def test_box_AdvectiveCFL(x_basis_class, Nx, Nz, timestepper, dtype,
z_velocity_mag, dealias):
# Bases
Lx = 2
Lz = 1
c = coords.CartesianCoordinates('x', 'z')
d = distributor.Distributor((c, ))
xb = x_basis_class(c.coords[0], size=Nx, bounds=(0, Lx), dealias=dealias)
x = xb.local_grid(1)
zb = basis.ChebyshevT(c.coords[1],
size=Nz,
bounds=(0, Lz),
dealias=dealias)
z = zb.local_grid(1)
b = (xb, zb)
# Fields
u = field.Field(name='u', dist=d, tensorsig=(c, ), bases=b, dtype=dtype)
print(u.domain.get_basis(c))
# Test Fourier CFL
fourier_velocity = lambda x: np.sin(4 * np.pi * x / Lx)
chebyshev_velocity = lambda z: -z_velocity_mag * z
u['g'][0] = fourier_velocity(x)
u['g'][1] = chebyshev_velocity(z)
# AdvectiveCFL initialization
cfl = operators.AdvectiveCFL(u, c)
cfl_freq = cfl.evaluate()['g']
comparison_freq = np.abs(u['g'][0]) / cfl.cfl_spacing(u)[0]
comparison_freq += np.abs(u['g'][1]) / cfl.cfl_spacing(u)[1]
assert np.allclose(cfl_freq, comparison_freq)
def test_cartesian_output(dtype, dealias, output_scales, output_layout):
Nx = Ny = Nz = 16
Lx = Ly = Lz = 2 * np.pi
# Bases
c = coords.CartesianCoordinates('x', 'y', 'z')
d = distributor.Distributor((c, ))
Fourier = {
np.float64: basis.RealFourier,
np.complex128: basis.ComplexFourier
}[dtype]
xb = Fourier(c.coords[0], size=Nx, bounds=(0, Lx), dealias=dealias)
yb = Fourier(c.coords[1], size=Ny, bounds=(0, Ly), dealias=dealias)
zb = basis.ChebyshevT(c.coords[2],
size=Nz,
bounds=(0, Lz),
dealias=dealias)
x = xb.local_grid(1)
y = yb.local_grid(1)
z = zb.local_grid(1)
# Fields
u = field.Field(name='u', dist=d, bases=(xb, yb, zb), dtype=dtype)
u['g'] = np.sin(x) * np.sin(y) * np.sin(z)
# Problem
dt = operators.TimeDerivative
problem = problems.IVP([u])
problem.add_equation((dt(u) + u, 0))
# Solver
solver = solvers.InitialValueSolver(problem, timesteppers.RK222)
# Output
tasks = [
u,
u(x=0),
u(y=0),
u(z=0),
u(x=0, y=0),
u(x=0, z=0),
u(y=0, z=0),
u(x=0, y=0, z=0)
]
with tempfile.TemporaryDirectory(dir='.') as tempdir:
tempdir = pathlib.Path(tempdir).stem
output = solver.evaluator.add_file_handler(tempdir, iter=1)
for task in tasks:
output.add_task(task,
layout=output_layout,
name=str(task),
scales=output_scales)
solver.evaluator.evaluate_handlers([output])
output.process_virtual_file()
# Check solution
#post.merge_process_files('test_output')
errors = []
with h5py.File(f'{tempdir}/{tempdir}_s1.h5', mode='r') as file:
for task in tasks:
task_saved = file['tasks'][str(task)][-1]
task = task.evaluate()
task.change_scales(output_scales)
errors.append(np.max(np.abs(task[output_layout] - task_saved)))
assert np.allclose(errors, 0)
def build_2d_box(Nx, Nz, dealias, dtype, k=0):
c = coords.CartesianCoordinates('x', 'z')
d = distributor.Distributor((c,))
if dtype == np.complex128:
xb = basis.ComplexFourier(c.coords[0], size=Nx, bounds=(0, Lx))
elif dtype == np.float64:
xb = basis.RealFourier(c.coords[0], size=Nx, bounds=(0, Lx))
zb = basis.ChebyshevT(c.coords[1], size=Nz, bounds=(0, Lz))
b = (xb, zb)
x = xb.local_grid(1)
z = zb.local_grid(1)
return c, d, b, x, z
def build_RF_RF(Nx, Ny, dealias_x, dealias_y):
c = coords.CartesianCoordinates('x', 'y')
d = distributor.Distributor((c, ))
xb = basis.RealFourier(c.coords[0],
size=Nx,
bounds=(0, np.pi),
dealias=dealias_x)
yb = basis.RealFourier(c.coords[1],
size=Ny,
bounds=(0, np.pi),
dealias=dealias_y)
x = xb.local_grid(dealias_x)
y = yb.local_grid(dealias_y)
return c, d, xb, yb, x, y
def test_cartesian_output_virtual(dtype, dealias, output_scales):
Nx = Ny = Nz = 16
Lx = Ly = Lz = 2 * np.pi
# Bases
c = coords.CartesianCoordinates('x', 'y', 'z')
d = distributor.Distributor((c,), mesh=(2,2))
Fourier = {np.float64: basis.RealFourier, np.complex128: basis.ComplexFourier}[dtype]
xb = Fourier(c.coords[0], size=Nx, bounds=(0, Lx), dealias=dealias)
yb = Fourier(c.coords[1], size=Ny, bounds=(0, Ly), dealias=dealias)
zb = Fourier(c.coords[2], size=Nz, bounds=(0, Lz), dealias=dealias)
x = xb.local_grid(1)
y = yb.local_grid(1)
z = zb.local_grid(1)
# Fields
u = field.Field(name='u', dist=d, bases=(xb,yb,zb), dtype=dtype)
v = field.Field(name='v', dist=d, bases=(xb,yb,zb), tensorsig=(c,), dtype=dtype)
u['g'] = np.sin(x) * np.sin(y) * np.sin(z)
# Problem
dt = operators.TimeDerivative
problem = problems.IVP([u, v])
problem.add_equation((dt(u) + u, 0))
problem.add_equation((dt(v) + v, 0))
# Solver
solver = solvers.InitialValueSolver(problem, timesteppers.RK222)
# Output
tasks = [u, u(x=0), u(y=0), u(z=0), u(x=0,y=0), u(x=0,z=0), u(y=0,z=0), u(x=0,y=0,z=0),
v, v(x=0), v(y=0), v(z=0), v(x=0,y=0), v(x=0,z=0), v(y=0,z=0), v(x=0,y=0,z=0)]
output = solver.evaluator.add_file_handler('test_output', iter=1, max_writes=1, virtual_file=True)
for task in tasks:
output.add_task(task, layout='g', name=str(task), scales=output_scales)
solver.evaluator.evaluate_handlers([output])
# Check solution
errors = []
d.comm.Barrier()
with h5py.File('test_output/test_output_s1.h5', mode='r') as file:
for task in tasks:
task_name = str(task)
task = task.evaluate()
task.change_scales(output_scales)
local_slices = (slice(None),) * len(task.tensorsig) + d.grid_layout.slices(task.domain, task.scales)
task_saved = file['tasks'][task_name][-1]
task_saved = task_saved[local_slices]
local_error = task['g'] - task_saved
if local_error.size:
errors.append(np.max(np.abs(task['g'] - task_saved)))
with Sync() as sync:
if sync.comm.rank == 0:
shutil.rmtree('test_output')
assert np.allclose(errors, 0)
def build_CF_J(a, b, Nx, Ny, dealias_x, dealias_y):
c = coords.CartesianCoordinates('x', 'y')
d = distributor.Distributor((c, ))
xb = basis.ComplexFourier(c.coords[0],
size=Nx,
bounds=(0, np.pi),
dealias=dealias_x)
yb = basis.Jacobi(c.coords[1],
a=a,
b=b,
size=Ny,
bounds=(0, 1),
dealias=dealias_y)
x = xb.local_grid(dealias_x)
y = yb.local_grid(dealias_y)
return c, d, xb, yb, x, y
def test_flow_tools_cfl(x_basis_class, Nx, Nz, timestepper, dtype, safety,
z_velocity_mag, dealias):
# Bases
Lx = 2
Lz = 1
c = coords.CartesianCoordinates('x', 'z')
d = distributor.Distributor((c, ))
xb = x_basis_class(c.coords[0], size=Nx, bounds=(0, Lx), dealias=dealias)
x = xb.local_grid(1)
zb = basis.ChebyshevT(c.coords[1],
size=Nz,
bounds=(0, Lz),
dealias=dealias)
z = zb.local_grid(1)
b = (xb, zb)
# Fields
u = field.Field(name='u', dist=d, tensorsig=(c, ), bases=b, dtype=dtype)
# Problem
ddt = operators.TimeDerivative
problem = problems.IVP([u])
problem.add_equation((ddt(u), 0))
# Solver
solver = solvers.InitialValueSolver(problem, timestepper)
# cfl initialization
dt = 1
cfl = flow_tools.CFL(solver, dt, safety=safety, cadence=1)
cfl.add_velocity(u)
# Test Fourier CFL
fourier_velocity = lambda x: np.sin(4 * np.pi * x / Lx)
chebyshev_velocity = lambda z: -z_velocity_mag * z
u['g'][0] = fourier_velocity(x)
u['g'][1] = chebyshev_velocity(z)
solver.step(dt)
solver.step(
dt
) #need two timesteps to get past stored_dt per compute_timestep logic
dt = cfl.compute_timestep()
op = operators.AdvectiveCFL(u, c)
cfl_freq = np.abs(u['g'][0] / op.cfl_spacing(u)[0])
cfl_freq += np.abs(u['g'][1] / op.cfl_spacing(u)[1])
cfl_freq = np.max(cfl_freq)
dt_comparison = safety * (cfl_freq)**(-1)
assert np.allclose(dt, dt_comparison)
def test_fourier_AdvectiveCFL(x_basis_class, Nx, timestepper, dtype, dealias):
Lx = 1
# Bases
c = coords.CartesianCoordinates('x')
d = distributor.Distributor((c, ))
xb = x_basis_class(c.coords[0], size=Nx, bounds=(0, Lx), dealias=dealias)
x = xb.local_grid(1)
# Fields
u = field.Field(name='u',
dist=d,
tensorsig=(c, ),
bases=(xb, ),
dtype=dtype)
velocity = lambda x: np.sin(2 * np.pi * x / Lx)
u['g'][0] = velocity(x)
# AdvectiveCFL initialization
cfl = operators.AdvectiveCFL(u, c)
cfl_freq = cfl.evaluate()['g']
comparison_freq = np.abs(u['g']) / cfl.cfl_spacing(u)[0]
assert np.allclose(cfl_freq, comparison_freq)
def __init__(self, Nx, Ny, Lx, Ly, dtype, **kw):
self.Nx = Nx
self.Ny = Ny
self.Lx = Lx
self.Ly = Ly
self.dtype = dtype
self.N = Nx * Ny
self.R = 2 * Nx + 2 * Ny
self.M = self.N + self.R
# Bases
self.c = c = coords.CartesianCoordinates('x', 'y')
self.d = d = distributor.Distributor((c, ))
self.xb = xb = basis.ChebyshevT(c.coords[0], Nx, bounds=(0, Lx))
self.yb = yb = basis.ChebyshevT(c.coords[1], Ny, bounds=(0, Ly))
self.x = x = xb.local_grid(1)
self.y = y = yb.local_grid(1)
xb2 = xb._new_a_b(1.5, 1.5)
yb2 = yb._new_a_b(1.5, 1.5)
# Forcing
self.f = f = field.Field(name='f',
dist=d,
bases=(xb2, yb2),
dtype=dtype)
# Boundary conditions
self.uL = uL = field.Field(name='f', dist=d, bases=(yb, ), dtype=dtype)
self.uR = uR = field.Field(name='f', dist=d, bases=(yb, ), dtype=dtype)
self.uT = uT = field.Field(name='f', dist=d, bases=(xb, ), dtype=dtype)
self.uB = uB = field.Field(name='f', dist=d, bases=(xb, ), dtype=dtype)
# Fields
self.u = u = field.Field(name='u', dist=d, bases=(xb, yb), dtype=dtype)
self.tx1 = tx1 = field.Field(name='tx1',
dist=d,
bases=(xb2, ),
dtype=dtype)
self.tx2 = tx2 = field.Field(name='tx2',
dist=d,
bases=(xb2, ),
dtype=dtype)
self.ty1 = ty1 = field.Field(name='ty1',
dist=d,
bases=(yb2, ),
dtype=dtype)
self.ty2 = ty2 = field.Field(name='ty2',
dist=d,
bases=(yb2, ),
dtype=dtype)
# Problem
Lap = lambda A: operators.Laplacian(A, c)
self.problem = problem = problems.LBVP([u, tx1, tx2, ty1, ty2])
problem.add_equation((Lap(u), f))
problem.add_equation((u(y=Ly), uT))
problem.add_equation((u(x=Lx), uR))
problem.add_equation((u(y=0), uB))
problem.add_equation((u(x=0), uL))
# Solver
self.solver = solver = solvers.LinearBoundaryValueSolver(
problem,
bc_top=False,
tau_left=False,
store_expanded_matrices=False,
**kw)
# Tau entries
L = solver.subproblems[0].L_min.tolil()
# Taus
for nx in range(Nx):
L[Ny - 1 + nx * Ny, Nx * Ny + 0 * Nx + nx] = 1 # tx1 * Py1
L[Ny - 2 + nx * Ny, Nx * Ny + 1 * Nx + nx] = 1 # tx2 * Py2
for ny in range(Ny - 2):
L[(Nx - 1) * Ny + ny,
Nx * Ny + 2 * Nx + 0 * Ny + ny] = 1 # ty1 * Px1
L[(Nx - 2) * Ny + ny,
Nx * Ny + 2 * Nx + 1 * Ny + ny] = 1 # ty2 * Px2
# BC taus not resolution safe
if Nx != Ny:
raise ValueError("Current implementation requires Nx == Ny.")
else:
# Remember L is left preconditoined but not right preconditioned
L[-7, Nx * Ny + 2 * Nx + 0 * Ny + Ny - 2] = 1 # Right -2
L[-5, Nx * Ny + 2 * Nx + 0 * Ny + Ny - 1] = 1 # Right -1
L[-3, Nx * Ny + 2 * Nx + 1 * Ny + Ny - 2] = 1 # Left -2
L[-1, Nx * Ny + 2 * Nx + 1 * Ny + Ny - 1] = 1 # Left -1
solver.subproblems[0].L_min = L.tocsr()
# Neumann operators
ux = operators.Differentiate(u, c.coords[0])
uy = operators.Differentiate(u, c.coords[1])
self.duL = -ux(x='left')
self.duR = ux(x='right')
self.duT = uy(y='right')
self.duB = -uy(y='left')
# Neumann matrix
duT_mat = self.duT.expression_matrices(solver.subproblems[0],
vars=[u])[u]
duR_mat = self.duR.expression_matrices(solver.subproblems[0],
vars=[u])[u]
duB_mat = self.duB.expression_matrices(solver.subproblems[0],
vars=[u])[u]
duL_mat = self.duL.expression_matrices(solver.subproblems[0],
vars=[u])[u]
self.interior_to_neumann_matrix = sp.vstack(
[duT_mat, duR_mat, duB_mat, duL_mat], format='csr')
import numpy as np
from dedalus.core import coords, distributor, basis, field, operators, problems, solvers
from dedalus.tools import logging
from mpi4py import MPI
rank = MPI.COMM_WORLD.rank
import logging
logger = logging.getLogger(__name__)
dtype = np.complex128 #np.float64
Nx = 64
Nz = 32
Lz = 2*np.pi
# Bases
c = coords.CartesianCoordinates('x', 'z')
d = distributor.Distributor((c,))
if dtype == np.complex128:
xb = basis.ComplexFourier(c.coords[0], size=Nx, bounds=(0, 2*np.pi), dealias=3/2)
elif dtype == np.float64:
xb = basis.RealFourier(c.coords[0], size=Nx, bounds=(0, 2*np.pi), dealias=3/2)
zb = basis.ChebyshevT(c.coords[1], size=Nz, bounds=(0, Lz),dealias=3/2)
x = xb.local_grid(1)
z = zb.local_grid(1)
zb1 = basis.ChebyshevU(c.coords[1], size=Nz, bounds=(0, Lz), alpha0=0)
t1 = field.Field(name='t1', dist=d, bases=(xb,), dtype=dtype)
t2 = field.Field(name='t2', dist=d, bases=(xb,), dtype=dtype)
P1 = field.Field(name='P1', dist=d, bases=(zb1,), dtype=dtype)
if rank == 0:
P1['c'][0,-1] = 1
dz = lambda A: operators.Differentiate(A, c.coords[1])
P2 = dz(P1).evaluate()