def tail(self, t, it, logger):
cc = self.cc
pv = self.pv
# Get div(v) locally
div_v = self.div_v
if div_v is not None:
div_v.assign(
df.project(df.div(pv["v"]), div_v.function_space()))
# Compute required functionals
keys = ["t", "E_kin", "Psi", "mean_p"]
vals = {}
vals[keys[0]] = t
vals[keys[1]] = df.assemble(0.5 * cc["rho"] *
df.inner(pv["v"], pv["v"]) * df.dx)
vals[keys[2]] = df.assemble((
0.25 * cc["a"] * cc["eps"] *\
df.inner(df.dot(cc["LA"], df.grad(pv["phi"])), df.grad(pv["phi"]))
+ (cc["b"] / cc["eps"]) * cc["F"]
) * df.dx)
vals[keys[3]] = df.assemble(pv["p"] * df.dx)
if it % self.mod == 0:
for key in keys:
self.functionals[key].append(vals[key])
# Logging and reporting
df.info("")
df.begin("Reported functionals:")
for key in keys[1:]:
desc = "{:6s} = %g".format(key)
logger.info(desc, (vals[key], ), (key, ), t)
df.end()
df.info("")
def _create_coefficients(r_dens, r_visc):
c = OrderedDict()
c[r"r_dens"] = r_dens
c[r"r_visc"] = r_visc
# Problem parameters
c[r"\rho_1"] = 1.0
c[r"\rho_2"] = r_dens * c[r"\rho_1"]
c[r"\nu_1"] = 1.0
c[r"\nu_2"] = r_visc * c[r"\nu_1"]
c[r"\eps"] = 0.1
c[r"g_a"] = 1.0
# Characteristic quantities
c[r"L_0"] = 1.0
c[r"V_0"] = 1.0
c[r"\rho_0"] = c[r"\rho_1"]
df.begin("\nDimensionless numbers")
At = (c[r"\rho_1"] - c[r"\rho_2"]) / (c[r"\rho_1"] + c[r"\rho_2"])
Re_1 = c[r"\rho_1"] / c[r"\nu_1"]
Re_2 = c[r"\rho_2"] / c[r"\nu_2"]
df.info("r_dens = {}".format(r_dens))
df.info("r_visc = {}".format(r_visc))
df.info("Re_1 = {}".format(Re_1))
df.info("Re_2 = {}".format(Re_2))
df.info("At = {}".format(At))
df.end()
return c
def _load_from_file(cls, h5name, h5group, comm):
df.begin(LogLevel.PROGRESS, "Load mesh from h5 file")
geo = load_geometry_from_h5(h5name,
h5group,
include_sheets=False,
comm=comm)
df.end()
f0 = get_attribute(geo, "f0", "fiber", None)
s0 = get_attribute(geo, "s0", "sheet", None)
n0 = get_attribute(geo, "n0", "sheet_normal", None)
c0 = get_attribute(geo, "c0", "circumferential", None)
r0 = get_attribute(geo, "r0", "radial", None)
l0 = get_attribute(geo, "l0", "longitudinal", None)
vfun = get_attribute(geo, "vfun", None)
ffun = get_attribute(geo, "ffun", None)
cfun = get_attribute(geo, "cfun", "sfun", None)
kwargs = {
"mesh": geo.mesh,
"markers": geo.markers,
"markerfunctions": MarkerFunctions2D(vfun=vfun,
ffun=ffun,
cfun=cfun),
"microstructure": Microstructure(f0=f0, s0=s0, n0=n0),
"crl_basis": CRLBasis(c0=c0, r0=r0, l0=l0),
}
return kwargs
def time_step(self, rhs):
dfn.begin("Computing velocity correction")
if params['all_steps_adaptive']:
self.adaptive_step(rhs)
else:
[bc.apply(self.A, rhs) for bc in self.bcs]
dfn.solve(self.A, self.cur_vel.vector(), rhs, "cg", "amg")
dfn.end()
def log(level, msg):
"""Write a message to the logger.
Parameters
----------
level : int
Log level of the message.
msg : str
Log message.
"""
df.begin(level, msg)
df.end()
def copy(self, deepcopy=False):
"""Returns a copy of self.
Parameters
----------
deepcopy : bool
True if copy should be deep, default False.
"""
msg = "Copying geometry"
if deepcopy:
msg += " with deepcopy."
df.begin(LogLevel.DEBUG, msg)
cp = self.__class__(**self._copy(deepcopy))
df.end()
return cp
def solve(self, flag):
"""
:param flag : "p" to plot
"""
nSteps = 20
for i in range(nSteps):
try:
self.solver.solve()
except RuntimeError as message:
print message
d.end()
response = raw_input('Press ENTER to continue ("q" to quit) ')
if response == 'q': sys.exit()
self.plot(i)
self.update_mesh()
def save(self,
h5name,
h5group="",
other_functions=None,
other_attributes=None,
overwrite_file=False,
overwrite_group=True):
"""Saves a geometry to a h5 file.
Parameters
----------
h5name : str
The location and name of the output file without file extension.
h5group : str
The h5 group of the geometry.
other_functions :
Extra mesh functions.
other_attributes :
Extra mesh attributes.
overwrite_file : bool
True if existing file should be overwritten.
overwrite_group : bool
True if existing group should be overwritten.
"""
df.begin(LogLevel.PROGRESS, "Saving geometry to {}...".format(h5name))
save_geometry_to_h5(
self.mesh,
h5name,
h5group=h5group,
markers=self.markers,
markerfunctions=namedtuple_as_dict(self.markerfunctions),
microstructure=namedtuple_as_dict(self.microstructure),
local_basis=namedtuple_as_dict(self.crl_basis),
overwrite_file=overwrite_file,
overwrite_group=overwrite_group)
df.end()
def check_h5group(h5name, h5group, delete=False, comm=mpi_comm_world):
if not isinstance(h5group, str):
msg = "Error! h5group has to be of type string. Your h5group is of type {}".format(
type(h5group))
raise TypeError(msg)
h5group_in_h5file = False
if not os.path.isfile(h5name):
return False
filemode = "a" if delete else "r"
if not os.access(h5name, os.W_OK):
filemode = "r"
if delete:
df.begin(
df.LogLevel.WARNING, "You do not have write access to file "
"{}".format(h5name))
delete = False
df.end()
with open_h5py(h5name, filemode, comm) as h5file:
if h5group in h5file:
h5group_in_h5file = True
if delete:
if parallel_h5py:
df.begin(
df.LogLevel.DEBUG, "Deleting existing group: "
"'{}'".format(h5group))
del h5file[h5group]
df.end()
else:
if df.MPI.rank(comm) == 0:
df.begin(
df.LogLevel.DEBUG, "Deleting existing group: "
"'{}'".format(h5group))
del h5file[h5group]
df.end()
return h5group_in_h5file
def solve(self):
"""
Perform one solution step (in time).
"""
solver = self.data["solver"]
begin("Advance-phase")
for i, A in enumerate(self.data["A"]["chi"]):
b = assemble(self.data["rhs"]["chi"][i])
solver["chi"].solve(A, self.data["sol"]["chi"][i].vector(), b)
for i, A in enumerate(self.data["A"]["phi"]):
b = assemble(self.data["rhs"]["phi"][i])
solver["phi"].solve(A, self.data["sol"]["phi"][i].vector(), b)
end()
begin("Pressure step")
b = assemble(self.data["rhs"]["p"])
for bc in self.data["bcs"].get("p", []):
bc.apply(b)
if self._flags["fix_p"]:
# Orthogonalize RHS vector b with respect to the null space
self.data["null_space"].orthogonalize(b)
solver["p"].solve(self.data["A"]["p"], self.data["sol"]["p"].vector(),
b)
if self._flags["fix_p"]:
self._calibrate_pressure(self.data["sol"]["p"],
self.data["null_fcn"])
end()
begin("Velocity step")
for i, A in enumerate(self.data["A"]["v"]):
b = assemble(self.data["rhs"]["v"][i])
# FIXME: How to apply bcs in a symmetric fashion?
for bc in self.data["bcs"].get("v", []):
if bc[i] is not None:
bc[i].apply(b)
solver["v"].solve(A, self.data["sol"]["v"][i].vector(), b)
end()
def test_karman(num_steps=2, lcar=0.1, show=False):
mesh = create_mesh(lcar)
W_element = VectorElement('Lagrange', mesh.ufl_cell(), 2)
P_element = FiniteElement('Lagrange', mesh.ufl_cell(), 1)
WP = FunctionSpace(mesh, W_element * P_element)
W = WP.sub(0)
# P = WP.sub(1)
mesh_eps = 1.0e-12
# Define mesh and boundaries.
# pylint: disable=no-self-use
class LeftBoundary(SubDomain):
def inside(self, x, on_boundary):
return on_boundary and x[0] < x0 + mesh_eps
left_boundary = LeftBoundary()
class RightBoundary(SubDomain):
def inside(self, x, on_boundary):
return on_boundary and x[0] > x1 - mesh_eps
right_boundary = RightBoundary()
class LowerBoundary(SubDomain):
def inside(self, x, on_boundary):
return on_boundary and x[1] < y0 + mesh_eps
lower_boundary = LowerBoundary()
class UpperBoundary(SubDomain):
def inside(self, x, on_boundary):
return on_boundary and x[1] > y1 - mesh_eps
upper_boundary = UpperBoundary()
class ObstacleBoundary(SubDomain):
def inside(self, x, on_boundary):
return (on_boundary and x0 + mesh_eps < x[0] < x1 - mesh_eps
and y0 + mesh_eps < x[1] < y1 - mesh_eps)
obstacle_boundary = ObstacleBoundary()
# Boundary conditions for the velocity.
# Proper inflow and outflow conditions are a matter of voodoo. See for
# example Gresho/Sani, or
#
# Boundary conditions for open boundaries for the incompressible
# Navier-Stokes equation;
# B.C.V. Johansson;
# J. Comp. Phys. 105, 233-251 (1993).
#
# The latter in particularly suggest for the inflow:
#
# u = u0,
# d^r v / dx^r = v_r,
# div(u) = 0,
#
# where u and v are the velocities in normal and tangential directions,
# respectively, and r\in{0,1,2}. The setting r=0 essentially means to set
# (u,v) statically at the left boundary, r=1 means to set u and control
# dv/dn, which is what we do here (namely implicitly by dv/dn=0).
# At the outflow,
#
# d^j u / dx^j = 0,
# d^q v / dx^q = 0,
# p = p0,
#
# is suggested with j=q+1. Choosing q=0, j=1 means setting the tangential
# component of the outflow to 0, and letting the normal component du/dn=0
# (again, this is achieved implicitly by the weak formulation).
#
inflow = Expression('%e * (%e - x[1]) * (x[1] - %e) / %e' %
(entrance_velocity, y1, y0, (0.5 * (y1 - y0))**2),
degree=2)
outflow = Expression('%e * (%e - x[1]) * (x[1] - %e) / %e' %
(entrance_velocity, y1, y0, (0.5 * (y1 - y0))**2),
degree=2)
u_bcs = [
DirichletBC(W, (0.0, 0.0), upper_boundary),
DirichletBC(W, (0.0, 0.0), lower_boundary),
DirichletBC(W, (0.0, 0.0), obstacle_boundary),
DirichletBC(W.sub(0), inflow, left_boundary),
#
DirichletBC(W.sub(0), outflow, right_boundary),
]
# dudt_bcs = [
# DirichletBC(W, (0.0, 0.0), upper_boundary),
# DirichletBC(W, (0.0, 0.0), lower_boundary),
# DirichletBC(W, (0.0, 0.0), obstacle_boundary),
# DirichletBC(W.sub(0), 0.0, left_boundary),
# # DirichletBC(W.sub(1), 0.0, right_boundary),
# ]
# If there is a penetration boundary (i.e., n.u!=0), then the pressure must
# be set somewhere to make sure that the Navier-Stokes problem remains
# consistent.
# When solving Stokes with no Dirichlet conditions whatsoever, the pressure
# tends to 0 at the outlet. This is natural since there, the liquid can
# flow out at the rate it needs to be under no pressure at all.
# Hence, at outlets, set the pressure to 0.
p_bcs = [
# DirichletBC(P, 0.0, right_boundary)
]
# Getting vortices is not easy. If we take the actual viscosity of water,
# they don't appear.
mu = 0.002
# mu = materials.water.dynamic_viscosity(T=293.0)
# For starting off, solve the Stokes equation.
u0, p0 = flow.stokes.solve(WP,
u_bcs + p_bcs,
mu,
f=Constant((0.0, 0.0)),
verbose=False,
tol=1.0e-13,
max_iter=10000)
u0.rename('velocity', 'velocity')
p0.rename('pressure', 'pressure')
rho = materials.water.density(T=293.0)
# stepper = flow.navier_stokes.Chorin()
# stepper = flow.navier_stokes.IPCS()
stepper = flow.navier_stokes.Rotational()
W2 = u0.function_space()
P2 = p0.function_space()
u_bcs = [
DirichletBC(W2, (0.0, 0.0), upper_boundary),
DirichletBC(W2, (0.0, 0.0), lower_boundary),
DirichletBC(W2, (0.0, 0.0), obstacle_boundary),
DirichletBC(W2.sub(0), inflow, left_boundary),
#
DirichletBC(W2.sub(0), outflow, right_boundary),
]
# TODO settting the outflow _and_ the pressure at the outlet is actually
# not necessary. Even without the pressure Dirichlet conditions, the
# pressure correction system should be consistent.
p_bcs = [DirichletBC(P2, 0.0, right_boundary)]
# Report Reynolds number.
# https://en.wikipedia.org/wiki/Reynolds_number#Sphere_in_a_fluid
reynolds = entrance_velocity * obstacle_diameter * rho / mu
print('Reynolds number: %e' % reynolds)
dt = 1.0e-5
dt_max = 1.0
t = 0.0
with XDMFFile(mpi_comm_world(), 'karman.xdmf') as xdmf_file:
xdmf_file.parameters['flush_output'] = True
xdmf_file.parameters['rewrite_function_mesh'] = False
k = 0
while k < num_steps:
k += 1
print()
print('t = %f' % t)
if show:
plot(u0)
plot(p0)
xdmf_file.write(u0, t)
xdmf_file.write(p0, t)
u1, p1 = stepper.step(Constant(dt), {0: u0},
p0,
u_bcs,
p_bcs,
Constant(rho),
Constant(mu),
f={
0: Constant((0.0, 0.0)),
1: Constant((0.0, 0.0))
},
verbose=False,
tol=1.0e-10)
u0.assign(u1)
p0.assign(p1)
# Adaptive stepsize control based solely on the velocity field.
# CFL-like condition for time step. This should be some sort of
# average of the temperature in the current step and the target
# step.
#
# More on step-size control for Navier--Stokes:
#
# Adaptive time step control for the incompressible
# Navier-Stokes equations;
# Volker John, Joachim Rang;
# Comput. Methods Appl. Mech. Engrg. 199 (2010) 514-524;
# <http://www.wias-berlin.de/people/john/ELECTRONIC_PAPERS/JR10.CMAME.pdf>.
#
# Section 3.3 in that paper notes that time-adaptivity for theta-
# schemes is too costly. They rather reside to DIRK- and
# Rosenbrock-methods.
#
begin('Step size adaptation...')
ux, uy = u0.split()
unorm = project(sqrt(ux**2 + uy**2),
FunctionSpace(mesh, 'Lagrange', 2),
form_compiler_parameters={'quadrature_degree': 4})
unorm = norm(unorm.vector(), 'linf')
# print('||u||_inf = %e' % unorm)
# Some smooth step-size adaption.
target_dt = 1.0 * mesh.hmax() / unorm
print('current dt: %e' % dt)
print('target dt: %e' % target_dt)
# alpha is the aggressiveness factor. The distance between the
# current step size and the target step size is reduced by
# |1-alpha|. Hence, if alpha==1 then dt_next==target_dt. Otherwise
# target_dt is approached more slowly.
alpha = 0.5
dt = min(
dt_max,
# At most double the step size from step to step.
dt * min(2.0, 1.0 + alpha * (target_dt - dt) / dt))
print('next dt: %e' % dt)
t += dt
end()
return
def solve(self):
"""
Perform one solution step (in time).
"""
begin("Cahn-Hilliard step")
self.iters["CH"][-1] = self.data["solver"]["CH"]["nln"].solve(
self.data["problem_ch"], self.data["sol_ch"].vector())[0]
self.iters["CH"][0] += self.iters["CH"][-1]
end()
begin("Navier-Stokes step")
# Update stabilization terms
if self.data["model"].parameters["semi"]["sdstab"]:
self.data["model"]._update_sd_stab_parameter()
pcd_assembler = self.data.get("pcd_assembler", None)
if pcd_assembler:
# Symmetric assembly of the linear system
A, b = PETScMatrix(self.comm()), PETScVector(self.comm())
pcd_assembler.system_matrix(A)
pcd_assembler.rhs_vector(b)
else:
# Standard assembly of the linear system
A = assemble(self.data["forms"]["lin"]["lhs"])
b = assemble(self.data["forms"]["lin"]["rhs"])
for bc in self.data["bcs_ns"]:
bc.apply(A, b)
if self._flags["fix_p"]:
# Attach null space to PETSc matrix
as_backend_type(A).set_nullspace(self.data["null_space"])
# Orthogonalize RHS vector b with respect to the null space
self.data["null_space"].orthogonalize(b)
if pcd_assembler:
# Symmetric assembly of the preconditioner
P = PETScMatrix(self.comm())
pcd_assembler.pc_matrix(P)
# FIXME: Should we attach the null space also to preconditioner?
# Probably not as 'set_nullspace' is related to KSP (not PC).
# if P.empty():
# P = A
# else:
# as_backend_type(P).set_nullspace(self.data["null_space"])
P = A if P.empty() else P
# Standard assembly of the preconditioner matrix
# if self.data["forms"]["pcd"]["a_pc"] is not None:
# P = assemble(self.data["forms"]["pcd"]["a_pc"])
# for bc in self.data["bcs_ns"]:
# bc.apply(P)
# else:
# P = A
self.data["solver"]["NS"].set_operators(A, P)
if not self._flags["init_pcd_called"]: # only one call is allowed
self.data["solver"]["NS"].init_pcd(pcd_assembler)
self._flags["init_pcd_called"] = True
else:
# FIXME: Here we assume that LU solver is used
assert self.data["solver"]["NS"].parameter_type() == 'lu_solver'
self.data["solver"]["NS"].set_operator(A)
# NOTE: Preconditioner matrix can't be set for LUSolver.
self.iters["NS"][-1] = \
self.data["solver"]["NS"].solve(self.data["sol_ns"].vector(), b)
info("Navier-Stokes solver finished in {} iterations".format(
self.iters["NS"][-1]))
self.iters["NS"][0] += self.iters["NS"][-1]
if self._flags["fix_p"]:
self._calibrate_pressure(self.data["sol_ns"],
self.data["null_fcn"])
end()
def save_geometry_to_h5(mesh,
h5name,
h5group="",
markers=None,
markerfunctions={},
microstructure={},
local_basis={},
comm=mpi_comm_world,
other_functions={},
other_attributes={},
overwrite_file=False,
overwrite_group=True):
"""
Save geometry and other geometrical functions to a HDF file.
Parameters
----------
mesh : :class:`dolfin.mesh`
The mesh
h5name : str
Path to the file
h5group : str
Folder within the file. Default is "" which means in
the top folder.
markers : dict
A dictionary with markers. See `get_markers`.
fields : list
A list of functions for the microstructure
local_basis : list
A list of functions for the crl basis
meshfunctions : dict
A dictionary with keys being the dimensions the the values
beeing the meshfunctions.
comm : :class:`dolfin.MPI`
MPI communicator
other_functions : dict
Dictionary with other functions you want to save
other_attributes: dict
Dictionary with other attributes you want to save
overwrite_file : bool
If true, and the file exists, the file will be overwritten (default: False)
overwrite_group : bool
If true and h5group exist, the group will be overwritten.
"""
h5name = os.path.splitext(h5name)[0] + ".h5"
assert isinstance(mesh, Mesh)
file_mode = "a" if os.path.isfile(h5name) and not overwrite_file else "w"
# IF we should append the file but overwrite the group we need to
# check that the group does not exist. If so we need to open it in
# h5py and delete it.
if file_mode == "a" and overwrite_group and h5group != "":
check_h5group(h5name, h5group, delete=True, comm=comm)
with HDF5File(comm, h5name, file_mode) as h5file:
# Save mesh
ggroup = "{}/geometry".format(h5group)
mgroup = "{}/mesh".format(ggroup)
h5file.write(mesh, mgroup)
# Save markerfunctions
df.begin(LogLevel.PROGRESS, "Saving marker functions.")
for dim, key in enumerate(markerfunctions.keys()):
mf = markerfunctions[key]
if mf is not None:
dgroup = "{}/mesh/meshfunction_{}".format(ggroup, dim)
h5file.write(mf, dgroup)
df.end()
# Save markers
df.begin(LogLevel.PROGRESS, "Saving markers.")
for name, (marker, dim) in markers.items():
for key_str in ["domain", "meshfunction"]:
dgroup = "{}/mesh/{}_{}".format(ggroup, key_str, dim)
if h5file.has_dataset(dgroup):
aname = "marker_name_{}".format(name)
h5file.attributes(dgroup)[aname] = marker
df.end()
# Save microstructure
df.begin(LogLevel.PROGRESS, "Saving microstructure.")
for key in microstructure.keys():
ms = microstructure[key]
if ms is not None:
fgroup = "{}/microstructure".format(h5group)
fsubgroup = "{}/{}".format(fgroup, key)
h5file.write(microstructure[key], fsubgroup)
h5file.attributes(fsubgroup)["name"] = key
elm = ms.function_space().ufl_element()
try:
family, degree = elm.family(), elm.degree()
fspace = "{}_{}".format(family, degree)
h5file.attributes(fgroup)["space"] = fspace
h5file.attributes(fgroup)["names"] = ":".join(
microstructure.keys())
except:
pass
df.end()
# Save local basis
df.begin(LogLevel.PROGRESS, "Saving local basis.")
for key in local_basis.keys():
ml = local_basis[key]
if ml is not None:
lgroup = "{}/local basis functions".format(h5group)
h5file.write(ml, lgroup + "/{}".format(key))
elm = ml.function_space().ufl_element()
try:
family, degree = elm.family(), elm.degree()
lspace = "{}_{}".format(family, degree)
h5file.attributes(lgroup)["space"] = lspace
h5file.attributes(lgroup)["names"] = ":".join(local_basis.keys())
except:
pass
df.end()
# Save other functions
df.begin(LogLevel.PROGRESS, "Saving other functions")
for key in other_functions.keys():
mo = other_functions[key]
if mo is not None:
fungroup = "/".join([h5group, key])
h5file.write(mo, fungroup)
elm = mo.function_space().ufl_element()
try:
family, degree, vsize = elm.family(), elm.degree(), elm.value_size(
)
fspace = "{}_{}".format(family, degree)
h5file.attributes(fungroup)["space"] = fspace
h5file.attributes(fungroup)["value_size"] = vsize
except:
pass
df.end()
# Save other attributes
df.begin(LogLevel.PROGRESS, "Saving other attributes")
for key in other_attributes:
if isinstance(other_attributes[key], str) and isinstance(key, str):
h5file.attributes(h5group)[key] = other_attributes[key]
else:
begin(
df.LogLevel.WARNING,
"Invalid attribute {} = {}".format(key,
other_attributes[key]))
end()
df.end()
df.begin(df.LogLevel.INFO, "Geometry saved to {}".format(h5name))
df.end()
def __exit__(self, tpe, value, traceback):
end()
return
def compute_boussinesq(target_time, lcar, supg=False):
mesh, hot_boundary, cool_boundary = create_mesh(lcar)
room_temp = 293.0
# Density depends on temperature.
rho = materials.water.density
# Take dynamic viscosity at room temperature.
mu = materials.water.dynamic_viscosity(room_temp)
cp = materials.water.specific_heat_capacity
kappa = materials.water.thermal_conductivity
# Start time, end time, time step.
dt_max = 1.0
dt0 = 1.0e-2
# This should be
# umax = 1.0e-1
# dt0 = 0.2 * mesh.hmin() / umax
t = 0.0
max_heater_temp = 320.0
# Gravity accelleration.
accelleration_constant = -9.81
g = Constant((0.0, accelleration_constant))
W_element = VectorElement('Lagrange', mesh.ufl_cell(), 2)
P_element = FiniteElement('Lagrange', mesh.ufl_cell(), 1)
WP = FunctionSpace(mesh, W_element * P_element)
Q = FunctionSpace(mesh, 'Lagrange', 2)
# Everything at room temperature for starters
theta0 = project(Constant(room_temp), Q)
theta0.rename('temperature', 'temperature')
u_bcs = [DirichletBC(WP.sub(0), (0.0, 0.0), 'on_boundary')]
p_bcs = []
# Solve Stokes for initial state.
# Make sure that the right-hand side is the same as in the first step of
# Navier-Stokes below. This avoids problems with the initial pressure being
# a bit off, which leads to errors.
# u0, p0 = flow.stokes.solve(
# WP,
# u_bcs + p_bcs,
# mu,
# f=rho(theta0) * g,
# verbose=False,
# tol=1.0e-15,
# max_iter=1000
# )
y = SpatialCoordinate(mesh)[1]
u0 = project(Constant([0, 0]), FunctionSpace(mesh, W_element))
u0.rename('velocity', 'velocity')
p0 = project(
rho(theta0) * accelleration_constant * y,
FunctionSpace(mesh, P_element))
p0.rename('pressure', 'pressure')
# div_u = Function(Q)
dt = dt0
with XDMFFile(mpi_comm_world(), 'boussinesq.xdmf') as xdmf_file:
xdmf_file.parameters['flush_output'] = True
xdmf_file.parameters['rewrite_function_mesh'] = False
while t < target_time + DOLFIN_EPS:
begin('Time step %e -> %e...' % (t, t + dt))
# Crank up the heater from room_temp to max_heater_temp in t1 secs.
t1 = 30.0
heater_temp = (+room_temp + min(1.0, t / t1) *
(max_heater_temp - room_temp))
# heater_temp = room_temp
# Velocity and heat and connected by
#
# theta1 = F_theta(u1, theta0)
# u1, p1 = F_u(u0, p0, theta1)
#
# One can either replace u1, theta1 on the right-hand side by u0,
# theta0, respectively, or wrap the whole thing in a Banach
# iteration 'a la
#
# theta = F_theta(u_prev, theta0)
# (u, p) = F_u(u0, p0, theta_prev)
#
# and do that until the residuals are close to 0.
u_prev = Function(u0.function_space())
u_prev.assign(u0)
theta_prev = Function(theta0.function_space())
theta_prev.assign(theta0)
is_banach_converged = False
banach_tol = 1.0e-1
max_banach_steps = 10
target_banach_steps = 5
banach_step = 0
while not is_banach_converged:
banach_step += 1
if banach_step > max_banach_steps:
info('\nBanach solver failed to converge. '
'Decrease time step from %e to %e and try again.\n' %
(dt, 0.25 * dt))
dt *= 0.25
end() # time step
break
begin('Banach step %d:' % banach_step)
# Do one heat time step.
begin('Computing heat...')
heat_bcs = [
DirichletBC(Q, heater_temp, hot_boundary),
DirichletBC(Q, room_temp, cool_boundary),
]
# Use all quantities at room temperature to avoid nonlinearity
stepper = parabolic.ImplicitEuler(
heat.Heat(Q,
u_prev,
kappa(room_temp),
rho(room_temp),
cp(room_temp),
heat_bcs,
Constant(0.0),
supg_stabilization=supg))
theta1 = stepper.step(theta0, t, dt)
end()
# Do one Navier-Stokes time step.
begin('Computing flux and pressure...')
# stepper = flow.navier_stokes.Chorin()
# stepper = flow.navier_stokes.IPCS()
stepper = flow.navier_stokes.Rotational()
W = u0.function_space()
u_bcs = [DirichletBC(W, (0.0, 0.0), 'on_boundary')]
p_bcs = []
try:
u1, p1 = stepper.step(
Constant(dt),
{0: u0},
p0,
u_bcs,
p_bcs,
# TODO use rho(theta)
rho(room_temp),
Constant(mu),
f={
0: rho(theta_prev) * g,
1: rho(theta_prev) * g
},
verbose=False,
tol=1.0e-10)
except RuntimeError:
info('Navier--Stokes solver failed to converge. '
'Decrease time step from %e to %e and try again.' %
(dt, 0.5 * dt))
dt *= 0.5
end() # navier-stokes
end() # banach step
end() # time step
# http://stackoverflow.com/a/1859099/353337
break
end() # navier-stokes
u1x, u1y = u1.split()
uprevx, uprevy = u_prev.split()
unorm = project(
abs(u1x - uprevx) + abs(u1y - uprevy),
Q,
form_compiler_parameters={'quadrature_degree': 4})
u_diff_norm = norm(unorm.vector(), 'linf')
theta_diff = Function(theta1.function_space())
theta_diff.vector()[:] = theta1.vector() - theta_prev.vector()
theta_diff_norm = norm(theta_diff.vector(), 'linf')
info('Banach residuals:')
info(' ||u - u_prev|| = %e' % u_diff_norm)
info(' ||theta - theta_prev|| = %e' % theta_diff_norm)
is_banach_converged = \
u_diff_norm < banach_tol and theta_diff_norm < banach_tol
u_prev.assign(u1)
theta_prev.assign(theta1)
end() # banach step
else:
# from dolfin import plot, interactive
# plot(u0)
# plot(p0)
# u1.rename('u1', 'u1')
# plot(u1)
# p1.rename('p1', 'p1')
# plot(p1)
# interactive()
# Assigning and plotting. We do that here so all methods have
# access to `x` and `x_1`.
theta0.assign(theta1)
u0.assign(u1)
p0.assign(p1)
# write to file
xdmf_file.write(theta0, t)
xdmf_file.write(u0, t)
xdmf_file.write(p0, t)
# from dolfin import plot, interactive
# plot(theta0, title='theta')
# plot(u0, title='u')
# # plot(div(u), title='div(u)', rescale=True)
# plot(p0, title='p')
# interactive()
end() # time step
begin('\nStep size adaptation...')
# Step-size control can be done purely based on the velocity
# field; see
#
# Adaptive time step control for the incompressible
# Navier-Stokes equations;
# Volker John, Joachim Rang;
# Comput. Methods Appl. Mech. Engrg. 199 (2010) 514-524;
# <http://www.wias-berlin.de/people/john/ELECTRONIC_PAPERS/JR10.CMAME.pdf>.
#
# Section 3.3 in that paper notes that time-adaptivity for
# theta- schemes is too costly. They rather reside to DIRK- and
# Rosenbrock- methods.
#
# Implementation:
# ux, uy = u0.split()
# unorm = project(
# abs(ux) + abs(uy),
# Q,
# form_compiler_parameters={'quadrature_degree': 4}
# )
# unorm = norm(unorm.vector(), 'linf')
# # print('||u||_inf = %e' % unorm)
# # Some smooth step-size adaption.
# target_dt = 0.2 * mesh.hmax() / unorm
# In our case, step failures are almost always because Banach
# didn't converge. Hence, design a step size adaptation based
# on the Banach steps.
target_dt = dt * target_banach_steps / banach_step
info('current dt: %e' % dt)
info('target dt: %e' % target_dt)
# alpha is the aggressiveness factor. The distance between the
# current step size and the target step size is reduced by
# |1-alpha|. Hence, if alpha==1 then dt_next==target_dt.
# Otherwise target_dt is approached more slowly.
alpha = 0.5
dt = min(
dt_max,
# At most double the step size from step to step.
dt * min(2.0, 1.0 + alpha * (target_dt - dt) / dt))
info('next dt: %e\n' % dt)
t += dt
end()
return u1, p1, theta1
def test(problem, max_num_steps=2, show=False):
# # Density depends on temperature.
# material = 'water'
# rho = params[material]['density'](293.0)
# mu = params[material]['dynamic viscosity'](293.0)
rho = 1.0
mu = 1.0
# Start time, end time, time step.
t = 0.0
T = 8.0
dt = 1.0e-5
dt_max = 1.0e-1
num_subspaces = problem.W.num_sub_spaces()
if num_subspaces == 2:
# g = Constant((0.0, 0.0))
g = Constant((0.0, -9.81))
elif num_subspaces == 3:
# g = Constant((0.0, 0.0, 0.0))
g = Constant((0.0, -9.81, 0.0))
else:
raise RuntimeError("Illegal number of subspaces ({}).".format(num_subspaces))
initial_stokes = False
if initial_stokes:
u0, p0 = cyl_stokes.solve(
problem.W,
problem.P,
mu,
rho,
problem.u_bcs,
problem.p_bcs,
f=rho * g,
tol=1.0e-10,
maxiter=2000,
)
else:
# Initial states.
u0 = Function(problem.W, name="velocity")
u0.vector().zero()
p0 = Function(problem.P, name="pressure")
p0.vector().zero()
filename = "navier_stokes.xdmf"
with XDMFFile(mpi_comm_world(), filename) as xdmf_file:
xdmf_file.parameters["flush_output"] = True
xdmf_file.parameters["rewrite_function_mesh"] = False
if show:
xdmf_file.write(u0, t)
xdmf_file.write(p0, t)
stepper = cyl_ns.IPCS(time_step_method="backward euler")
steps = 0
while t < T + DOLFIN_EPS and steps < max_num_steps:
steps += 1
begin("Time step {:e} -> {:e}...".format(t, t + dt))
try:
u1, p1 = stepper.step(
Constant(dt),
{0: u0},
p0,
problem.W,
problem.P,
problem.u_bcs,
problem.p_bcs,
Constant(rho),
Constant(mu),
f={0: rho * g, 1: rho * g},
tol=1.0e-10,
)
except RuntimeError:
print(
"Navier--Stokes solver failed to converge. "
"Decrease time step from {} to {} and try again.".format(
dt, 0.5 * dt
)
)
dt *= 0.5
end()
end()
end()
continue
u0.assign(u1)
p0.assign(p1)
if show:
# Save to files.
xdmf_file.write(u0, t + dt)
xdmf_file.write(p0, t + dt)
# Plotting for some reason takes up a lot of memory.
plot(u0, title="velocity", rescale=True)
plot(p0, title="pressure", rescale=True)
# interactive()
begin("Step size adaptation...")
# unorm = project(abs(u[0]) + abs(u[1]) + abs(u[2]),
# P,
# form_compiler_parameters={'quadrature_degree': 4}
# )
unorm = project(
norm(u1), problem.P, form_compiler_parameters={"quadrature_degree": 4}
)
unorm = norm(unorm.vector(), "linf")
# print('||u||_inf = {:e}'.format(unorm))
# Some smooth step-size adaption.
target_dt = 0.2 * problem.mesh.hmax() / unorm
print("current dt: {:e}".format(dt))
print("target dt: {:e}".format(target_dt))
# alpha is the aggressiveness factor. The distance between the
# current step size and the target step size is reduced by
# |1-alpha|. Hence, if alpha==1 then dt_next==target_dt. Otherwise
# target_dt is approached slowlier.
alpha = 0.5
dt = min(
dt_max,
# At most double the step size from step to step.
dt * min(2.0, 1.0 + alpha * (target_dt - dt) / dt),
)
print("next dt: {:e}".format(dt))
t += dt
end()
end()
return