def solve(self, dt):
self.u = Function(self.V0)
self.w = TestFunction(self.V0)
self.du = TrialFunction(self.V0)
x = SpatialCoordinate(self.mesh0)
L = inner( self.S(), self.eps(self.w) )*dx(degree=4)\
- inner( self.b, self.w )*dx(degree=4)\
- inner( self.h, self.w )*ds(degree=4)\
+ inner( 1e-6*self.u, self.w )*ds(degree=4)\
- inner( min_value(x[2]+self.ut[2]+self.u[2], 0) * Constant((0,0,-1.0)), self.w )*ds(degree=4)
a = derivative(L, self.u, self.du)
problem = NonlinearVariationalProblem(L, self.u, bcs=[], J=a)
solver = NonlinearVariationalSolver(problem)
solver.solve()
self.ut.vector()[:] = self.ut.vector()[:] + self.u.vector()[:]
ALE.move(self.mesh, Function(self.V, self.u.vector()))
self.v.vector()[:] = self.u.vector()[:] / dt
self.n = FacetNormal(self.mesh)
def test_comparison_checker(self):
cell = triangle
element = FiniteElement("Lagrange", cell, 1)
u = TrialFunction(element)
v = TestFunction(element)
a = conditional(ge(abs(u), imag(v)), u, v)
b = conditional(le(sqrt(abs(u)), imag(v)), as_ufl(1), as_ufl(1j))
c = conditional(gt(abs(u), pow(imag(v), 0.5)), sin(u), cos(v))
d = conditional(lt(as_ufl(-1), as_ufl(1)), u, v)
e = max_value(as_ufl(0), real(u))
f = min_value(sin(u), cos(v))
g = min_value(sin(pow(u, 3)), cos(abs(v)))
assert do_comparison_check(a) == conditional(ge(real(abs(u)), real(imag(v))), u, v)
with pytest.raises(ComplexComparisonError):
b = do_comparison_check(b)
with pytest.raises(ComplexComparisonError):
c = do_comparison_check(c)
assert do_comparison_check(d) == conditional(lt(real(as_ufl(-1)), real(as_ufl(1))), u, v)
assert do_comparison_check(e) == max_value(real(as_ufl(0)), real(real(u)))
assert do_comparison_check(f) == min_value(real(sin(u)), real(cos(v)))
assert do_comparison_check(g) == min_value(real(sin(pow(u, 3))), real(cos(abs(v))))
def __init__(self, mesh, Vh, prior, misfit, simulation_times,
wind_velocity, gls_stab):
self.mesh = mesh
self.Vh = Vh
self.prior = prior
self.misfit = misfit
# Assume constant timestepping
self.simulation_times = simulation_times
dt = simulation_times[1] - simulation_times[0]
u = dl.TrialFunction(Vh[STATE])
v = dl.TestFunction(Vh[STATE])
kappa = dl.Constant(.001)
dt_expr = dl.Constant(dt)
r_trial = u + dt_expr * (-ufl.div(kappa * ufl.grad(u)) +
ufl.inner(wind_velocity, ufl.grad(u)))
r_test = v + dt_expr * (-ufl.div(kappa * ufl.grad(v)) +
ufl.inner(wind_velocity, ufl.grad(v)))
h = dl.CellDiameter(mesh)
vnorm = ufl.sqrt(ufl.inner(wind_velocity, wind_velocity))
if gls_stab:
tau = ufl.min_value((h * h) / (dl.Constant(2.) * kappa), h / vnorm)
else:
tau = dl.Constant(0.)
self.M = dl.assemble(ufl.inner(u, v) * dl.dx)
self.M_stab = dl.assemble(ufl.inner(u, v + tau * r_test) * dl.dx)
self.Mt_stab = dl.assemble(ufl.inner(u + tau * r_trial, v) * dl.dx)
Nvarf = (ufl.inner(kappa * ufl.grad(u), ufl.grad(v)) +
ufl.inner(wind_velocity, ufl.grad(u)) * v) * dl.dx
Ntvarf = (ufl.inner(kappa * ufl.grad(v), ufl.grad(u)) +
ufl.inner(wind_velocity, ufl.grad(v)) * u) * dl.dx
self.N = dl.assemble(Nvarf)
self.Nt = dl.assemble(Ntvarf)
stab = dl.assemble(tau * ufl.inner(r_trial, r_test) * dl.dx)
self.L = self.M + dt * self.N + stab
self.Lt = self.M + dt * self.Nt + stab
self.solver = dl.PETScLUSolver(dl.as_backend_type(self.L))
self.solvert = dl.PETScLUSolver(dl.as_backend_type(self.Lt))
# Part of model public API
self.gauss_newton_approx = False
def set_forms(self):
"""
Set up week forms
"""
# Assume constant timestepping
dt = self.simulation_times[1] - self.simulation_times[0]
self.wind_velocity = self.computeVelocityField()
u = dl.TrialFunction(self.Vh[STATE])
v = dl.TestFunction(self.Vh[STATE])
kappa = dl.Constant(self.kappa)
dt_expr = dl.Constant(dt)
r_trial = u + dt_expr * (-ufl.div(kappa * ufl.grad(u)) +
ufl.inner(self.wind_velocity, ufl.grad(u)))
r_test = v + dt_expr * (-ufl.div(kappa * ufl.grad(v)) +
ufl.inner(self.wind_velocity, ufl.grad(v)))
h = dl.CellDiameter(self.mesh)
vnorm = ufl.sqrt(ufl.inner(self.wind_velocity, self.wind_velocity))
if self.gls_stab:
tau = ufl.min_value((h * h) / (dl.Constant(2.) * kappa), h / vnorm)
else:
tau = dl.Constant(0.)
self.M = dl.assemble(ufl.inner(u, v) * ufl.dx)
self.M_stab = dl.assemble(ufl.inner(u, v + tau * r_test) * ufl.dx)
self.Mt_stab = dl.assemble(ufl.inner(u + tau * r_trial, v) * ufl.dx)
Nvarf = (ufl.inner(kappa * ufl.grad(u), ufl.grad(v)) +
ufl.inner(self.wind_velocity, ufl.grad(u)) * v) * ufl.dx
Ntvarf = (ufl.inner(kappa * ufl.grad(v), ufl.grad(u)) +
ufl.inner(self.wind_velocity, ufl.grad(v)) * u) * ufl.dx
self.N = dl.assemble(Nvarf)
self.Nt = dl.assemble(Ntvarf)
stab = dl.assemble(tau * ufl.inner(r_trial, r_test) * ufl.dx)
self.L = self.M + dt * self.N + stab
self.Lt = self.M + dt * self.Nt + stab
self.solver = PETScLUSolver(self.mpi_comm)
self.solver.set_operator(dl.as_backend_type(self.L))
self.solvert = PETScLUSolver(self.mpi_comm)
self.solvert.set_operator(dl.as_backend_type(self.Lt))
def solve(self, problem):
self.problem = problem
doSave = problem.doSave
save_this_step = False
onlyVel = problem.saveOnlyVel
dt = self.metadata['dt']
nu = Constant(self.problem.nu)
# TODO check proper use of watches
self.tc.init_watch('init', 'Initialization', True, count_to_percent=False)
self.tc.init_watch('rhs', 'Assembled right hand side', True, count_to_percent=True)
self.tc.init_watch('updateBC', 'Updated velocity BC', True, count_to_percent=True)
self.tc.init_watch('applybc1', 'Applied velocity BC 1st step', True, count_to_percent=True)
self.tc.init_watch('applybc3', 'Applied velocity BC 3rd step', True, count_to_percent=True)
self.tc.init_watch('applybcP', 'Applied pressure BC or othogonalized rhs', True, count_to_percent=True)
self.tc.init_watch('assembleMatrices', 'Initial matrix assembly', False, count_to_percent=True)
self.tc.init_watch('solve 1', 'Running solver on 1st step', True, count_to_percent=True)
self.tc.init_watch('solve 2', 'Running solver on 2nd step', True, count_to_percent=True)
self.tc.init_watch('solve 3', 'Running solver on 3rd step', True, count_to_percent=True)
self.tc.init_watch('solve 4', 'Running solver on 4th step', True, count_to_percent=True)
self.tc.init_watch('assembleA1', 'Assembled A1 matrix (without stabiliz.)', True, count_to_percent=True)
self.tc.init_watch('assembleA1stab', 'Assembled A1 stabilization', True, count_to_percent=True)
self.tc.init_watch('next', 'Next step assignments', True, count_to_percent=True)
self.tc.init_watch('saveVel', 'Saved velocity', True)
self.tc.start('init')
# Define function spaces (P2-P1)
mesh = self.problem.mesh
self.V = VectorFunctionSpace(mesh, "Lagrange", 2) # velocity
self.Q = FunctionSpace(mesh, "Lagrange", 1) # pressure
self.PS = FunctionSpace(mesh, "Lagrange", 2) # partial solution (must be same order as V)
self.D = FunctionSpace(mesh, "Lagrange", 1) # velocity divergence space
if self.bc == 'lagrange':
L = FunctionSpace(mesh, "R", 0)
QL = self.Q*L
problem.initialize(self.V, self.Q, self.PS, self.D)
# Define trial and test functions
u = TrialFunction(self.V)
v = TestFunction(self.V)
if self.bc == 'lagrange':
(pQL, rQL) = TrialFunction(QL)
(qQL, lQL) = TestFunction(QL)
else:
p = TrialFunction(self.Q)
q = TestFunction(self.Q)
n = FacetNormal(mesh)
I = Identity(u.geometric_dimension())
# Initial conditions: u0 velocity at previous time step u1 velocity two time steps back p0 previous pressure
[u1, u0, p0] = self.problem.get_initial_conditions([{'type': 'v', 'time': -dt},
{'type': 'v', 'time': 0.0},
{'type': 'p', 'time': 0.0}])
if doSave:
problem.save_vel(False, u0, 0.0)
problem.save_vel(True, u0, 0.0)
u_ = Function(self.V) # current tentative velocity
u_cor = Function(self.V) # current corrected velocity
if self.bc == 'lagrange':
p_QL = Function(QL) # current pressure or pressure help function from rotation scheme
pQ = Function(self.Q) # auxiliary function for conversion between QL.sub(0) and Q
else:
p_ = Function(self.Q) # current pressure or pressure help function from rotation scheme
p_mod = Function(self.Q) # current modified pressure from rotation scheme
# Define coefficients
k = Constant(self.metadata['dt'])
f = Constant((0, 0, 0))
# Define forms
# step 1: Tentative velocity, solve to u_
u_ext = 1.5*u0 - 0.5*u1 # extrapolation for convection term
# Stabilisation
h = CellSize(mesh)
# CBC delta:
if self.cbcDelta:
delta = Constant(self.stabCoef)*h/(sqrt(inner(u_ext, u_ext))+h)
else:
delta = Constant(self.stabCoef)*h**2/(2*nu*k + k*h*inner(u_ext, u_ext)+h**2)
if self.use_full_SUPG:
v1 = v + delta*0.5*k*dot(grad(v), u_ext)
parameters['form_compiler']['quadrature_degree'] = 6
else:
v1 = v
def nonlinearity(function):
if self.use_ema:
return 2*inner(dot(sym(grad(function)), u_ext), v1) * dx + inner(div(function)*u_ext, v1) * dx
# return 2*inner(dot(sym(grad(function)), u_ext), v) * dx + inner(div(u_ext)*function, v) * dx
# QQ implement this way?
else:
return inner(dot(grad(function), u_ext), v1) * dx
def diffusion(fce):
if self.useLaplace:
return nu*inner(grad(fce), grad(v1)) * dx
else:
form = inner(nu * 2 * sym(grad(fce)), sym(grad(v1))) * dx
if self.bcv == 'CDN':
# IMP will work only if p=0 on output, or we must add term
# inner(p0*n, v)*problem.get_outflow_measure_form() to avoid boundary layer
return form
if self.bcv == 'LAP':
return form - inner(nu*dot(grad(fce).T, n), v1) * problem.get_outflow_measure_form()
if self.bcv == 'DDN':
# IMP will work only if p=0 on output, or we must add term
# inner(p0*n, v)*problem.get_outflow_measure_form() to avoid boundary layer
return form # additional term must be added to non-constant part
def pressure_rhs():
if self.useLaplace or self.bcv == 'LAP':
return inner(p0, div(v1)) * dx - inner(p0*n, v1) * problem.get_outflow_measure_form()
# NT term inner(inner(p, n), v) is 0 when p=0 on outflow
else:
return inner(p0, div(v1)) * dx
a1_const = (1./k)*inner(u, v1)*dx + diffusion(0.5*u)
a1_change = nonlinearity(0.5*u)
if self.bcv == 'DDN':
# IMP Problem: Does not penalize influx for current step, only for the next one
# IMP this can lead to oscilation: DDN correct next step, but then u_ext is OK so in next step DDN is not used, leading to new influx...
# u and u_ext cannot be switched, min_value is nonlinear function
a1_change += -0.5*min_value(Constant(0.), inner(u_ext, n))*inner(u, v1)*problem.get_outflow_measure_form()
# IMP works only with uflacs compiler
L1 = (1./k)*inner(u0, v1)*dx - nonlinearity(0.5*u0) - diffusion(0.5*u0) + pressure_rhs()
if self.bcv == 'DDN':
L1 += 0.5*min_value(0., inner(u_ext, n))*inner(u0, v1)*problem.get_outflow_measure_form()
# Non-consistent SUPG stabilisation
if self.stabilize and not self.use_full_SUPG:
# a1_stab = delta*inner(dot(grad(u), u_ext), dot(grad(v), u_ext))*dx
a1_stab = 0.5*delta*inner(dot(grad(u), u_ext), dot(grad(v), u_ext))*dx(None, {'quadrature_degree': 6})
# NT optional: use Crank Nicolson in stabilisation term: change RHS
# L1 += -0.5*delta*inner(dot(grad(u0), u_ext), dot(grad(v), u_ext))*dx(None, {'quadrature_degree': 6})
outflow_area = Constant(problem.outflow_area)
need_outflow = Constant(0.0)
if self.useRotationScheme:
# Rotation scheme
if self.bc == 'lagrange':
F2 = inner(grad(pQL), grad(qQL))*dx + (1./k)*qQL*div(u_)*dx + pQL*lQL*dx + qQL*rQL*dx
else:
F2 = inner(grad(p), grad(q))*dx + (1./k)*q*div(u_)*dx
else:
# Projection, solve to p_
if self.bc == 'lagrange':
F2 = inner(grad(pQL - p0), grad(qQL))*dx + (1./k)*qQL*div(u_)*dx + pQL*lQL*dx + qQL*rQL*dx
else:
if self.forceOutflow and problem.can_force_outflow:
info('Forcing outflow.')
F2 = inner(grad(p - p0), grad(q))*dx + (1./k)*q*div(u_)*dx
for m in problem.get_outflow_measures():
F2 += (1./k)*(1./outflow_area)*need_outflow*q*m
else:
F2 = inner(grad(p - p0), grad(q))*dx + (1./k)*q*div(u_)*dx
a2, L2 = system(F2)
# step 3: Finalize, solve to u_
if self.useRotationScheme:
# Rotation scheme
if self.bc == 'lagrange':
F3 = (1./k)*inner(u - u_, v)*dx + inner(grad(p_QL.sub(0)), v)*dx
else:
F3 = (1./k)*inner(u - u_, v)*dx + inner(grad(p_), v)*dx
else:
if self.bc == 'lagrange':
F3 = (1./k)*inner(u - u_, v)*dx + inner(grad(p_QL.sub(0) - p0), v)*dx
else:
F3 = (1./k)*inner(u - u_, v)*dx + inner(grad(p_ - p0), v)*dx
a3, L3 = system(F3)
if self.useRotationScheme:
# Rotation scheme: modify pressure
if self.bc == 'lagrange':
pr = TrialFunction(self.Q)
qr = TestFunction(self.Q)
F4 = (pr - p0 - p_QL.sub(0) + nu*div(u_))*qr*dx
else:
F4 = (p - p0 - p_ + nu*div(u_))*q*dx
# TODO zkusit, jestli to nebude rychlejsi? nepocitat soustavu, ale p.assign(...), nutno project(div(u),Q) coz je pocitani podobne soustavy
# TODO zkusit v project zadat solver_type='lu' >> primy resic by mel byt efektivnejsi
a4, L4 = system(F4)
# Assemble matrices
self.tc.start('assembleMatrices')
A1_const = assemble(a1_const) # need to be here, so A1 stays one Python object during repeated assembly
A1_change = A1_const.copy() # copy to get matrix with same sparse structure (data will be overwriten)
if self.stabilize and not self.use_full_SUPG:
A1_stab = A1_const.copy() # copy to get matrix with same sparse structure (data will be overwriten)
A2 = assemble(a2)
A3 = assemble(a3)
if self.useRotationScheme:
A4 = assemble(a4)
self.tc.end('assembleMatrices')
if self.solvers == 'direct':
self.solver_vel_tent = LUSolver('mumps')
self.solver_vel_cor = LUSolver('mumps')
self.solver_p = LUSolver('umfpack')
if self.useRotationScheme:
self.solver_rot = LUSolver('umfpack')
else:
# NT not needed, chosen not to use hypre_parasails
# if self.prec_v == 'hypre_parasails': # in FEniCS 1.6.0 inaccessible using KrylovSolver class
# self.solver_vel_tent = PETScKrylovSolver('gmres') # PETSc4py object
# self.solver_vel_tent.ksp().getPC().setType('hypre')
# PETScOptions.set('pc_hypre_type', 'parasails')
# # this is global setting, but preconditioners for pressure solvers are set by their constructors
# else:
self.solver_vel_tent = KrylovSolver('gmres', self.prec_v) # nonsymetric > gmres
# IMP cannot use 'ilu' in parallel (choose different default option)
self.solver_vel_cor = KrylovSolver('cg', 'hypre_amg') # nonsymetric > gmres
self.solver_p = KrylovSolver('cg', self.prec_p) # symmetric > CG
if self.useRotationScheme:
self.solver_rot = KrylovSolver('cg', self.prec_p)
solver_options = {'monitor_convergence': True, 'maximum_iterations': 1000, 'nonzero_initial_guess': True}
# 'nonzero_initial_guess': True with solver.solbe(A, u, b) means that
# Solver will use anything stored in u as an initial guess
# Get the nullspace if there are no pressure boundary conditions
foo = Function(self.Q) # auxiliary vector for setting pressure nullspace
if self.bc in ['nullspace', 'nullspace_s']:
null_vec = Vector(foo.vector())
self.Q.dofmap().set(null_vec, 1.0)
null_vec *= 1.0/null_vec.norm('l2')
self.null_space = VectorSpaceBasis([null_vec])
if self.bc == 'nullspace':
as_backend_type(A2).set_nullspace(self.null_space)
# apply global options for Krylov solvers
self.solver_vel_tent.parameters['relative_tolerance'] = 10 ** (-self.precision_rel_v_tent)
self.solver_vel_tent.parameters['absolute_tolerance'] = 10 ** (-self.precision_abs_v_tent)
self.solver_vel_cor.parameters['relative_tolerance'] = 10E-12
self.solver_vel_cor.parameters['absolute_tolerance'] = 10E-4
self.solver_p.parameters['relative_tolerance'] = 10**(-self.precision_p)
self.solver_p.parameters['absolute_tolerance'] = 10E-10
if self.useRotationScheme:
self.solver_rot.parameters['relative_tolerance'] = 10**(-self.precision_p)
self.solver_rot.parameters['absolute_tolerance'] = 10E-10
if self.solvers == 'krylov':
for solver in [self.solver_vel_tent, self.solver_vel_cor, self.solver_p, self.solver_rot] if \
self.useRotationScheme else [self.solver_vel_tent, self.solver_vel_cor, self.solver_p]:
for key, value in solver_options.items():
try:
solver.parameters[key] = value
except KeyError:
info('Invalid option %s for KrylovSolver' % key)
return 1
solver.parameters['preconditioner']['structure'] = 'same'
# matrices A2-A4 do not change, so we can reuse preconditioners
self.solver_vel_tent.parameters['preconditioner']['structure'] = 'same_nonzero_pattern'
# matrix A1 changes every time step, so change of preconditioner must be allowed
if self.bc == 'lagrange':
fa = FunctionAssigner(self.Q, QL.sub(0))
# boundary conditions
bcu, bcp = problem.get_boundary_conditions(self.bc == 'outflow', self.V, self.Q)
self.tc.end('init')
# Time-stepping
info("Running of Incremental pressure correction scheme n. 1")
ttime = self.metadata['time']
t = dt
step = 1
while t < (ttime + dt/2.0):
info("t = %f" % t)
self.problem.update_time(t, step)
if self.MPI_rank == 0:
problem.write_status_file(t)
if doSave:
save_this_step = problem.save_this_step
# DDN debug
# u_ext_in = assemble(inner(u_ext, n)*problem.get_outflow_measure_form())
# DDN_triggered = assemble(min_value(Constant(0.), inner(u_ext, n))*problem.get_outflow_measure_form())
# print('DDN: u_ext*n dSout = ', u_ext_in)
# print('DDN: negative part of u_ext*n dSout = ', DDN_triggered)
# assemble matrix (it depends on solution)
self.tc.start('assembleA1')
assemble(a1_change, tensor=A1_change) # assembling into existing matrix is faster than assembling new one
A1 = A1_const.copy() # we dont want to change A1_const
A1.axpy(1, A1_change, True)
self.tc.end('assembleA1')
self.tc.start('assembleA1stab')
if self.stabilize and not self.use_full_SUPG:
assemble(a1_stab, tensor=A1_stab) # assembling into existing matrix is faster than assembling new one
A1.axpy(1, A1_stab, True)
self.tc.end('assembleA1stab')
# Compute tentative velocity step
begin("Computing tentative velocity")
self.tc.start('rhs')
b = assemble(L1)
self.tc.end('rhs')
self.tc.start('applybc1')
[bc.apply(A1, b) for bc in bcu]
self.tc.end('applybc1')
try:
self.tc.start('solve 1')
self.solver_vel_tent.solve(A1, u_.vector(), b)
self.tc.end('solve 1')
if save_this_step:
self.tc.start('saveVel')
problem.save_vel(True, u_, t)
self.tc.end('saveVel')
if save_this_step and not onlyVel:
problem.save_div(True, u_)
problem.compute_err(True, u_, t)
problem.compute_div(True, u_)
except RuntimeError as inst:
problem.report_fail(t)
return 1
end()
# DDN debug
# u_ext_in = assemble(inner(u_, n)*problem.get_outflow_measure_form())
# DDN_triggered = assemble(min_value(Constant(0.), inner(u_, n))*problem.get_outflow_measure_form())
# print('DDN: u_tent*n dSout = ', u_ext_in)
# print('DDN: negative part of u_tent*n dSout = ', DDN_triggered)
if self.useRotationScheme:
begin("Computing tentative pressure")
else:
begin("Computing pressure")
if self.forceOutflow and problem.can_force_outflow:
out = problem.compute_outflow(u_)
info('Tentative outflow: %f' % out)
n_o = -problem.last_inflow-out
info('Needed outflow: %f' % n_o)
need_outflow.assign(n_o)
self.tc.start('rhs')
b = assemble(L2)
self.tc.end('rhs')
self.tc.start('applybcP')
[bc.apply(A2, b) for bc in bcp]
if self.bc in ['nullspace', 'nullspace_s']:
self.null_space.orthogonalize(b)
self.tc.end('applybcP')
try:
self.tc.start('solve 2')
if self.bc == 'lagrange':
self.solver_p.solve(A2, p_QL.vector(), b)
else:
self.solver_p.solve(A2, p_.vector(), b)
self.tc.end('solve 2')
except RuntimeError as inst:
problem.report_fail(t)
return 1
if self.useRotationScheme:
foo = Function(self.Q)
if self.bc == 'lagrange':
fa.assign(pQ, p_QL.sub(0))
foo.assign(pQ + p0)
else:
foo.assign(p_+p0)
problem.averaging_pressure(foo)
if save_this_step and not onlyVel:
problem.save_pressure(True, foo)
else:
if self.bc == 'lagrange':
fa.assign(pQ, p_QL.sub(0))
problem.averaging_pressure(pQ)
if save_this_step and not onlyVel:
problem.save_pressure(False, pQ)
else:
# we do not want to change p=0 on outflow, it conflicts with do-nothing conditions
foo = Function(self.Q)
foo.assign(p_)
problem.averaging_pressure(foo)
if save_this_step and not onlyVel:
problem.save_pressure(False, foo)
end()
begin("Computing corrected velocity")
self.tc.start('rhs')
b = assemble(L3)
self.tc.end('rhs')
if not self.B:
self.tc.start('applybc3')
[bc.apply(A3, b) for bc in bcu]
self.tc.end('applybc3')
try:
self.tc.start('solve 3')
self.solver_vel_cor.solve(A3, u_cor.vector(), b)
self.tc.end('solve 3')
problem.compute_err(False, u_cor, t)
problem.compute_div(False, u_cor)
except RuntimeError as inst:
problem.report_fail(t)
return 1
if save_this_step:
self.tc.start('saveVel')
problem.save_vel(False, u_cor, t)
self.tc.end('saveVel')
if save_this_step and not onlyVel:
problem.save_div(False, u_cor)
end()
# DDN debug
# u_ext_in = assemble(inner(u_cor, n)*problem.get_outflow_measure_form())
# DDN_triggered = assemble(min_value(Constant(0.), inner(u_cor, n))*problem.get_outflow_measure_form())
# print('DDN: u_cor*n dSout = ', u_ext_in)
# print('DDN: negative part of u_cor*n dSout = ', DDN_triggered)
if self.useRotationScheme:
begin("Rotation scheme pressure correction")
self.tc.start('rhs')
b = assemble(L4)
self.tc.end('rhs')
try:
self.tc.start('solve 4')
self.solver_rot.solve(A4, p_mod.vector(), b)
self.tc.end('solve 4')
except RuntimeError as inst:
problem.report_fail(t)
return 1
problem.averaging_pressure(p_mod)
if save_this_step and not onlyVel:
problem.save_pressure(False, p_mod)
end()
# compute functionals (e. g. forces)
problem.compute_functionals(u_cor,
p_mod if self.useRotationScheme else (pQ if self.bc == 'lagrange' else p_), t)
# Move to next time step
self.tc.start('next')
u1.assign(u0)
u0.assign(u_cor)
u_.assign(u_cor) # use corretced velocity as initial guess in first step
if self.useRotationScheme:
p0.assign(p_mod)
else:
if self.bc == 'lagrange':
p0.assign(pQ)
else:
p0.assign(p_)
t = round(t + dt, 6) # round time step to 0.000001
step += 1
self.tc.end('next')
info("Finished: Incremental pressure correction scheme n. 1")
problem.report()
return 0
def solve(self, problem):
self.problem = problem
doSave = problem.doSave
save_this_step = False
onlyVel = problem.saveOnlyVel
dt = self.metadata['dt']
nu = Constant(self.problem.nu)
self.tc.init_watch('init',
'Initialization',
True,
count_to_percent=False)
self.tc.init_watch('rhs',
'Assembled right hand side',
True,
count_to_percent=True)
self.tc.init_watch('applybc1',
'Applied velocity BC 1st step',
True,
count_to_percent=True)
self.tc.init_watch('applybc3',
'Applied velocity BC 3rd step',
True,
count_to_percent=True)
self.tc.init_watch('applybcP',
'Applied pressure BC or othogonalized rhs',
True,
count_to_percent=True)
self.tc.init_watch('assembleMatrices',
'Initial matrix assembly',
False,
count_to_percent=True)
self.tc.init_watch('solve 1',
'Running solver on 1st step',
True,
count_to_percent=True)
self.tc.init_watch('solve 2',
'Running solver on 2nd step',
True,
count_to_percent=True)
self.tc.init_watch('solve 3',
'Running solver on 3rd step',
True,
count_to_percent=True)
self.tc.init_watch('solve 4',
'Running solver on 4th step',
True,
count_to_percent=True)
self.tc.init_watch('assembleA1',
'Assembled A1 matrix (without stabiliz.)',
True,
count_to_percent=True)
self.tc.init_watch('assembleA1stab',
'Assembled A1 stabilization',
True,
count_to_percent=True)
self.tc.init_watch('next',
'Next step assignments',
True,
count_to_percent=True)
self.tc.init_watch('saveVel', 'Saved velocity', True)
self.tc.start('init')
# Define function spaces (P2-P1)
mesh = self.problem.mesh
self.V = VectorFunctionSpace(mesh, "Lagrange", 2) # velocity
self.Q = FunctionSpace(mesh, "Lagrange", 1) # pressure
self.PS = FunctionSpace(
mesh, "Lagrange", 2) # partial solution (must be same order as V)
self.D = FunctionSpace(mesh, "Lagrange",
1) # velocity divergence space
problem.initialize(self.V, self.Q, self.PS, self.D)
# Define trial and test functions
u = TrialFunction(self.V)
v = TestFunction(self.V)
p = TrialFunction(self.Q)
q = TestFunction(self.Q)
n = FacetNormal(mesh)
I = Identity(find_geometric_dimension(u))
# Initial conditions: u0 velocity at previous time step u1 velocity two time steps back p0 previous pressure
[u1, u0, p0] = self.problem.get_initial_conditions([{
'type': 'v',
'time': -dt
}, {
'type': 'v',
'time': 0.0
}, {
'type': 'p',
'time': 0.0
}])
u_ = Function(self.V) # current tentative velocity
u_cor = Function(self.V) # current corrected velocity
p_ = Function(
self.Q
) # current pressure or pressure help function from rotation scheme
p_mod = Function(
self.Q) # current modified pressure from rotation scheme
# Define coefficients
k = Constant(self.metadata['dt'])
f = Constant((0, 0, 0))
# Define forms
# step 1: Tentative velocity, solve to u_
u_ext = 1.5 * u0 - 0.5 * u1 # extrapolation for convection term
# Stabilisation
h = CellSize(mesh)
if self.args.cbc_tau:
# used in Simula cbcflow project
tau = Constant(self.stabCoef) * h / (sqrt(inner(u_ext, u_ext)) + h)
else:
# proposed in R. Codina: On stabilized finite element methods for linear systems of
# convection-diffusion-reaction equations.
tau = Constant(self.stabCoef) * k * h**2 / (
2 * nu * k + k * h * sqrt(DOLFIN_EPS + inner(u_ext, u_ext)) +
h**2)
# DOLFIN_EPS is added because of FEniCS bug that inner(u_ext, u_ext) can be negative when u_ext = 0
if self.use_full_SUPG:
v1 = v + tau * 0.5 * dot(grad(v), u_ext)
parameters['form_compiler']['quadrature_degree'] = 6
else:
v1 = v
def nonlinearity(function):
if self.args.ema:
return 2 * inner(dot(sym(grad(function)), u_ext), v1
) * dx + inner(div(function) * u_ext, v1) * dx
else:
return inner(dot(grad(function), u_ext), v1) * dx
def diffusion(fce):
if self.useLaplace:
return nu * inner(grad(fce), grad(v1)) * dx
else:
form = inner(nu * 2 * sym(grad(fce)), sym(grad(v1))) * dx
if self.bcv == 'CDN':
return form
if self.bcv == 'LAP':
return form - inner(nu * dot(grad(fce).T, n), v1
) * problem.get_outflow_measure_form()
if self.bcv == 'DDN':
return form # additional term must be added to non-constant part
def pressure_rhs():
if self.args.bc == 'outflow':
return inner(p0, div(v1)) * dx
else:
return inner(p0, div(v1)) * dx - inner(
p0 * n, v1) * problem.get_outflow_measure_form()
a1_const = (1. / k) * inner(u, v1) * dx + diffusion(0.5 * u)
a1_change = nonlinearity(0.5 * u)
if self.bcv == 'DDN':
# does not penalize influx for current step, only for the next one
# this can lead to oscilation:
# DDN correct next step, but then u_ext is OK so in next step DDN is not used, leading to new influx...
# u and u_ext cannot be switched, min_value is nonlinear function
a1_change += -0.5 * min_value(Constant(0.), inner(
u_ext, n)) * inner(u, v1) * problem.get_outflow_measure_form()
# NT works only with uflacs compiler
L1 = (1. / k) * inner(u0, v1) * dx - nonlinearity(
0.5 * u0) - diffusion(0.5 * u0) + pressure_rhs()
if self.bcv == 'DDN':
L1 += 0.5 * min_value(0., inner(u_ext, n)) * inner(
u0, v1) * problem.get_outflow_measure_form()
# Non-consistent SUPG stabilisation
if self.stabilize and not self.use_full_SUPG:
# a1_stab = tau*inner(dot(grad(u), u_ext), dot(grad(v), u_ext))*dx
a1_stab = 0.5 * tau * inner(dot(grad(u), u_ext), dot(
grad(v), u_ext)) * dx(None, {'quadrature_degree': 6})
# optional: to use Crank Nicolson in stabilisation term following change of RHS is needed:
# L1 += -0.5*tau*inner(dot(grad(u0), u_ext), dot(grad(v), u_ext))*dx(None, {'quadrature_degree': 6})
outflow_area = Constant(problem.outflow_area)
need_outflow = Constant(0.0)
if self.useRotationScheme:
# Rotation scheme
F2 = inner(grad(p), grad(q)) * dx + (1. / k) * q * div(u_) * dx
else:
# Projection, solve to p_
if self.forceOutflow and problem.can_force_outflow:
info('Forcing outflow.')
F2 = inner(grad(p - p0),
grad(q)) * dx + (1. / k) * q * div(u_) * dx
for m in problem.get_outflow_measures():
F2 += (1. / k) * (1. / outflow_area) * need_outflow * q * m
else:
F2 = inner(grad(p - p0),
grad(q)) * dx + (1. / k) * q * div(u_) * dx
a2, L2 = system(F2)
# step 3: Finalize, solve to u_
if self.useRotationScheme:
# Rotation scheme
F3 = (1. / k) * inner(u - u_, v) * dx + inner(grad(p_), v) * dx
else:
F3 = (1. / k) * inner(u - u_, v) * dx + inner(grad(p_ - p0),
v) * dx
a3, L3 = system(F3)
if self.useRotationScheme:
# Rotation scheme: modify pressure
F4 = (p - p0 - p_ + nu * div(u_)) * q * dx
a4, L4 = system(F4)
# Assemble matrices
self.tc.start('assembleMatrices')
A1_const = assemble(
a1_const
) # must be here, so A1 stays one Python object during repeated assembly
A1_change = A1_const.copy(
) # copy to get matrix with same sparse structure (data will be overwritten)
if self.stabilize and not self.use_full_SUPG:
A1_stab = A1_const.copy(
) # copy to get matrix with same sparse structure (data will be overwritten)
A2 = assemble(a2)
A3 = assemble(a3)
if self.useRotationScheme:
A4 = assemble(a4)
self.tc.end('assembleMatrices')
if self.solvers == 'direct':
self.solver_vel_tent = LUSolver('mumps')
self.solver_vel_cor = LUSolver('mumps')
self.solver_p = LUSolver('mumps')
if self.useRotationScheme:
self.solver_rot = LUSolver('mumps')
else:
# NT 2016-1 KrylovSolver >> PETScKrylovSolver
# not needed, chosen not to use hypre_parasails:
# if self.prec_v == 'hypre_parasails': # in FEniCS 1.6.0 inaccessible using KrylovSolver class
# self.solver_vel_tent = PETScKrylovSolver('gmres') # PETSc4py object
# self.solver_vel_tent.ksp().getPC().setType('hypre')
# PETScOptions.set('pc_hypre_type', 'parasails')
# # this is global setting, but preconditioners for pressure solvers are set by their constructors
# else:
self.solver_vel_tent = PETScKrylovSolver(
'gmres', self.args.precV) # nonsymetric > gmres
# cannot use 'ilu' in parallel
self.solver_vel_cor = PETScKrylovSolver('cg', self.args.precVC)
self.solver_p = PETScKrylovSolver(
self.args.solP,
self.args.precP) # almost (up to BC) symmetric > CG
if self.useRotationScheme:
self.solver_rot = PETScKrylovSolver('cg', 'hypre_amg')
# setup Krylov solvers
if self.solvers == 'krylov':
# Get the nullspace if there are no pressure boundary conditions
foo = Function(
self.Q) # auxiliary vector for setting pressure nullspace
if self.args.bc == 'nullspace':
null_vec = Vector(foo.vector())
self.Q.dofmap().set(null_vec, 1.0)
null_vec *= 1.0 / null_vec.norm('l2')
self.null_space = VectorSpaceBasis([null_vec])
as_backend_type(A2).set_nullspace(self.null_space)
# apply global options for Krylov solvers
solver_options = {
'monitor_convergence': True,
'maximum_iterations': 10000,
'nonzero_initial_guess': True
}
# 'nonzero_initial_guess': True with solver.solve(A, u, b) means that
# Solver will use anything stored in u as an initial guess
for solver in [self.solver_vel_tent, self.solver_vel_cor, self.solver_rot, self.solver_p] if \
self.useRotationScheme else [self.solver_vel_tent, self.solver_vel_cor, self.solver_p]:
for key, value in solver_options.items():
try:
solver.parameters[key] = value
except KeyError:
info('Invalid option %s for KrylovSolver' % key)
return 1
if self.args.solP == 'richardson':
self.solver_p.parameters['monitor_convergence'] = False
self.solver_vel_tent.parameters['relative_tolerance'] = 10**(
-self.args.prv1)
self.solver_vel_tent.parameters['absolute_tolerance'] = 10**(
-self.args.pav1)
self.solver_vel_cor.parameters['relative_tolerance'] = 10E-12
self.solver_vel_cor.parameters['absolute_tolerance'] = 10E-4
self.solver_p.parameters['relative_tolerance'] = 10**(
-self.args.prp)
self.solver_p.parameters['absolute_tolerance'] = 10**(
-self.args.pap)
if self.useRotationScheme:
self.solver_rot.parameters['relative_tolerance'] = 10E-10
self.solver_rot.parameters['absolute_tolerance'] = 10E-10
if self.args.Vrestart > 0:
self.solver_vel_tent.parameters['gmres'][
'restart'] = self.args.Vrestart
if self.args.solP == 'gmres' and self.args.Prestart > 0:
self.solver_p.parameters['gmres'][
'restart'] = self.args.Prestart
# boundary conditions
bcu, bcp = problem.get_boundary_conditions(self.args.bc == 'outflow',
self.V, self.Q)
self.tc.end('init')
# Time-stepping
info("Running of Incremental pressure correction scheme n. 1")
ttime = self.metadata['time']
t = dt
step = 1
# debug function
if problem.args.debug_rot:
plot_cor_v = Function(self.V)
while t < (ttime + dt / 2.0):
self.problem.update_time(t, step)
if self.MPI_rank == 0:
problem.write_status_file(t)
if doSave:
save_this_step = problem.save_this_step
# assemble matrix (it depends on solution)
self.tc.start('assembleA1')
assemble(
a1_change, tensor=A1_change
) # assembling into existing matrix is faster than assembling new one
A1 = A1_const.copy() # we dont want to change A1_const
A1.axpy(1, A1_change, True)
self.tc.end('assembleA1')
self.tc.start('assembleA1stab')
if self.stabilize and not self.use_full_SUPG:
assemble(
a1_stab, tensor=A1_stab
) # assembling into existing matrix is faster than assembling new one
A1.axpy(1, A1_stab, True)
self.tc.end('assembleA1stab')
# Compute tentative velocity step
begin("Computing tentative velocity")
self.tc.start('rhs')
b = assemble(L1)
self.tc.end('rhs')
self.tc.start('applybc1')
[bc.apply(A1, b) for bc in bcu]
self.tc.end('applybc1')
try:
self.tc.start('solve 1')
self.solver_vel_tent.solve(A1, u_.vector(), b)
self.tc.end('solve 1')
if save_this_step:
self.tc.start('saveVel')
problem.save_vel(True, u_)
self.tc.end('saveVel')
if save_this_step and not onlyVel:
problem.save_div(True, u_)
problem.compute_err(True, u_, t)
problem.compute_div(True, u_)
except RuntimeError as inst:
problem.report_fail(t)
return 1
end()
if self.useRotationScheme:
begin("Computing tentative pressure")
else:
begin("Computing pressure")
if self.forceOutflow and problem.can_force_outflow:
out = problem.compute_outflow(u_)
info('Tentative outflow: %f' % out)
n_o = -problem.last_inflow - out
info('Needed outflow: %f' % n_o)
need_outflow.assign(n_o)
self.tc.start('rhs')
b = assemble(L2)
self.tc.end('rhs')
self.tc.start('applybcP')
[bc.apply(A2, b) for bc in bcp]
if self.args.bc == 'nullspace':
self.null_space.orthogonalize(b)
self.tc.end('applybcP')
try:
self.tc.start('solve 2')
self.solver_p.solve(A2, p_.vector(), b)
self.tc.end('solve 2')
except RuntimeError as inst:
problem.report_fail(t)
return 1
if self.useRotationScheme:
foo = Function(self.Q)
foo.assign(p_ + p0)
if save_this_step and not onlyVel:
problem.averaging_pressure(foo)
problem.save_pressure(True, foo)
else:
foo = Function(self.Q)
foo.assign(p_) # we do not want to change p_ by averaging
if save_this_step and not onlyVel:
problem.averaging_pressure(foo)
problem.save_pressure(False, foo)
end()
begin("Computing corrected velocity")
self.tc.start('rhs')
b = assemble(L3)
self.tc.end('rhs')
if not self.args.B:
self.tc.start('applybc3')
[bc.apply(A3, b) for bc in bcu]
self.tc.end('applybc3')
try:
self.tc.start('solve 3')
self.solver_vel_cor.solve(A3, u_cor.vector(), b)
self.tc.end('solve 3')
problem.compute_err(False, u_cor, t)
problem.compute_div(False, u_cor)
except RuntimeError as inst:
problem.report_fail(t)
return 1
if save_this_step:
self.tc.start('saveVel')
problem.save_vel(False, u_cor)
self.tc.end('saveVel')
if save_this_step and not onlyVel:
problem.save_div(False, u_cor)
end()
if self.useRotationScheme:
begin("Rotation scheme pressure correction")
self.tc.start('rhs')
b = assemble(L4)
self.tc.end('rhs')
try:
self.tc.start('solve 4')
self.solver_rot.solve(A4, p_mod.vector(), b)
self.tc.end('solve 4')
except RuntimeError as inst:
problem.report_fail(t)
return 1
if save_this_step and not onlyVel:
problem.averaging_pressure(p_mod)
problem.save_pressure(False, p_mod)
end()
if problem.args.debug_rot:
# save applied pressure correction (expressed as a term added to RHS of next tentative vel. step)
# see comment next to argument definition
plot_cor_v.assign(project(k * grad(nu * div(u_)), self.V))
problem.fileDict['grad_cor']['file'].write(plot_cor_v, t)
# compute functionals (e. g. forces)
problem.compute_functionals(
u_cor, p_mod if self.useRotationScheme else p_, t, step)
# Move to next time step
self.tc.start('next')
u1.assign(u0)
u0.assign(u_cor)
u_.assign(
u_cor) # use corrected velocity as initial guess in first step
if self.useRotationScheme:
p0.assign(p_mod)
else:
p0.assign(p_)
t = round(t + dt, 6) # round time step to 0.000001
step += 1
self.tc.end('next')
info("Finished: Incremental pressure correction scheme n. 1")
problem.report()
return 0
def solve(self, problem):
self.problem = problem
doSave = problem.doSave
save_this_step = False
onlyVel = problem.saveOnlyVel
dt = self.metadata['dt']
nu = Constant(self.problem.nu)
self.tc.init_watch('init', 'Initialization', True, count_to_percent=False)
self.tc.init_watch('rhs', 'Assembled right hand side', True, count_to_percent=True)
self.tc.init_watch('applybc1', 'Applied velocity BC 1st step', True, count_to_percent=True)
self.tc.init_watch('applybc3', 'Applied velocity BC 3rd step', True, count_to_percent=True)
self.tc.init_watch('applybcP', 'Applied pressure BC or othogonalized rhs', True, count_to_percent=True)
self.tc.init_watch('assembleMatrices', 'Initial matrix assembly', False, count_to_percent=True)
self.tc.init_watch('solve 1', 'Running solver on 1st step', True, count_to_percent=True)
self.tc.init_watch('solve 2', 'Running solver on 2nd step', True, count_to_percent=True)
self.tc.init_watch('solve 3', 'Running solver on 3rd step', True, count_to_percent=True)
self.tc.init_watch('solve 4', 'Running solver on 4th step', True, count_to_percent=True)
self.tc.init_watch('assembleA1', 'Assembled A1 matrix (without stabiliz.)', True, count_to_percent=True)
self.tc.init_watch('assembleA1stab', 'Assembled A1 stabilization', True, count_to_percent=True)
self.tc.init_watch('next', 'Next step assignments', True, count_to_percent=True)
self.tc.init_watch('saveVel', 'Saved velocity', True)
self.tc.start('init')
# Define function spaces (P2-P1)
mesh = self.problem.mesh
self.V = VectorFunctionSpace(mesh, "Lagrange", 2) # velocity
self.Q = FunctionSpace(mesh, "Lagrange", 1) # pressure
self.PS = FunctionSpace(mesh, "Lagrange", 2) # partial solution (must be same order as V)
self.D = FunctionSpace(mesh, "Lagrange", 1) # velocity divergence space
problem.initialize(self.V, self.Q, self.PS, self.D)
# Define trial and test functions
u = TrialFunction(self.V)
v = TestFunction(self.V)
p = TrialFunction(self.Q)
q = TestFunction(self.Q)
n = FacetNormal(mesh)
I = Identity(find_geometric_dimension(u))
# Initial conditions: u0 velocity at previous time step u1 velocity two time steps back p0 previous pressure
[u1, u0, p0] = self.problem.get_initial_conditions([{'type': 'v', 'time': -dt},
{'type': 'v', 'time': 0.0},
{'type': 'p', 'time': 0.0}])
u_ = Function(self.V) # current tentative velocity
u_cor = Function(self.V) # current corrected velocity
p_ = Function(self.Q) # current pressure or pressure help function from rotation scheme
p_mod = Function(self.Q) # current modified pressure from rotation scheme
# Define coefficients
k = Constant(self.metadata['dt'])
f = Constant((0, 0, 0))
# Define forms
# step 1: Tentative velocity, solve to u_
u_ext = 1.5 * u0 - 0.5 * u1 # extrapolation for convection term
# Stabilisation
h = CellSize(mesh)
if self.args.cbc_tau:
# used in Simula cbcflow project
tau = Constant(self.stabCoef) * h / (sqrt(inner(u_ext, u_ext)) + h)
else:
# proposed in R. Codina: On stabilized finite element methods for linear systems of
# convection-diffusion-reaction equations.
tau = Constant(self.stabCoef) * k * h ** 2 / (
2 * nu * k + k * h * sqrt(DOLFIN_EPS + inner(u_ext, u_ext)) + h ** 2)
# DOLFIN_EPS is added because of FEniCS bug that inner(u_ext, u_ext) can be negative when u_ext = 0
if self.use_full_SUPG:
v1 = v + tau * 0.5 * dot(grad(v), u_ext)
parameters['form_compiler']['quadrature_degree'] = 6
else:
v1 = v
def nonlinearity(function):
if self.args.ema:
return 2 * inner(dot(sym(grad(function)), u_ext), v1) * dx + inner(div(function) * u_ext, v1) * dx
else:
return inner(dot(grad(function), u_ext), v1) * dx
def diffusion(fce):
if self.useLaplace:
return nu * inner(grad(fce), grad(v1)) * dx
else:
form = inner(nu * 2 * sym(grad(fce)), sym(grad(v1))) * dx
if self.bcv == 'CDN':
return form
if self.bcv == 'LAP':
return form - inner(nu * dot(grad(fce).T, n), v1) * problem.get_outflow_measure_form()
if self.bcv == 'DDN':
return form # additional term must be added to non-constant part
def pressure_rhs():
if self.args.bc == 'outflow':
return inner(p0, div(v1)) * dx
else:
return inner(p0, div(v1)) * dx - inner(p0 * n, v1) * problem.get_outflow_measure_form()
a1_const = (1. / k) * inner(u, v1) * dx + diffusion(0.5 * u)
a1_change = nonlinearity(0.5 * u)
if self.bcv == 'DDN':
# does not penalize influx for current step, only for the next one
# this can lead to oscilation:
# DDN correct next step, but then u_ext is OK so in next step DDN is not used, leading to new influx...
# u and u_ext cannot be switched, min_value is nonlinear function
a1_change += -0.5 * min_value(Constant(0.), inner(u_ext, n)) * inner(u,
v1) * problem.get_outflow_measure_form()
# NT works only with uflacs compiler
L1 = (1. / k) * inner(u0, v1) * dx - nonlinearity(0.5 * u0) - diffusion(0.5 * u0) + pressure_rhs()
if self.bcv == 'DDN':
L1 += 0.5 * min_value(0., inner(u_ext, n)) * inner(u0, v1) * problem.get_outflow_measure_form()
# Non-consistent SUPG stabilisation
if self.stabilize and not self.use_full_SUPG:
# a1_stab = tau*inner(dot(grad(u), u_ext), dot(grad(v), u_ext))*dx
a1_stab = 0.5 * tau * inner(dot(grad(u), u_ext), dot(grad(v), u_ext)) * dx(None, {'quadrature_degree': 6})
# optional: to use Crank Nicolson in stabilisation term following change of RHS is needed:
# L1 += -0.5*tau*inner(dot(grad(u0), u_ext), dot(grad(v), u_ext))*dx(None, {'quadrature_degree': 6})
outflow_area = Constant(problem.outflow_area)
need_outflow = Constant(0.0)
if self.useRotationScheme:
# Rotation scheme
F2 = inner(grad(p), grad(q)) * dx + (1. / k) * q * div(u_) * dx
else:
# Projection, solve to p_
if self.forceOutflow and problem.can_force_outflow:
info('Forcing outflow.')
F2 = inner(grad(p - p0), grad(q)) * dx + (1. / k) * q * div(u_) * dx
for m in problem.get_outflow_measures():
F2 += (1. / k) * (1. / outflow_area) * need_outflow * q * m
else:
F2 = inner(grad(p - p0), grad(q)) * dx + (1. / k) * q * div(u_) * dx
a2, L2 = system(F2)
# step 3: Finalize, solve to u_
if self.useRotationScheme:
# Rotation scheme
F3 = (1. / k) * inner(u - u_, v) * dx + inner(grad(p_), v) * dx
else:
F3 = (1. / k) * inner(u - u_, v) * dx + inner(grad(p_ - p0), v) * dx
a3, L3 = system(F3)
if self.useRotationScheme:
# Rotation scheme: modify pressure
F4 = (p - p0 - p_ + nu * div(u_)) * q * dx
a4, L4 = system(F4)
# Assemble matrices
self.tc.start('assembleMatrices')
A1_const = assemble(a1_const) # must be here, so A1 stays one Python object during repeated assembly
A1_change = A1_const.copy() # copy to get matrix with same sparse structure (data will be overwritten)
if self.stabilize and not self.use_full_SUPG:
A1_stab = A1_const.copy() # copy to get matrix with same sparse structure (data will be overwritten)
A2 = assemble(a2)
A3 = assemble(a3)
if self.useRotationScheme:
A4 = assemble(a4)
self.tc.end('assembleMatrices')
if self.solvers == 'direct':
self.solver_vel_tent = LUSolver('mumps')
self.solver_vel_cor = LUSolver('mumps')
self.solver_p = LUSolver('mumps')
if self.useRotationScheme:
self.solver_rot = LUSolver('mumps')
else:
# NT 2016-1 KrylovSolver >> PETScKrylovSolver
# not needed, chosen not to use hypre_parasails:
# if self.prec_v == 'hypre_parasails': # in FEniCS 1.6.0 inaccessible using KrylovSolver class
# self.solver_vel_tent = PETScKrylovSolver('gmres') # PETSc4py object
# self.solver_vel_tent.ksp().getPC().setType('hypre')
# PETScOptions.set('pc_hypre_type', 'parasails')
# # this is global setting, but preconditioners for pressure solvers are set by their constructors
# else:
self.solver_vel_tent = PETScKrylovSolver('gmres', self.args.precV) # nonsymetric > gmres
# cannot use 'ilu' in parallel
self.solver_vel_cor = PETScKrylovSolver('cg', self.args.precVC)
self.solver_p = PETScKrylovSolver(self.args.solP, self.args.precP) # almost (up to BC) symmetric > CG
if self.useRotationScheme:
self.solver_rot = PETScKrylovSolver('cg', 'hypre_amg')
# setup Krylov solvers
if self.solvers == 'krylov':
# Get the nullspace if there are no pressure boundary conditions
foo = Function(self.Q) # auxiliary vector for setting pressure nullspace
if self.args.bc == 'nullspace':
null_vec = Vector(foo.vector())
self.Q.dofmap().set(null_vec, 1.0)
null_vec *= 1.0 / null_vec.norm('l2')
self.null_space = VectorSpaceBasis([null_vec])
as_backend_type(A2).set_nullspace(self.null_space)
# apply global options for Krylov solvers
solver_options = {'monitor_convergence': True, 'maximum_iterations': 10000, 'nonzero_initial_guess': True}
# 'nonzero_initial_guess': True with solver.solve(A, u, b) means that
# Solver will use anything stored in u as an initial guess
for solver in [self.solver_vel_tent, self.solver_vel_cor, self.solver_rot, self.solver_p] if \
self.useRotationScheme else [self.solver_vel_tent, self.solver_vel_cor, self.solver_p]:
for key, value in solver_options.items():
try:
solver.parameters[key] = value
except KeyError:
info('Invalid option %s for KrylovSolver' % key)
return 1
if self.args.solP == 'richardson':
self.solver_p.parameters['monitor_convergence'] = False
self.solver_vel_tent.parameters['relative_tolerance'] = 10 ** (-self.args.prv1)
self.solver_vel_tent.parameters['absolute_tolerance'] = 10 ** (-self.args.pav1)
self.solver_vel_cor.parameters['relative_tolerance'] = 10E-12
self.solver_vel_cor.parameters['absolute_tolerance'] = 10E-4
self.solver_p.parameters['relative_tolerance'] = 10 ** (-self.args.prp)
self.solver_p.parameters['absolute_tolerance'] = 10 ** (-self.args.pap)
if self.useRotationScheme:
self.solver_rot.parameters['relative_tolerance'] = 10E-10
self.solver_rot.parameters['absolute_tolerance'] = 10E-10
if self.args.Vrestart > 0:
self.solver_vel_tent.parameters['gmres']['restart'] = self.args.Vrestart
if self.args.solP == 'gmres' and self.args.Prestart > 0:
self.solver_p.parameters['gmres']['restart'] = self.args.Prestart
# boundary conditions
bcu, bcp = problem.get_boundary_conditions(self.args.bc == 'outflow', self.V, self.Q)
self.tc.end('init')
# Time-stepping
info("Running of Incremental pressure correction scheme n. 1")
ttime = self.metadata['time']
t = dt
step = 1
# debug function
if problem.args.debug_rot:
plot_cor_v = Function(self.V)
while t < (ttime + dt / 2.0):
self.problem.update_time(t, step)
if self.MPI_rank == 0:
problem.write_status_file(t)
if doSave:
save_this_step = problem.save_this_step
# assemble matrix (it depends on solution)
self.tc.start('assembleA1')
assemble(a1_change, tensor=A1_change) # assembling into existing matrix is faster than assembling new one
A1 = A1_const.copy() # we dont want to change A1_const
A1.axpy(1, A1_change, True)
self.tc.end('assembleA1')
self.tc.start('assembleA1stab')
if self.stabilize and not self.use_full_SUPG:
assemble(a1_stab, tensor=A1_stab) # assembling into existing matrix is faster than assembling new one
A1.axpy(1, A1_stab, True)
self.tc.end('assembleA1stab')
# Compute tentative velocity step
begin("Computing tentative velocity")
self.tc.start('rhs')
b = assemble(L1)
self.tc.end('rhs')
self.tc.start('applybc1')
[bc.apply(A1, b) for bc in bcu]
self.tc.end('applybc1')
try:
self.tc.start('solve 1')
self.solver_vel_tent.solve(A1, u_.vector(), b)
self.tc.end('solve 1')
if save_this_step:
self.tc.start('saveVel')
problem.save_vel(True, u_)
self.tc.end('saveVel')
if save_this_step and not onlyVel:
problem.save_div(True, u_)
problem.compute_err(True, u_, t)
problem.compute_div(True, u_)
except RuntimeError as inst:
problem.report_fail(t)
return 1
end()
if self.useRotationScheme:
begin("Computing tentative pressure")
else:
begin("Computing pressure")
if self.forceOutflow and problem.can_force_outflow:
out = problem.compute_outflow(u_)
info('Tentative outflow: %f' % out)
n_o = -problem.last_inflow - out
info('Needed outflow: %f' % n_o)
need_outflow.assign(n_o)
self.tc.start('rhs')
b = assemble(L2)
self.tc.end('rhs')
self.tc.start('applybcP')
[bc.apply(A2, b) for bc in bcp]
if self.args.bc == 'nullspace':
self.null_space.orthogonalize(b)
self.tc.end('applybcP')
try:
self.tc.start('solve 2')
self.solver_p.solve(A2, p_.vector(), b)
self.tc.end('solve 2')
except RuntimeError as inst:
problem.report_fail(t)
return 1
if self.useRotationScheme:
foo = Function(self.Q)
foo.assign(p_ + p0)
if save_this_step and not onlyVel:
problem.averaging_pressure(foo)
problem.save_pressure(True, foo)
else:
foo = Function(self.Q)
foo.assign(p_) # we do not want to change p_ by averaging
if save_this_step and not onlyVel:
problem.averaging_pressure(foo)
problem.save_pressure(False, foo)
end()
begin("Computing corrected velocity")
self.tc.start('rhs')
b = assemble(L3)
self.tc.end('rhs')
if not self.args.B:
self.tc.start('applybc3')
[bc.apply(A3, b) for bc in bcu]
self.tc.end('applybc3')
try:
self.tc.start('solve 3')
self.solver_vel_cor.solve(A3, u_cor.vector(), b)
self.tc.end('solve 3')
problem.compute_err(False, u_cor, t)
problem.compute_div(False, u_cor)
except RuntimeError as inst:
problem.report_fail(t)
return 1
if save_this_step:
self.tc.start('saveVel')
problem.save_vel(False, u_cor)
self.tc.end('saveVel')
if save_this_step and not onlyVel:
problem.save_div(False, u_cor)
end()
if self.useRotationScheme:
begin("Rotation scheme pressure correction")
self.tc.start('rhs')
b = assemble(L4)
self.tc.end('rhs')
try:
self.tc.start('solve 4')
self.solver_rot.solve(A4, p_mod.vector(), b)
self.tc.end('solve 4')
except RuntimeError as inst:
problem.report_fail(t)
return 1
if save_this_step and not onlyVel:
problem.averaging_pressure(p_mod)
problem.save_pressure(False, p_mod)
end()
if problem.args.debug_rot:
# save applied pressure correction (expressed as a term added to RHS of next tentative vel. step)
# see comment next to argument definition
plot_cor_v.assign(project(k * grad(nu * div(u_)), self.V))
problem.fileDict['grad_cor']['file'].write(plot_cor_v, t)
# compute functionals (e. g. forces)
problem.compute_functionals(u_cor, p_mod if self.useRotationScheme else p_, t, step)
# Move to next time step
self.tc.start('next')
u1.assign(u0)
u0.assign(u_cor)
u_.assign(u_cor) # use corrected velocity as initial guess in first step
if self.useRotationScheme:
p0.assign(p_mod)
else:
p0.assign(p_)
t = round(t + dt, 6) # round time step to 0.000001
step += 1
self.tc.end('next')
info("Finished: Incremental pressure correction scheme n. 1")
problem.report()
return 0
def __init__(self, mesh, Vh, t_init, t_final, t_1, dt, wind_velocity, gls_stab, Prior):
self.mesh = mesh
self.Vh = Vh
self.t_init = t_init
self.t_final = t_final
self.t_1 = t_1
self.dt = dt
self.sim_times = np.arange(self.t_init, self.t_final+.5*self.dt, self.dt)
u = dl.TrialFunction(Vh[STATE])
v = dl.TestFunction(Vh[STATE])
kappa = dl.Constant(.001)
dt_expr = dl.Constant(self.dt)
r_trial = u + dt_expr*( -dl.div(kappa*dl.nabla_grad(u))+ dl.inner(wind_velocity, dl.nabla_grad(u)) )
r_test = v + dt_expr*( -dl.div(kappa*dl.nabla_grad(v))+ dl.inner(wind_velocity, dl.nabla_grad(v)) )
h = dl.CellDiameter(mesh)
vnorm = dl.sqrt(dl.inner(wind_velocity, wind_velocity))
if gls_stab:
tau = ufl.min_value((h*h)/(dl.Constant(2.)*kappa), h/vnorm )
else:
tau = dl.Constant(0.)
self.M = dl.assemble( dl.inner(u,v)*dl.dx )
self.M_stab = dl.assemble( dl.inner(u, v+tau*r_test)*dl.dx )
self.Mt_stab = dl.assemble( dl.inner(u+tau*r_trial,v)*dl.dx )
Nvarf = (dl.inner(kappa *dl.nabla_grad(u), dl.nabla_grad(v)) + dl.inner(wind_velocity, dl.nabla_grad(u))*v )*dl.dx
Ntvarf = (dl.inner(kappa *dl.nabla_grad(v), dl.nabla_grad(u)) + dl.inner(wind_velocity, dl.nabla_grad(v))*u )*dl.dx
self.N = dl.assemble( Nvarf )
self.Nt = dl.assemble(Ntvarf)
stab = dl.assemble( tau*dl.inner(r_trial, r_test)*dl.dx)
self.L = self.M + dt*self.N + stab
self.Lt = self.M + dt*self.Nt + stab
boundaries = dl.MeshFunction("size_t", mesh,1)
boundaries.set_all(0)
class InsideBoundary(dl.SubDomain):
def inside(self,x,on_boundary):
x_in = x[0] > dl.DOLFIN_EPS and x[0] < 1 - dl.DOLFIN_EPS
y_in = x[1] > dl.DOLFIN_EPS and x[1] < 1 - dl.DOLFIN_EPS
return on_boundary and x_in and y_in
Gamma_M = InsideBoundary()
Gamma_M.mark(boundaries,1)
ds_marked = dl.Measure("ds", subdomain_data=boundaries)
self.Q = dl.assemble( self.dt*dl.inner(u, v) * ds_marked(1) )
self.Prior = Prior
self.solver = dl.PETScLUSolver( dl.as_backend_type(self.L) )
self.solvert = dl.PETScLUSolver( dl.as_backend_type(self.Lt) )
self.ud = self.generate_vector(STATE)
self.noise_variance = 0
# Part of model public API
self.gauss_newton_approx = False