factor".format(LU.nnz/solver.pencils[0].LHS.tocsc().nnz))
start_time = time.time()
first_loop = False
N_iterations = solver.iteration - 1
except:
logger.error('Exception raised, triggering end of main loop.')
raise
finally:
end_time = time.time()
logger.info('Iterations: {}'.format(N_iterations))
logger.info('seconds/iteration: {}'.format((end_time-start_time)/N_iterations))
logger.info('Sim end time: {}'.format(solver.sim_time))
logger.info('Run time: %.2f sec' %(end_time-start_time))
logger.info('Run time: {} cpu-hr'.format((end_time-start_time)/60/60*domain.dist.comm_cart.size))
if (domain.distributor.rank==0):
N_TOTAL_CPU = domain.distributor.comm_cart.size
print('-' * 40)
total_time = end_time-initial_time
main_loop_time = end_time - start_time
startup_time = start_time-initial_time
n_steps = solver.iteration-1
print(' startup time:', startup_time)
print('main loop time:', main_loop_time)
print(' total time:', total_time)
print(' iterations:', solver.iteration)
print(' loop sec/iter:', main_loop_time/solver.iteration)
print(' average dt:', solver.sim_time / n_steps)
print(" N_cores, Nx, Nz, startup main loop, main loop/iter, main loop/iter/grid, n_cores*main loop/iter/grid")
print('scaling:',
' {:d} {:d} {:d}'.format(N_TOTAL_CPU,nx,nz),
' {:8.3g} {:8.3g} {:8.3g} {:8.3g} {:8.3g}'.format(startup_time,
main_loop_time,
main_loop_time/n_steps,
main_loop_time/n_steps/(nx*nz),
N_TOTAL_CPU*main_loop_time/n_steps/(nx*nz)))
print('-' * 40)