def solve(self, annotate=True):
''' Solve the shallow water equations '''
############################### Setting up the equations ###########################
# Initialise solver settings
if not type(self.problem) == SWProblem:
raise TypeError("Do not know how to solve problem of type %s." %
type(self.problem))
# Get parameters
problem_params = self.problem.parameters
solver_params = self.parameters
farm = problem_params.tidal_farm
if farm:
turbine_friction = farm.friction_function
# Performance settings
parameters['form_compiler']['quadrature_degree'] = \
solver_params.quadrature_degree
parameters['form_compiler']['cpp_optimize_flags'] = \
" ".join(solver_params.cpp_flags)
parameters['form_compiler']['cpp_optimize'] = True
parameters['form_compiler']['optimize'] = True
# Get domain measures
ds = problem_params.domain.ds
dx = problem_params.domain.dx
# Get the boundary normal direction
n = FacetNormal(self.mesh)
# Get temporal settings
theta = Constant(problem_params.theta)
dt = Constant(problem_params.dt)
finish_time = Constant(problem_params.finish_time)
t = Constant(problem_params.start_time)
# Get equation settings
g = problem_params.g
h = problem_params.depth
nu = problem_params.viscosity
include_advection = problem_params.include_advection
include_viscosity = problem_params.include_viscosity
linear_divergence = problem_params.linear_divergence
f_u = problem_params.f_u
include_les = solver_params.les_model
# Get boundary conditions
bcs = problem_params.bcs
# Get function spaces
V, Q = self.V, self.Q
dgu = "Discontinuous" in str(V)
# Test and trial functions
v = TestFunction(V)
u = TrialFunction(V)
q = TestFunction(Q)
eta = TrialFunction(Q)
# Functions
u00 = Function(V)
u0 = Function(V, name="u0")
ut = Function(V) # Tentative velocity
u1 = Function(V, name="u")
eta0 = Function(Q, name="eta0")
eta1 = Function(Q, name="eta")
# Large eddy model
if include_les:
les_V = FunctionSpace(problem_params.domain.mesh, "CG", 1)
les = LES(les_V, u0,
solver_params.les_parameters['smagorinsky_coefficient'])
eddy_viscosity = les.eddy_viscosity
nu += eddy_viscosity
else:
eddy_viscosity = None
# Define the water depth
if linear_divergence:
H = h
else:
H = eta0 + h
if f_u is None:
f_u = Constant((0, 0))
# Bottom friction
friction = problem_params.friction
if farm:
friction += Function(turbine_friction, name="turbine_friction",
annotate=annotate)
# Load initial conditions
# Projection is necessary to obtain 2nd order convergence
# FIXME: The problem should specify the ic for each component separately.
u_ic = project(problem_params.initial_condition_u, self.V)
u0.assign(u_ic, annotate=False)
u00.assign(u_ic, annotate=False)
eta_ic = project(problem_params.initial_condition_eta, self.Q)
eta0.assign(eta_ic, annotate=False)
eta1.assign(eta_ic, annotate=False)
# Tentative velocity step
u_mean = theta * u + (1. - theta) * u0
u_bash = 3./2 * u0 - 1./2 * u00
u_diff = u - u0
norm_u0 = inner(u0, u0)**0.5
F_u_tent = ((1/dt) * inner(v, u_diff) * dx()
+ inner(v, grad(u_bash)*u_mean) * dx()
+ g * inner(v, grad(eta0)) * dx()
+ friction / H * norm_u0 * inner(u_mean, v) * dx
- inner(v, f_u) * dx())
# Viscosity term
if dgu:
# Taken from http://maths.dur.ac.uk/~dma0mpj/summer_school/IPHO.pdf
sigma = 1. # Penalty parameter.
# Set tau=-1 for SIPG, tau=0 for IIPG, and tau=1 for NIPG
tau = 0.
edgelen = FacetArea(self.mesh)('+') # Facetarea is continuous, so
# we can select either side
alpha = sigma/edgelen
F_u_tent += nu * inner(grad(v), grad(u_mean)) * dx()
for d in range(2):
F_u_tent += - nu * inner(avg(grad(u_mean[d])), jump(v[d], n))*dS
F_u_tent += - nu * tau * inner(avg(grad(v[d])), jump(u[d], n))*dS
F_u_tent += alpha * nu * inner(jump(u[d], n), jump(v[d], n))*dS
else:
F_u_tent += nu * inner(grad(v), grad(u_mean)) * dx()
a_u_tent = lhs(F_u_tent)
L_u_tent = rhs(F_u_tent)
# Pressure correction
eta_diff = eta - eta0
ut_mean = theta * ut + (1. - theta) * u0
F_p_corr = (q*eta_diff + g * dt**2 * theta**2 * H * inner(grad(q),
grad(eta_diff)))*dx() + dt*q*div(H*ut_mean)*dx()
a_p_corr = lhs(F_p_corr)
L_p_corr = rhs(F_p_corr)
# Velocity correction
eta_diff = eta1 - eta0
a_u_corr = inner(v, u)*dx()
L_u_corr = inner(v, ut)*dx() - dt*g*theta*inner(v, grad(eta_diff))*dx()
bcu, bceta = self._generate_strong_bcs(dgu)
# Assemble matrices
A_u_corr = assemble(a_u_corr)
for bc in bcu: bc.apply(A_u_corr)
a_u_corr_solver = LUSolver(A_u_corr)
a_u_corr_solver.parameters["reuse_factorization"] = True
if linear_divergence:
A_p_corr = assemble(a_p_corr)
for bc in bceta: bc.apply(A_p_corr)
a_p_corr_solver = LUSolver(A_p_corr)
a_p_corr_solver.parameters["reuse_factorization"] = True
yield({"time": t,
"u": u0,
"eta": eta0,
"eddy_viscosity": eddy_viscosity,
"is_final": self._finished(t, finish_time)})
log(INFO, "Start of time loop")
adjointer.time.start(t)
timestep = 0
# De/activate annotation
annotate_orig = parameters["adjoint"]["stop_annotating"]
parameters["adjoint"]["stop_annotating"] = not annotate
while not self._finished(t, finish_time):
# Update timestep
timestep += 1
t = Constant(t + dt)
# Update bc's
t_theta = Constant(t - (1.0 - theta) * dt)
bcs.update_time(t, only_type=["strong_dirichlet"])
bcs.update_time(t_theta, exclude_type=["strong_dirichlet"])
# Update source term
if f_u is not None:
f_u.t = Constant(t_theta)
if include_les:
log(PROGRESS, "Compute eddy viscosity.")
les.solve()
# Compute tentative velocity step
log(PROGRESS, "Solve for tentative velocity.")
A_u_tent = assemble(a_u_tent)
b = assemble(L_u_tent)
for bc in bcu: bc.apply(A_u_tent, b)
solve(A_u_tent, ut.vector(), b)
# Pressure correction
log(PROGRESS, "Solve for pressure correction.")
b = assemble(L_p_corr)
for bc in bceta: bc.apply(b)
if linear_divergence:
a_p_corr_solver.solve(eta1.vector(), b)
else:
A_p_corr = assemble(a_p_corr)
for bc in bceta: bc.apply(A_p_corr)
solve(A_p_corr, eta1.vector(), b)
# Velocity correction
log(PROGRESS, "Solve for velocity update.")
b = assemble(L_u_corr)
for bc in bcu: bc.apply(b)
a_u_corr_solver.solve(u1.vector(), b)
# Rotate functions for next timestep
u00.assign(u0)
u0.assign(u1)
eta0.assign(eta1)
# Increase the adjoint timestep
adj_inc_timestep(time=float(t), finished=self._finished(t,
finish_time))
yield({"time": t,
"u": u0,
"eta": eta0,
"eddy_viscosity": eddy_viscosity,
"is_final": self._finished(t, finish_time)})
# Reset annotation flag
parameters["adjoint"]["stop_annotating"] = annotate_orig
log(INFO, "End of time loop.")
# A time vector, noting 1600sps is used.
tt = np.linspace(0, 32*10/1600, 32*10, endpoint=False)
# A phase comparison vector. This should be the idea output.
pt = np.concatenate((((2*np.pi*50.0*tt+np.pi) % (2*np.pi) - np.pi),(2*np.pi*ft*tt+np.pi) % (2*np.pi) - np.pi))
# The test input vector
yt = np.concatenate((mag*np.cos(2*np.pi*50*tt) + dc_offset, mag*np.cos(2*np.pi*ft*tt) + dc_offset))
# Re-define tt to extend the full length.
tt = np.linspace(0, 2*32*10/1600, 2*32*10, endpoint=False)
step_time = (32*10)/1600 # used for drawing a line of the plots
# Create and run the filter, noting increasing the number of iterations
# will reduce the LES filter settling time at the cost of higher computation time.
les = LES(iterations=1)
les_out = les.run_les(yt)
# Visualisation of the output
fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2, sharex=True, sharey=False)
fig.suptitle('LES Freq Step Test', fontsize=16)
# Plots have the LES generated lines wider so the correct lines is overlayed and visable.
# Plot the phases
ax1.plot(tt, les_out[1], linewidth=3)
ax1.plot(tt, pt)
ax1.set_title('Phase (rad)')
ax1.axvline(x=step_time, ls='--', c='red')
# Plot the freqency
def solve(self, annotate=True):
''' Returns an iterator for solving the shallow water equations. '''
############################### Setting up the equations ###########################
# Get parameters
problem_params = self.problem.parameters
solver_params = self.parameters
farm = problem_params.tidal_farm
# Performance settings
parameters['form_compiler']['quadrature_degree'] = \
solver_params.quadrature_degree
parameters['form_compiler']['cpp_optimize_flags'] = \
" ".join(solver_params.cpp_flags)
parameters['form_compiler']['cpp_optimize'] = True
parameters['form_compiler']['optimize'] = True
# Get domain measures
ds = problem_params.domain.ds
# Initialise solver settings
if type(self.problem) == SWProblem:
log(INFO, "Solve a transient shallow water problem")
theta = Constant(problem_params.theta)
dt = Constant(problem_params.dt)
finish_time = Constant(problem_params.finish_time)
t = Constant(problem_params.start_time)
include_time_term = True
elif type(self.problem) == MultiSteadySWProblem:
log(INFO, "Solve a multi steady-state shallow water problem")
theta = Constant(1)
dt = Constant(problem_params.dt)
finish_time = Constant(problem_params.finish_time)
# The multi steady-state case solves the steady-state equation also
# for the start time
t = Constant(problem_params.start_time - dt)
include_time_term = False
elif type(self.problem) == SteadySWProblem:
log(INFO, "Solve a steady-state shallow water problem")
theta = Constant(1.)
dt = Constant(1.)
finish_time = Constant(0.5)
t = Constant(0.)
include_time_term = False
else:
raise TypeError("Do not know how to solve problem of type %s." %
type(self.problem))
g = problem_params.g
depth = problem_params.depth
include_advection = problem_params.include_advection
include_viscosity = problem_params.include_viscosity
viscosity = problem_params.viscosity
bcs = problem_params.bcs
linear_divergence = problem_params.linear_divergence
cache_forward_state = solver_params.cache_forward_state
f_u = problem_params.f_u
u_dg = "Discontinuous" in str(self.function_space.split()[0])
# Define test functions
v, q = TestFunctions(self.function_space)
# Define functions
state = Function(self.function_space, name="Current_state")
self.state = state
state_new = Function(self.function_space, name="New_state")
# Load initial condition (or initial guess for stady problems)
# Projection is necessary to obtain 2nd order convergence
ic = project(problem_params.initial_condition, self.function_space)
state.assign(ic, annotate=False)
# Split mixed functions
u, h = split(state_new)
u0, h0 = split(state)
# Define the water depth
if linear_divergence:
H = depth
else:
H = h + depth
# Create initial conditions and interpolate
state_new.assign(state, annotate=annotate)
# u_(n+theta) and h_(n+theta)
u_mid = (1.0 - theta) * u0 + theta * u
h_mid = (1.0 - theta) * h0 + theta * h
# The normal direction
n = FacetNormal(self.mesh)
# Large eddy model
include_les = solver_params.les_model
if include_les:
les_V = FunctionSpace(problem_params.domain.mesh, "CG", 1)
les = LES(les_V, u0, solver_params.les_parameters['smagorinsky_coefficient'])
eddy_viscosity = les.eddy_viscosity
viscosity += eddy_viscosity
else:
eddy_viscosity = None
# k-eps RANS model
#include_keps = solver_params.keps_model
#if include_keps:
# keps_V = FunctionSpace(problem_params.domain.mesh, "CG", 1)
# keps = KEpsilon(keps_V, u, dt, problem_params.domain.mesh)
# eddy_viscosity = keps.eddy_viscosity_old
# viscosity += eddy_viscosity
#else:
# eddy_viscosity = None
# Mass matrix contributions
M = inner(v, u) * dx
M += inner(q, h) * dx
M0 = inner(v, u0) * dx
M0 += inner(q, h0) * dx
# Divergence term.
Ct_mid = -H * inner(u_mid, grad(q)) * dx
#+inner(avg(u_mid),jump(q,n))*dS # This term is only needed for dg
# element pairs which is not supported
# The surface integral contribution from the divergence term
bc_contr = -H * dot(u_mid, n) * q * ds
for function_name, u_expr, facet_id, bctype in bcs.filter(function_name='u'):
if bctype in ('weak_dirichlet', 'free_slip'):
# Subtract the divergence integral again
bc_contr -= -H * dot(u_mid, n) * q * ds(facet_id)
# for weak Dirichlet we replace it with the bc expression
if bctype=='weak_dirichlet':
bc_contr -= H * dot(u_expr, n) * q * ds(facet_id)
elif bctype == 'flather':
# Subtract the divergence integral again
bc_contr -= -H * dot(u_mid, n) * q * ds(facet_id)
# The Flather boundary condition
#bc_contr -= H * dot(u_expr, n) * q * ds(facet_id)
Ct_mid += sqrt(g * H) * inner(h_mid, q) * ds(facet_id) + H * dot(u_expr, n) * q * ds(facet_id)
# Pressure gradient term
weak_eta_bcs = bcs.filter(function_name='eta', bctype='weak_dirichlet')
# don't integrate pressure gradient by parts (a.o. allows dg test function v)
C_mid = g * inner(v, grad(h_mid)) * dx
for function_name, eta_expr, facet_id, bctype in weak_eta_bcs:
# Apply the eta boundary conditions weakly on boundary IDs 1 and 2
C_mid += g * inner(dot(v, n), (eta_expr-h_mid)) * ds(facet_id)
# Bottom friction
friction = problem_params.friction
if not farm:
tf = Constant(0)
elif type(farm.friction_function) == list:
tf = Function(farm.friction_function[0], name="turbine_friction", annotate=annotate)
else:
tf = Function(farm.friction_function, name="turbine_friction", annotate=annotate)
# Friction term
# FIXME: FEniCS fails on assembling the below form for u_mid = 0, even
# though it is differentiable. Even this potential fix does not help:
#norm_u_mid = conditional(inner(u_mid, u_mid)**0.5 < DOLFIN_EPS, Constant(0),
# inner(u_mid, u_mid)**0.5)
norm_u_mid = inner(u_mid, u_mid)**0.5
R_mid = friction / H * norm_u_mid * inner(u_mid, v) * dx(self.mesh)
if farm:
if not farm.turbine_specification.thrust:
R_mid += tf/H*dot(u_mid, u_mid)**0.5*inner(u_mid, v)*farm.site_dx
else:
u_mag = dot(u_mid, u_mid)**0.5
C_t = farm.turbine_specification.compute_C_t(u_mag)
R_mid += (tf * farm.turbine_specification.turbine_parametrisation_constant * \
C_t / H) * u_mag * inner(u_mid, v) * farm.site_dx
# Advection term
if include_advection:
Ad_mid = inner(dot(grad(u_mid), u_mid), v) * dx
# un is |u.n| on the down-side (incoming), and 0 on the up-side of a facet (outgoing)
un = (abs(dot(u, n))-dot(u,n))/2.0
if u_dg:
# at the downside, we want inner(|u.n|*(u_down-u_up),v_down) - u_down-u_up being the gradient along the flow
Ad_mid += (inner(un('+')*(u_mid('+')-u_mid('-')), v('+')) + inner(un('-')*(u_mid('-')-u_mid('+')), v('-')))*dS
# apply weak_diricihlet bc for the advection term at the incoming boundaries only
for function_name, u_expr, facet_id, bctype in bcs:
if function_name =="u" and bctype == 'weak_dirichlet':
# this is the same thing as for DG above, except u_up is the boundary value and u_down is u+ or u- (they are the same)
# the fact that these are the same also means that the DG term above vanishes at the boundary and is replaced here
Ad_mid += inner(un*(u_mid-u_expr), v)*ds(facet_id)
if include_viscosity:
# Check that we are not using a DG velocity function space, as the facet integrals are not implemented.
if u_dg:
raise NotImplementedError("The viscosity term for \
discontinuous elements is not supported.")
#D_mid = viscosity*inner(grad(u_mid) + grad(u_mid).T, grad(v))*dx - viscosity*(2.0/3.0)*inner(div(u_mid)*Identity(2), grad(v))*dx
D_mid = viscosity * inner(2*sym(grad(u_mid)), grad(v)) * dx
# Create the final form
G_mid = C_mid + Ct_mid + R_mid
# Add the advection term
if include_advection:
G_mid += Ad_mid
# Add the viscosity term
if include_viscosity:
G_mid += D_mid
# Add the source term
G_mid -= inner(f_u, v) * dx
F = dt * G_mid - dt * bc_contr
# Add the time term
if include_time_term:
F += M - M0
# Generate the scheme specific strong boundary conditions
strong_bcs = self._generate_strong_bcs()
############################### Perform the simulation ###########################
if solver_params.dump_period > 0:
writer = StateWriter(solver=self)
if type(self.problem) == SWProblem:
log(INFO, "Writing state to disk...")
writer.write(state)
result = {"time": t,
"u": u0,
"eta": h0,
"tf": tf,
"state": state,
"is_final": self._finished(t, finish_time)}
solver_params.callback(result)
yield(result)
print "Power at %.2f = %.2f" % (float(t), assemble(1000.0*tf*dot(u_mid, u_mid)**1.5*dx))
log(INFO, "Start of time loop")
adjointer.time.start(t)
timestep = 0
while not self._finished(t, finish_time):
# Update timestep
timestep += 1
t = Constant(t + dt)
# Update bc's
t_theta = Constant(t - (1.0 - theta) * dt)
bcs.update_time(t, only_type=["strong_dirichlet"])
bcs.update_time(t_theta, exclude_type=["strong_dirichlet"])
# Update source term
f_u.t = Constant(t_theta)
if include_les:
log(PROGRESS, "Compute eddy viscosity from LES model.")
les.solve()
#if include_keps:
# log(PROGRESS, "Compute eddy viscosity from k-epsilon RANS model.")
# e = keps.solve(u0)
# eddy_viscosity.assign(e)
# Set the initial guess for the solve
if cache_forward_state and self.state_cache.has_key(float(t)):
log(INFO, "Read initial guess from cache for t=%f." % t)
# Load initial guess for solver from cache
state_new.assign(self.state_cache[float(t)], annotate=False)
elif not include_time_term:
log(INFO, "Set the initial guess for the nonlinear solver to the initial condition.")
# Reset the initial guess after each timestep
ic = problem_params.initial_condition
state_new.assign(ic, annotate=False)
# Solve non-linear system with a Newton solver
if self.problem._is_transient:
log(INFO, "Solve shallow water equations at time %s" % float(t))
else:
log(INFO, "Solve shallow water equations.")
solve(F == 0, state_new, bcs=strong_bcs,
solver_parameters=solver_params.dolfin_solver,
annotate=annotate,
J=derivative(F, state_new))
# After the timestep solve, update state
state.assign(state_new)
if cache_forward_state:
# Save state for initial guess cache
log(INFO, "Cache solution t=%f as next initial guess." % t)
if not self.state_cache.has_key(float(t)):
self.state_cache[float(t)] = Function(self.function_space)
self.state_cache[float(t)].assign(state_new, annotate=False)
# Set the control function for the upcoming timestep.
if farm:
if type(farm.friction_function) == list:
tf.assign(farm.friction_function[timestep])
else:
tf.assign(farm.friction_function)
if (solver_params.dump_period > 0 and
timestep % solver_params.dump_period == 0):
log(INFO, "Write state to disk...")
writer.write(state)
# Return the results
result = {"time": t,
"u": u0,
"eta": h0,
"tf": tf,
"state": state,
"is_final": self._finished(t, finish_time)}
solver_params.callback(result)
yield(result)
# Increase the adjoint timestep
adj_inc_timestep(time=float(t), finished=self._finished(t,
finish_time))
print "Power at %.2f = %.2f" % (float(t), assemble(1000.0*tf*dot(u_mid, u_mid)**1.5*dx))
# If we're outputting the individual turbine power
if self.parameters.print_individual_turbine_power:
self.parameters.output_writer.individual_turbine_power(self)
log(INFO, "End of time loop.")
def solve(self, annotate=True):
''' Solve the shallow water equations '''
############################### Setting up the equations ###########################
# Initialise solver settings
if not type(self.problem) == SWProblem:
raise TypeError("Do not know how to solve problem of type %s." %
type(self.problem))
# Get parameters
problem_params = self.problem.parameters
solver_params = self.parameters
farm = problem_params.tidal_farm
if farm:
turbine_friction = farm.friction_function
# Performance settings
parameters['form_compiler']['quadrature_degree'] = \
solver_params.quadrature_degree
parameters['form_compiler']['cpp_optimize_flags'] = \
" ".join(solver_params.cpp_flags)
parameters['form_compiler']['cpp_optimize'] = True
parameters['form_compiler']['optimize'] = True
# Get domain measures
ds = problem_params.domain.ds
dx = problem_params.domain.dx
# Get the boundary normal direction
n = FacetNormal(self.mesh)
# Get temporal settings
theta = Constant(problem_params.theta)
dt = Constant(problem_params.dt)
finish_time = Constant(problem_params.finish_time)
t = Constant(problem_params.start_time)
# Get equation settings
g = problem_params.g
h = problem_params.depth
nu = problem_params.viscosity
include_advection = problem_params.include_advection
include_viscosity = problem_params.include_viscosity
linear_divergence = problem_params.linear_divergence
f_u = problem_params.f_u
include_les = solver_params.les_model
# Get boundary conditions
bcs = problem_params.bcs
# Get function spaces
V, Q = self.V, self.Q
dgu = "Discontinuous" in str(V)
# Test and trial functions
v = TestFunction(V)
u = TrialFunction(V)
q = TestFunction(Q)
eta = TrialFunction(Q)
# Functions
u00 = Function(V)
u0 = Function(V, name="u0")
ut = Function(V) # Tentative velocity
u1 = Function(V, name="u")
eta0 = Function(Q, name="eta0")
eta1 = Function(Q, name="eta")
# Large eddy model
if include_les:
les_V = FunctionSpace(problem_params.domain.mesh, "CG", 1)
les = LES(les_V, u0,
solver_params.les_parameters['smagorinsky_coefficient'])
eddy_viscosity = les.eddy_viscosity
nu += eddy_viscosity
else:
eddy_viscosity = None
# Define the water depth
if linear_divergence:
H = h
else:
H = eta0 + h
if f_u is None:
f_u = Constant((0, 0))
# Bottom friction
friction = problem_params.friction
if farm:
friction += Function(turbine_friction,
name="turbine_friction",
annotate=annotate)
# Load initial conditions
# Projection is necessary to obtain 2nd order convergence
# FIXME: The problem should specify the ic for each component separately.
u_ic = project(problem_params.initial_condition_u, self.V)
u0.assign(u_ic, annotate=False)
u00.assign(u_ic, annotate=False)
eta_ic = project(problem_params.initial_condition_eta, self.Q)
eta0.assign(eta_ic, annotate=False)
eta1.assign(eta_ic, annotate=False)
# Tentative velocity step
u_mean = theta * u + (1. - theta) * u0
u_bash = 3. / 2 * u0 - 1. / 2 * u00
u_diff = u - u0
norm_u0 = inner(u0, u0)**0.5
F_u_tent = ((1 / dt) * inner(v, u_diff) * dx() +
inner(v,
grad(u_bash) * u_mean) * dx() +
g * inner(v, grad(eta0)) * dx() +
friction / H * norm_u0 * inner(u_mean, v) * dx -
inner(v, f_u) * dx())
# Viscosity term
if dgu:
# Taken from http://maths.dur.ac.uk/~dma0mpj/summer_school/IPHO.pdf
sigma = 1. # Penalty parameter.
# Set tau=-1 for SIPG, tau=0 for IIPG, and tau=1 for NIPG
tau = 0.
edgelen = FacetArea(self.mesh)('+') # Facetarea is continuous, so
# we can select either side
alpha = sigma / edgelen
F_u_tent += nu * inner(grad(v), grad(u_mean)) * dx()
for d in range(2):
F_u_tent += -nu * inner(avg(grad(u_mean[d])), jump(v[d],
n)) * dS
F_u_tent += -nu * tau * inner(avg(grad(v[d])), jump(u[d],
n)) * dS
F_u_tent += alpha * nu * inner(jump(u[d], n), jump(v[d],
n)) * dS
else:
F_u_tent += nu * inner(grad(v), grad(u_mean)) * dx()
a_u_tent = lhs(F_u_tent)
L_u_tent = rhs(F_u_tent)
# Pressure correction
eta_diff = eta - eta0
ut_mean = theta * ut + (1. - theta) * u0
F_p_corr = (q * eta_diff + g * dt**2 * theta**2 * H *
inner(grad(q), grad(eta_diff))) * dx() + dt * q * div(
H * ut_mean) * dx()
a_p_corr = lhs(F_p_corr)
L_p_corr = rhs(F_p_corr)
# Velocity correction
eta_diff = eta1 - eta0
a_u_corr = inner(v, u) * dx()
L_u_corr = inner(v, ut) * dx() - dt * g * theta * inner(
v, grad(eta_diff)) * dx()
bcu, bceta = self._generate_strong_bcs(dgu)
# Assemble matrices
A_u_corr = assemble(a_u_corr)
for bc in bcu:
bc.apply(A_u_corr)
a_u_corr_solver = LUSolver(A_u_corr)
a_u_corr_solver.parameters["reuse_factorization"] = True
if linear_divergence:
A_p_corr = assemble(a_p_corr)
for bc in bceta:
bc.apply(A_p_corr)
a_p_corr_solver = LUSolver(A_p_corr)
a_p_corr_solver.parameters["reuse_factorization"] = True
yield ({
"time": t,
"u": u0,
"eta": eta0,
"eddy_viscosity": eddy_viscosity,
"is_final": self._finished(t, finish_time)
})
log(INFO, "Start of time loop")
adjointer.time.start(t)
timestep = 0
# De/activate annotation
annotate_orig = parameters["adjoint"]["stop_annotating"]
parameters["adjoint"]["stop_annotating"] = not annotate
while not self._finished(t, finish_time):
# Update timestep
timestep += 1
t = Constant(t + dt)
# Update bc's
t_theta = Constant(t - (1.0 - theta) * dt)
bcs.update_time(t, only_type=["strong_dirichlet"])
bcs.update_time(t_theta, exclude_type=["strong_dirichlet"])
# Update source term
if f_u is not None:
f_u.t = Constant(t_theta)
if include_les:
log(PROGRESS, "Compute eddy viscosity.")
les.solve()
# Compute tentative velocity step
log(PROGRESS, "Solve for tentative velocity.")
A_u_tent = assemble(a_u_tent)
b = assemble(L_u_tent)
for bc in bcu:
bc.apply(A_u_tent, b)
solve(A_u_tent, ut.vector(), b)
# Pressure correction
log(PROGRESS, "Solve for pressure correction.")
b = assemble(L_p_corr)
for bc in bceta:
bc.apply(b)
if linear_divergence:
a_p_corr_solver.solve(eta1.vector(), b)
else:
A_p_corr = assemble(a_p_corr)
for bc in bceta:
bc.apply(A_p_corr)
solve(A_p_corr, eta1.vector(), b)
# Velocity correction
log(PROGRESS, "Solve for velocity update.")
b = assemble(L_u_corr)
for bc in bcu:
bc.apply(b)
a_u_corr_solver.solve(u1.vector(), b)
# Rotate functions for next timestep
u00.assign(u0)
u0.assign(u1)
eta0.assign(eta1)
# Increase the adjoint timestep
adj_inc_timestep(time=float(t),
finished=self._finished(t, finish_time))
yield ({
"time": t,
"u": u0,
"eta": eta0,
"eddy_viscosity": eddy_viscosity,
"is_final": self._finished(t, finish_time)
})
# Reset annotation flag
parameters["adjoint"]["stop_annotating"] = annotate_orig
log(INFO, "End of time loop.")