def __init__(self,
F_fluid,
F_solid,
w,
wdot,
bcs_mesh,
bcs,
dF_fluid_u,
dF_fluid_udot,
dF_solid_u,
dF_solid_udot,
update=None,
report=None,
*args,
**kwargs):
self.F_fluid_form = F_fluid
self.dF_fluid_u_form = dF_fluid_u
self.dF_fluid_udot_form = dF_fluid_udot
self.F_solid_form = F_solid
self.dF_solid_u_form = dF_solid_u
self.dF_solid_udot_form = dF_solid_udot
self.bcs_mesh = bcs_mesh
self.bcs = bcs
self.w = w
self.wdot = wdot
self.a = df.Constant(1.0)
self.dF_fluid_form = self.dF_fluid_u_form + self.a * self.dF_fluid_udot_form
self.dF_solid_form = self.dF_solid_u_form + self.a * self.dF_solid_udot_form
self.report = report
self.update = update
self.form_compiler_parameters = {"optimize": True}
if "form_compiler_parameters" in kwargs:
self.form_compiler_parameters = kwargs["form_compiler_parameters"]
self.assembler = df.SystemAssembler(
self.dF_fluid_form + self.dF_solid_form,
self.F_fluid_form + self.F_solid_form, self.bcs + self.bcs_mesh)
self.x = df.as_backend_type(w.vector())
self.x_petsc = self.x.vec()
self.xdot = df.as_backend_type(wdot.vector())
self.xdot_petsc = self.xdot.vec()
self.b_petsc = self.x_petsc.duplicate()
# We need to initialise the matrix size and local-to-global maps
self.A_dolfin = df.PETScMatrix()
self.assembler.init_global_tensor(
self.A_dolfin, df.Form(self.dF_fluid_form + self.dF_fluid_form))
self.A_petsc = self.A_dolfin.mat()
self.xx = self.A_petsc.createVecRight()
self.xxdot = self.A_petsc.createVecRight()
self.A1_dolfin = df.PETScMatrix()
self.assembler.init_global_tensor(
self.A1_dolfin, df.Form(self.dF_fluid_form + self.dF_fluid_form))
self.A2_dolfin = df.PETScMatrix()
self.assembler.init_global_tensor(
self.A2_dolfin, df.Form(self.dF_fluid_form + self.dF_fluid_form))
def _construct(self, field_inp):
# Read the input
self.name = field_inp.get_value('name', required_type='string')
self.var_name = field_inp.get_value('variable_name', 'phi', 'string')
self.stationary = field_inp.get_value('stationary', False, 'bool')
self.radius = field_inp.get_value('radius', required_type='float')
self.plot = field_inp.get_value('plot', False, 'bool')
# Show the input
sim = self.simulation
sim.log.info('Creating a free surface zone field %r' % self.name)
sim.log.info(' Variable: %r' % self.var_name)
sim.log.info(' Stationary: %r' % self.stationary)
# Create the level set model
mesh = sim.data['mesh']
func_name = '%s_%s' % (self.name, self.var_name)
self.V = dolfin.FunctionSpace(mesh, 'DG', 0)
self.function = dolfin.Function(self.V)
self.function.rename(func_name, func_name)
sim.data[func_name] = self.function
# Get the level set view
level_set_view = sim.multi_phase_model.get_level_set_view()
level_set_view.add_update_callback(self.update)
# Form to compute the cell average distance to the free surface
v = dolfin.TestFunction(self.V)
ls = level_set_view.level_set_function
cv = dolfin.CellVolume(self.V.mesh())
self.dist_form = dolfin.Form(ls * v / cv * dolfin.dx)
if self.plot:
sim.io.add_extra_output_function(self.function)
def __init__(self, simulation, u_conv):
"""
Given a velocity in DG, e.g DG2, produce a velocity in DGT0,
i.e. a constant on each facet
"""
V = u_conv[0].function_space()
V_dgt0 = dolfin.FunctionSpace(V.mesh(), 'DGT', 0)
u = dolfin.TrialFunction(V_dgt0)
v = dolfin.TestFunction(V_dgt0)
ndim = simulation.ndim
w = u_conv
w_new = dolfin.as_vector(
[dolfin.Function(V_dgt0) for _ in range(ndim)])
dot, avg, dS, ds = dolfin.dot, dolfin.avg, dolfin.dS, dolfin.ds
a = dot(avg(u), avg(v)) * dS + dot(u, v) * ds
L = []
for d in range(ndim):
L.append(avg(w[d]) * avg(v) * dS + w[d] * v * ds)
self.lhs = [dolfin.Form(Li) for Li in L]
self.A = dolfin.assemble(a)
self.solver = dolfin.PETScKrylovSolver('cg')
self.velocity = simulation.data['u_conv_dgt0'] = w_new
def _interp(self, name, expr=None, func=None):
"""
Interpolate the expression into the given function
"""
sim = self.simulation
# Determine the function space
V = self.V
quad_degree = None
if name == 'c' and self.colour_projection_degree >= 0:
# Perform projection for c instead of interpolation to better
# capture the discontinuous nature of the colour field
if 'Vc' not in sim.data:
ocellaris_error(
'Error in wave field %r input' % self.name,
'Cannot specify colour_to_dg_degree when c is '
'not used in the multiphase_solver.',
)
V = sim.data['Vc']
quad_degree = self.colour_projection_degree
# Get the expression
if expr is None:
expr = self._get_expression(name, quad_degree)
# Get the function
if func is None:
if name not in self._functions:
self._functions[name] = dolfin.Function(V)
func = self._functions[name]
if quad_degree is not None:
if self.colour_projection_form is None:
# Ensure that we can use the DG0 trick of dividing by the mass
# matrix diagonal to get the projected value
if V.ufl_element().degree() != 0:
ocellaris_error(
'Error in wave field %r input' % self.name,
'The colour_to_dg_degree projection is '
'currently only implemented when c is DG0',
)
v = dolfin.TestFunction(V)
dx = dolfin.dx(metadata={'quadrature_degree': quad_degree})
d = dolfin.CellVolume(V.mesh()) # mass matrix diagonal
form = expr * v / d * dx
self.colour_projection_form = dolfin.Form(form)
# Perform projection by assembly (DG0 only!)
dolfin.assemble(self.colour_projection_form, tensor=func.vector())
else:
# Perform standard interpolation
func.interpolate(expr)
def get_variable(self, name):
if not name == self.var_name:
ocellaris_error(
'Scalar field does not define %r' % name,
'This scalar field defines %r' % self.var_name,
)
if self.func is not None:
return self.func
if self.colour_projection_degree >= 0:
quad_degree = self.colour_projection_degree
degree = None
else:
quad_degree = None
degree = self.polydeg
expr = OcellarisCppExpression(
self.simulation,
self.cpp_code,
'Scalar field %r' % self.name,
degree=degree,
update=False,
quad_degree=quad_degree,
)
self.func = dolfin.Function(self.V)
if quad_degree is not None:
# Ensure that we can use the DG0 trick of dividing by the mass
# matrix diagonal to get the projected value
if self.V.ufl_element().degree() != 0:
ocellaris_error(
'Error in wave field %r input' % self.name,
'The colour_to_dg_degree projection is '
'currently only implemented when c is DG0',
)
v = dolfin.TestFunction(self.V)
dx = dolfin.dx(metadata={'quadrature_degree': quad_degree})
d = dolfin.CellVolume(self.V.mesh()) # mass matrix diagonal
form = expr * v / d * dx
compiled_form = dolfin.Form(form)
# Perform projection by assembly (DG0 only!)
dolfin.assemble(compiled_form, tensor=self.func.vector())
else:
# Perform standard interpolation
self.func.interpolate(expr)
return self.func
def tune_factors(self, setup=False):
if setup:
# Incoming wave data
u_inlet = self.inflow_field.get_variable('uhoriz')
c_inlet = self.inflow_field.get_variable('c')
ds_inlet = self.simulation.data['ds'](self.inflow_ds_mark_id)
# Outlet data
u_outlet = self._get_expression('uhoriz')
c_outlet = self._get_expression('c')
ds_outlet = self.simulation.data['ds'](self.outflow_ds_mark_id)
# Compute unit fluxes
self.const_speed_above.assign(dolfin.Constant(1.0))
self.const_speed_below.assign(dolfin.Constant(1.0))
self.uf_above = dolfin.assemble(
(1 - c_outlet) * u_outlet * ds_outlet)
self.uf_below = dolfin.assemble(c_outlet * u_outlet * ds_outlet)
self.form_inlet_above = dolfin.Form(
(1 - c_inlet) * u_inlet * ds_inlet)
self.form_inlet_below = dolfin.Form(c_inlet * u_inlet * ds_inlet)
self.form_inlet_total = dolfin.Form(u_inlet * ds_inlet)
self.form_outlet_above = dolfin.Form(
(1 - c_outlet) * u_outlet * ds_outlet)
self.form_outlet_below = dolfin.Form(c_outlet * u_outlet *
ds_outlet)
self.form_outlet_total = dolfin.Form(u_outlet * ds_outlet)
import time
t1 = time.time()
# Compute flux above and below at the inlet
inlet_flux_above = dolfin.assemble(self.form_inlet_above)
inlet_flux_below = dolfin.assemble(self.form_inlet_below)
inlet_flux_total = dolfin.assemble(self.form_inlet_total)
is_motion = abs(inlet_flux_above) > 0 or abs(inlet_flux_below) > 0
# Estimate the fluxes at the outlet (this gets within 99.99% of total zero flux)
self.const_speed_above.assign(
dolfin.Constant(inlet_flux_above / self.uf_above))
self.const_speed_below.assign(
dolfin.Constant(inlet_flux_below / self.uf_below))
if OPTIMISE_FLUXES and is_motion:
# Use root finding to adjust the speed above the free surface
# in order to get zero total volume flux in the domain
def func_to_minimise(vel_above):
"Compute the difference in total flux"
# Adjust outflow speed above the FS
self.const_speed_above.assign(dolfin.Constant(vel_above))
outlet_flux_total = dolfin.assemble(self.form_outlet_total)
return (outlet_flux_total - inlet_flux_total)**2
# Starting values - use the basic unit fluxes
x1 = inlet_flux_above / self.uf_above
x0 = x1 * 0.99
xN, niter = find_root_secant(x0, x1, func_to_minimise)
if False and abs(inlet_flux_below) > 0:
outlet_flux_above = dolfin.assemble(self.form_outlet_above)
outlet_flux_below = dolfin.assemble(self.form_outlet_below)
outlet_flux_total = dolfin.assemble(self.form_outlet_total)
print('uf ab & be', self.uf_above, self.uf_below)
print(
'flux_above',
inlet_flux_above,
outlet_flux_above,
outlet_flux_above / inlet_flux_above,
)
print(
'flux_below',
inlet_flux_below,
outlet_flux_below,
outlet_flux_below / inlet_flux_below,
)
print(
'flux_total',
inlet_flux_total,
outlet_flux_total,
outlet_flux_total / inlet_flux_total,
)
print(xN - x0)
print(niter)
print('Took %g seconds' % (time.time() - t1))
def define_simple_equations(self):
"""
Setup weak forms for SIMPLE form
"""
sim = self.simulation
self.Vuvw = sim.data['uvw_star'].function_space()
Vp = sim.data['Vp']
# The trial and test functions in a coupled space (to be split)
func_spaces = [self.Vuvw, Vp]
e_mixed = dolfin.MixedElement([fs.ufl_element() for fs in func_spaces])
Vcoupled = dolfin.FunctionSpace(sim.data['mesh'], e_mixed)
tests = dolfin.TestFunctions(Vcoupled)
trials = dolfin.TrialFunctions(Vcoupled)
# Split into components
v = dolfin.as_vector(tests[0][:])
u = dolfin.as_vector(trials[0][:])
q = tests[-1]
p = trials[-1]
lm_trial = lm_test = None
# Define the full coupled form and split it into subforms depending
# on the test and trial functions
eq = define_dg_equations(
u,
v,
p,
q,
lm_trial,
lm_test,
self.simulation,
include_hydrostatic_pressure=self.include_hydrostatic_pressure,
incompressibility_flux_type=self.incompressibility_flux_type,
use_grad_q_form=self.use_grad_q_form,
use_grad_p_form=self.use_grad_p_form,
use_stress_divergence_form=self.use_stress_divergence_form,
)
mat, vec = split_form_into_matrix(eq,
Vcoupled,
Vcoupled,
check_zeros=True)
# Check matrix and vector shapes and that the matrix is a saddle point matrix
assert mat.shape == (2, 2)
assert vec.shape == (2, )
assert mat[
-1,
-1] is None, 'Found p-q coupling, this is not a saddle point system!'
# Store the forms
self.eqA = mat[0, 0]
self.eqB = mat[0, 1]
self.eqC = mat[1, 0]
self.eqD = vec[0]
self.eqE = vec[1]
if self.eqE is None:
self.eqE = dolfin.TrialFunction(Vp) * dolfin.Constant(
0) * dolfin.dx
if self.a_tilde_is_mass:
# The mass matrix. Consistent with the implementation in define_dg_equations
rho = sim.multi_phase_model.get_density(0)
c1 = sim.data['time_coeffs'][0]
dt = sim.data['dt']
eqM = rho * c1 / dt * dolfin.dot(u, v) * dolfin.dx
matM, _vecM = split_form_into_matrix(eqM,
Vcoupled,
Vcoupled,
check_zeros=True)
self.eqM = dolfin.Form(matM[0, 0])
self.M = None
def to_dolfin_cpp_form(a):
if isinstance(a, ufl.form.Form):
return dolfin.Form(a)
return a
def define_weak_forms(self):
sim = self.simulation
self.Vuvw = sim.data['uvw_star'].function_space()
Vp = sim.data['Vp']
# The trial and test functions in a coupled space (to be split)
func_spaces = [self.Vuvw, Vp]
e_mixed = dolfin.MixedElement([fs.ufl_element() for fs in func_spaces])
Vcoupled = dolfin.FunctionSpace(sim.data['mesh'], e_mixed)
tests = dolfin.TestFunctions(Vcoupled)
trials = dolfin.TrialFunctions(Vcoupled)
# Split into components
v = dolfin.as_vector(tests[0][:])
u = dolfin.as_vector(trials[0][:])
q = tests[-1]
p = trials[-1]
lm_trial = lm_test = None
# Define the full coupled form and split it into subforms depending
# on the test and trial functions
eq = define_dg_equations(
u,
v,
p,
q,
lm_trial,
lm_test,
self.simulation,
include_hydrostatic_pressure=self.hydrostatic_pressure.
every_timestep,
incompressibility_flux_type=self.incompressibility_flux_type,
use_grad_q_form=self.use_grad_q_form,
use_grad_p_form=self.use_grad_p_form,
use_stress_divergence_form=self.use_stress_divergence_form,
)
sim.log.info(' Splitting coupled form')
mat, vec = split_form_into_matrix(eq,
Vcoupled,
Vcoupled,
check_zeros=True)
# Check matrix and vector shapes and that the matrix is a saddle point matrix
assert mat.shape == (2, 2)
assert vec.shape == (2, )
assert mat[
-1,
-1] is None, 'Found p-q coupling, this is not a saddle point system!'
# Compile and store the forms
sim.log.info(' Compiling IPCS-A forms')
self.eqA = dolfin.Form(mat[0, 0])
self.eqB = dolfin.Form(mat[0, 1])
self.eqC = dolfin.Form(mat[1, 0])
self.eqD = dolfin.Form(vec[0])
self.eqE = dolfin.Form(vec[1]) if vec[1] is not None else None
# The mass matrix. Consistent with the implementation in define_dg_equations
if self.splitting_approximation == SPLIT_APPROX_MASS_WITH_RHO:
rho_for_M = sim.multi_phase_model.get_density(0)
elif self.splitting_approximation == SPLIT_APPROX_MASS_MIN_RHO:
min_rho, _max_rho = sim.multi_phase_model.get_density_range()
rho_for_M = dolfin.Constant(min_rho)
else:
rho_for_M = None
if rho_for_M is not None:
c1 = sim.data['time_coeffs'][0]
dt = sim.data['dt']
eqM = rho_for_M * c1 / dt * dolfin.dot(u, v) * dolfin.dx
matM, _vecM = split_form_into_matrix(eqM,
Vcoupled,
Vcoupled,
check_zeros=True)
self.eqM = dolfin.Form(matM[0, 0])
# The mass matrix without density
if self.make_unscaled_M:
u2 = dolfin.as_vector(dolfin.TrialFunction(self.Vuvw)[:])
v2 = dolfin.as_vector(dolfin.TestFunction(self.Vuvw)[:])
a = dolfin.dot(u2, v2) * dolfin.dx
Mus = assemble_into(a, None)
self.M_unscaled_inv = invert_block_diagonal_matrix(self.Vuvw, Mus)
def define_advection_equation(self):
"""
Setup the advection equation for the colour function
This implementation assembles the full LHS and RHS each time they are needed
"""
sim = self.simulation
mesh = sim.data['mesh']
n = dolfin.FacetNormal(mesh)
dS, dx = dolfin.dS(mesh), dolfin.dx(mesh)
# Trial and test functions
Vc = self.Vc
c = dolfin.TrialFunction(Vc)
d = dolfin.TestFunction(Vc)
c1, c2, c3 = self.time_coeffs
dt = self.dt
u_conv = self.u_conv
if not self.colour_is_discontinuous:
# Continous Galerkin implementation of the advection equation
# FIXME: add stabilization
eq = (c1 * c + c2 * self.cp + c3 * self.cpp) / dt * d * dx + div(
c * u_conv) * d * dx
elif self.velocity_is_trace:
# Upstream and downstream normal velocities
w_nU = (dot(u_conv, n) + abs(dot(u_conv, n))) / 2
w_nD = (dot(u_conv, n) - abs(dot(u_conv, n))) / 2
if self.beta is not None:
# Define the blended flux
# The blending factor beta is not DG, so beta('+') == beta('-')
b = self.beta('+')
flux = (1 - b) * jump(c * w_nU) + b * jump(c * w_nD)
else:
flux = jump(c * w_nU)
# Discontinuous Galerkin implementation of the advection equation
eq = (c1 * c + c2 * self.cp +
c3 * self.cpp) / dt * d * dx + flux * jump(d) * dS
# On each facet either w_nD or w_nU will be 0, the other is multiplied
# with the appropriate flux, either the value c going out of the domain
# or the Dirichlet value coming into the domain
for dbc in self.dirichlet_bcs:
eq += w_nD * dbc.func() * d * dbc.ds()
eq += w_nU * c * d * dbc.ds()
elif self.beta is not None:
# Upstream and downstream normal velocities
w_nU = (dot(u_conv, n) + abs(dot(u_conv, n))) / 2
w_nD = (dot(u_conv, n) - abs(dot(u_conv, n))) / 2
if self.beta is not None:
# Define the blended flux
# The blending factor beta is not DG, so beta('+') == beta('-')
b = self.beta('+')
flux = (1 - b) * jump(c * w_nU) + b * jump(c * w_nD)
else:
flux = jump(c * w_nU)
# Discontinuous Galerkin implementation of the advection equation
eq = ((c1 * c + c2 * self.cp + c3 * self.cpp) / dt * d * dx -
dot(c * u_conv, grad(d)) * dx + flux * jump(d) * dS)
# Enforce Dirichlet BCs weakly
for dbc in self.dirichlet_bcs:
eq += w_nD * dbc.func() * d * dbc.ds()
eq += w_nU * c * d * dbc.ds()
else:
# Downstream normal velocities
w_nD = (dot(u_conv, n) - abs(dot(u_conv, n))) / 2
# Discontinuous Galerkin implementation of the advection equation
eq = (c1 * c + c2 * self.cp + c3 * self.cpp) / dt * d * dx
# Convection integrated by parts two times to bring back the original
# div form (this means we must subtract and add all fluxes)
eq += div(c * u_conv) * d * dx
# Replace downwind flux with upwind flux on downwind internal facets
eq -= jump(w_nD * d) * jump(c) * dS
# Replace downwind flux with upwind BC flux on downwind external facets
for dbc in self.dirichlet_bcs:
# Subtract the "normal" downwind flux
eq -= w_nD * c * d * dbc.ds()
# Add the boundary value upwind flux
eq += w_nD * dbc.func() * d * dbc.ds()
# Penalty forcing zones
for fz in self.forcing_zones:
eq += fz.penalty * fz.beta * (c - fz.target) * d * dx
a, L = dolfin.system(eq)
self.form_lhs = dolfin.Form(a)
self.form_rhs = dolfin.Form(L)
self.tensor_lhs = None
self.tensor_rhs = None
