def setup(self, state):
if not self._initialised:
space = state.fields("theta").function_space()
broken_space = FunctionSpace(state.mesh, BrokenElement(space.ufl_element()))
boundary_method = Boundary_Method.physics if (state.vertical_degree == 0 and state.horizontal_degree == 0) else None
super().setup(state, space=space)
# now let's attach all of our fields
self.u = state.fields("u")
self.rho = state.fields("rho")
self.theta = state.fields("theta")
self.rho_averaged = Function(space)
self.recoverer = Recoverer(self.rho, self.rho_averaged, VDG=broken_space, boundary_method=boundary_method)
try:
self.r_v = state.fields("water_v")
except NotImplementedError:
self.r_v = Constant(0.0)
try:
self.r_c = state.fields("water_c")
except NotImplementedError:
self.r_c = Constant(0.0)
try:
self.rain = state.fields("rain")
except NotImplementedError:
self.rain = Constant(0.0)
# now let's store the most common expressions
self.pi = thermodynamics.pi(state.parameters, self.rho_averaged, self.theta)
self.T = thermodynamics.T(state.parameters, self.theta, self.pi, r_v=self.r_v)
self.p = thermodynamics.p(state.parameters, self.pi)
self.r_l = self.r_c + self.rain
self.r_t = self.r_v + self.r_c + self.rain
def _setup(self, state, field, options):
if options.name in ["embedded_dg", "recovered"]:
self.fs = options.embedding_space
self.xdg_in = Function(self.fs)
self.xdg_out = Function(self.fs)
self.x_projected = Function(field.function_space())
parameters = {'ksp_type': 'cg',
'pc_type': 'bjacobi',
'sub_pc_type': 'ilu'}
self.Projector = Projector(self.xdg_out, self.x_projected,
solver_parameters=parameters)
if options.name == "recovered":
# set up the necessary functions
self.x_in = Function(field.function_space())
x_rec = Function(options.recovered_space)
x_brok = Function(options.broken_space)
# set up interpolators and projectors
self.x_rec_projector = Recoverer(self.x_in, x_rec, VDG=self.fs, boundary_method=options.boundary_method) # recovered function
self.x_brok_projector = Projector(x_rec, x_brok) # function projected back
self.xdg_interpolator = Interpolator(self.x_in + x_rec - x_brok, self.xdg_in)
if self.limiter is not None:
self.x_brok_interpolator = Interpolator(self.xdg_out, x_brok)
self.x_out_projector = Recoverer(x_brok, self.x_projected)
class ThermodynamicDiagnostic(DiagnosticField):
name = "thermodynamic_diagnostic"
def setup(self, state):
if not self._initialised:
space = state.fields("theta").function_space()
broken_space = FunctionSpace(state.mesh,
BrokenElement(space.ufl_element()))
h_deg = space.ufl_element().degree()[0]
v_deg = space.ufl_element().degree()[1] - 1
boundary_method = Boundary_Method.physics if (
v_deg == 0 and h_deg == 0) else None
super().setup(state, space=space)
# now let's attach all of our fields
self.u = state.fields("u")
self.rho = state.fields("rho")
self.theta = state.fields("theta")
self.rho_averaged = Function(space)
self.recoverer = Recoverer(self.rho,
self.rho_averaged,
VDG=broken_space,
boundary_method=boundary_method)
try:
self.r_v = state.fields("vapour_mixing_ratio")
except NotImplementedError:
self.r_v = Constant(0.0)
try:
self.r_c = state.fields("cloud_liquid_mixing_ratio")
except NotImplementedError:
self.r_c = Constant(0.0)
try:
self.rain = state.fields("rain_mixing_ratio")
except NotImplementedError:
self.rain = Constant(0.0)
# now let's store the most common expressions
self.exner = thermodynamics.exner_pressure(state.parameters,
self.rho_averaged,
self.theta)
self.T = thermodynamics.T(state.parameters,
self.theta,
self.exner,
r_v=self.r_v)
self.p = thermodynamics.p(state.parameters, self.exner)
self.r_l = self.r_c + self.rain
self.r_t = self.r_v + self.r_c + self.rain
def compute(self, state):
self.recoverer.project()
def unsaturated_hydrostatic_balance(state,
theta_d,
H,
exner0=None,
top=False,
exner_boundary=Constant(1.0),
max_outer_solve_count=40,
max_inner_solve_count=20):
"""
Given vertical profiles for dry potential temperature
and relative humidity compute hydrostatically balanced
virtual potential temperature, dry density and water vapour profiles.
The general strategy is to split up the solving into two steps:
1) finding rho to balance the theta profile
2) finding theta_v and r_v to get back theta_d and H
We iteratively solve these steps until we (hopefully)
converge to a solution.
:arg state: The :class:`State` object.
:arg theta_d: The initial dry potential temperature profile.
:arg H: The relative humidity profile.
:arg exner0: Optional function to put exner pressure into.
:arg top: If True, set a boundary condition at the top, otherwise
it will be at the bottom.
:arg exner_boundary: The value of exner on the specified boundary.
:arg max_outer_solve_count: Max number of iterations for outer loop of balance solver.
:arg max_inner_solve_count: Max number of iterations for inner loop of balanace solver.
"""
theta0 = state.fields('theta')
rho0 = state.fields('rho')
mr_v0 = state.fields('vapour_mixing_ratio')
# Calculate hydrostatic exner pressure
Vt = theta0.function_space()
Vr = rho0.function_space()
R_d = state.parameters.R_d
R_v = state.parameters.R_v
epsilon = R_d / R_v
VDG = state.spaces("DG")
if any(deg > 2 for deg in VDG.ufl_element().degree()):
logger.warning(
"default quadrature degree most likely not sufficient for this degree element"
)
# apply first guesses
theta0.assign(theta_d * 1.01)
mr_v0.assign(0.01)
v_deg = Vr.ufl_element().degree()[1]
if v_deg == 0:
method = Boundary_Method.physics
else:
method = None
rho_h = Function(Vr)
rho_averaged = Function(Vt)
Vt_broken = FunctionSpace(state.mesh, BrokenElement(Vt.ufl_element()))
rho_recoverer = Recoverer(rho0,
rho_averaged,
VDG=Vt_broken,
boundary_method=method)
w_h = Function(Vt)
delta = 1.0
# make expressions for determining mr_v0
exner = thermodynamics.exner_pressure(state.parameters, rho_averaged,
theta0)
p = thermodynamics.p(state.parameters, exner)
T = thermodynamics.T(state.parameters, theta0, exner, mr_v0)
r_v_expr = thermodynamics.r_v(state.parameters, H, T, p)
# make expressions to evaluate residual
exner_ev = thermodynamics.exner_pressure(state.parameters, rho_averaged,
theta0)
p_ev = thermodynamics.p(state.parameters, exner_ev)
T_ev = thermodynamics.T(state.parameters, theta0, exner_ev, mr_v0)
RH_ev = thermodynamics.RH(state.parameters, mr_v0, T_ev, p_ev)
RH = Function(Vt)
for i in range(max_outer_solve_count):
# solve for rho with theta_vd and w_v guesses
compressible_hydrostatic_balance(state,
theta0,
rho_h,
top=top,
exner_boundary=exner_boundary,
mr_t=mr_v0,
solve_for_rho=True)
# damp solution
rho0.assign(rho0 * (1 - delta) + delta * rho_h)
# calculate averaged rho
rho_recoverer.project()
RH.assign(RH_ev)
if errornorm(RH, H) < 1e-10:
break
# now solve for r_v
for j in range(max_inner_solve_count):
w_h.interpolate(r_v_expr)
mr_v0.assign(mr_v0 * (1 - delta) + delta * w_h)
# compute theta_vd
theta0.assign(theta_d * (1 + mr_v0 / epsilon))
# test quality of solution by re-evaluating expression
RH.assign(RH_ev)
if errornorm(RH, H) < 1e-10:
break
if i == max_outer_solve_count:
raise RuntimeError(
'Hydrostatic balance solve has not converged within %i' % i,
'iterations')
if exner0 is not None:
exner = thermodynamics.exner_pressure(state.parameters, rho0, theta0)
exner0.interpolate(exner)
# do one extra solve for rho
compressible_hydrostatic_balance(state,
theta0,
rho0,
top=top,
exner_boundary=exner_boundary,
mr_t=mr_v0,
solve_for_rho=True)
def saturated_hydrostatic_balance(state,
theta_e,
mr_t,
exner0=None,
top=False,
exner_boundary=Constant(1.0),
max_outer_solve_count=40,
max_theta_solve_count=5,
max_inner_solve_count=3):
"""
Given a wet equivalent potential temperature, theta_e, and the total moisture
content, mr_t, compute a hydrostatically balance virtual potential temperature,
dry density and water vapour profile.
The general strategy is to split up the solving into two steps:
1) finding rho to balance the theta profile
2) finding theta_v and r_v to get back theta_e and saturation
We iteratively solve these steps until we (hopefully)
converge to a solution.
:arg state: The :class:`State` object.
:arg theta_e: The initial wet equivalent potential temperature profile.
:arg mr_t: The total water pseudo-mixing ratio profile.
:arg exner0: Optional function to put exner pressure into.
:arg top: If True, set a boundary condition at the top, otherwise
it will be at the bottom.
:arg exner_boundary: The value of exner on the specified boundary.
:arg max_outer_solve_count: Max number of outer iterations for balance solver.
:arg max_theta_solve_count: Max number of iterations for theta solver (middle part of solve).
:arg max_inner_solve_count: Max number of iterations on the inner most
loop for the water vapour solver.
"""
theta0 = state.fields('theta')
rho0 = state.fields('rho')
mr_v0 = state.fields('vapour_mixing_ratio')
# Calculate hydrostatic exner pressure
Vt = theta0.function_space()
Vr = rho0.function_space()
VDG = state.spaces("DG")
if any(deg > 2 for deg in VDG.ufl_element().degree()):
logger.warning(
"default quadrature degree most likely not sufficient for this degree element"
)
theta0.interpolate(theta_e)
mr_v0.interpolate(mr_t)
v_deg = Vr.ufl_element().degree()[1]
if v_deg == 0:
boundary_method = Boundary_Method.physics
else:
boundary_method = None
rho_h = Function(Vr)
Vt_broken = FunctionSpace(state.mesh, BrokenElement(Vt.ufl_element()))
rho_averaged = Function(Vt)
rho_recoverer = Recoverer(rho0,
rho_averaged,
VDG=Vt_broken,
boundary_method=boundary_method)
w_h = Function(Vt)
theta_h = Function(Vt)
theta_e_test = Function(Vt)
delta = 0.8
# expressions for finding theta0 and mr_v0 from theta_e and mr_t
exner = thermodynamics.exner_pressure(state.parameters, rho_averaged,
theta0)
p = thermodynamics.p(state.parameters, exner)
T = thermodynamics.T(state.parameters, theta0, exner, mr_v0)
r_v_expr = thermodynamics.r_sat(state.parameters, T, p)
theta_e_expr = thermodynamics.theta_e(state.parameters, T, p, mr_v0, mr_t)
for i in range(max_outer_solve_count):
# solve for rho with theta_vd and w_v guesses
compressible_hydrostatic_balance(state,
theta0,
rho_h,
top=top,
exner_boundary=exner_boundary,
mr_t=mr_t,
solve_for_rho=True)
# damp solution
rho0.assign(rho0 * (1 - delta) + delta * rho_h)
theta_e_test.assign(theta_e_expr)
if errornorm(theta_e_test, theta_e) < 1e-8:
break
# calculate averaged rho
rho_recoverer.project()
# now solve for r_v
for j in range(max_theta_solve_count):
theta_h.interpolate(theta_e / theta_e_expr * theta0)
theta0.assign(theta0 * (1 - delta) + delta * theta_h)
# break when close enough
if errornorm(theta_e_test, theta_e) < 1e-6:
break
for k in range(max_inner_solve_count):
w_h.interpolate(r_v_expr)
mr_v0.assign(mr_v0 * (1 - delta) + delta * w_h)
# break when close enough
theta_e_test.assign(theta_e_expr)
if errornorm(theta_e_test, theta_e) < 1e-6:
break
if i == max_outer_solve_count:
raise RuntimeError(
'Hydrostatic balance solve has not converged within %i' % i,
'iterations')
if exner0 is not None:
exner = thermodynamics.exner(state.parameters, rho0, theta0)
exner0.interpolate(exner)
# do one extra solve for rho
compressible_hydrostatic_balance(state,
theta0,
rho0,
top=top,
exner_boundary=exner_boundary,
mr_t=mr_t,
solve_for_rho=True)
def __init__(self, state, iterations=1):
super().__init__(state)
self.iterations = iterations
# obtain our fields
self.theta = state.fields('theta')
self.water_v = state.fields('water_v')
self.water_c = state.fields('water_c')
rho = state.fields('rho')
try:
rain = state.fields('rain')
water_l = self.water_c + rain
except NotImplementedError:
water_l = self.water_c
# declare function space
Vt = self.theta.function_space()
# make rho variables
# we recover rho into theta space
if state.vertical_degree == 0 and state.horizontal_degree == 0:
boundary_method = Boundary_Method.physics
else:
boundary_method = None
Vt_broken = FunctionSpace(state.mesh, BrokenElement(Vt.ufl_element()))
rho_averaged = Function(Vt)
self.rho_recoverer = Recoverer(rho,
rho_averaged,
VDG=Vt_broken,
boundary_method=boundary_method)
# define some parameters as attributes
dt = state.timestepping.dt
R_d = state.parameters.R_d
cp = state.parameters.cp
cv = state.parameters.cv
c_pv = state.parameters.c_pv
c_pl = state.parameters.c_pl
c_vv = state.parameters.c_vv
R_v = state.parameters.R_v
# make useful fields
Pi = thermodynamics.pi(state.parameters, rho_averaged, self.theta)
T = thermodynamics.T(state.parameters,
self.theta,
Pi,
r_v=self.water_v)
p = thermodynamics.p(state.parameters, Pi)
L_v = thermodynamics.Lv(state.parameters, T)
R_m = R_d + R_v * self.water_v
c_pml = cp + c_pv * self.water_v + c_pl * water_l
c_vml = cv + c_vv * self.water_v + c_pl * water_l
# use Teten's formula to calculate w_sat
w_sat = thermodynamics.r_sat(state.parameters, T, p)
# make appropriate condensation rate
dot_r_cond = ((self.water_v - w_sat) / (dt * (1.0 +
((L_v**2.0 * w_sat) /
(cp * R_v * T**2.0)))))
# make cond_rate function, that needs to be the same for all updates in one time step
cond_rate = Function(Vt)
# adjust cond rate so negative concentrations don't occur
self.lim_cond_rate = Interpolator(
conditional(dot_r_cond < 0,
max_value(dot_r_cond, -self.water_c / dt),
min_value(dot_r_cond, self.water_v / dt)), cond_rate)
# tell the prognostic fields what to update to
self.water_v_new = Interpolator(self.water_v - dt * cond_rate, Vt)
self.water_c_new = Interpolator(self.water_c + dt * cond_rate, Vt)
self.theta_new = Interpolator(
self.theta * (1.0 + dt * cond_rate *
(cv * L_v / (c_vml * cp * T) - R_v * cv * c_pml /
(R_m * cp * c_vml))), Vt)
class Advection(object, metaclass=ABCMeta):
"""
Base class for advection schemes.
:arg state: :class:`.State` object.
:arg field: field to be advected
:arg equation: :class:`.Equation` object, specifying the equation
that field satisfies
:arg solver_parameters: solver_parameters
:arg limiter: :class:`.Limiter` object.
:arg options: :class:`.AdvectionOptions` object
"""
def __init__(self, state, field, equation=None, *, solver_parameters=None,
limiter=None):
if equation is not None:
self.state = state
self.field = field
self.equation = equation
# get ubar from the equation class
self.ubar = self.equation.ubar
self.dt = self.state.timestepping.dt
# get default solver options if none passed in
if solver_parameters is None:
self.solver_parameters = equation.solver_parameters
else:
self.solver_parameters = solver_parameters
if logger.isEnabledFor(DEBUG):
self.solver_parameters["ksp_monitor_true_residual"] = True
self.limiter = limiter
if hasattr(equation, "options"):
self.discretisation_option = equation.options.name
self._setup(state, field, equation.options)
else:
self.discretisation_option = None
self.fs = field.function_space()
# setup required functions
self.dq = Function(self.fs)
self.q1 = Function(self.fs)
def _setup(self, state, field, options):
if options.name in ["embedded_dg", "recovered"]:
self.fs = options.embedding_space
self.xdg_in = Function(self.fs)
self.xdg_out = Function(self.fs)
self.x_projected = Function(field.function_space())
parameters = {'ksp_type': 'cg',
'pc_type': 'bjacobi',
'sub_pc_type': 'ilu'}
self.Projector = Projector(self.xdg_out, self.x_projected,
solver_parameters=parameters)
if options.name == "recovered":
# set up the necessary functions
self.x_in = Function(field.function_space())
x_rec = Function(options.recovered_space)
x_brok = Function(options.broken_space)
# set up interpolators and projectors
self.x_rec_projector = Recoverer(self.x_in, x_rec, VDG=self.fs, boundary_method=options.boundary_method) # recovered function
self.x_brok_projector = Projector(x_rec, x_brok) # function projected back
self.xdg_interpolator = Interpolator(self.x_in + x_rec - x_brok, self.xdg_in)
if self.limiter is not None:
self.x_brok_interpolator = Interpolator(self.xdg_out, x_brok)
self.x_out_projector = Recoverer(x_brok, self.x_projected)
def pre_apply(self, x_in, discretisation_option):
"""
Extra steps to advection if using an embedded method,
which might be either the plain embedded method or the
recovered space advection scheme.
:arg x_in: the input set of prognostic fields.
:arg discretisation option: string specifying which scheme to use.
"""
if discretisation_option == "embedded_dg":
try:
self.xdg_in.interpolate(x_in)
except NotImplementedError:
self.xdg_in.project(x_in)
elif discretisation_option == "recovered":
self.x_in.assign(x_in)
self.x_rec_projector.project()
self.x_brok_projector.project()
self.xdg_interpolator.interpolate()
def post_apply(self, x_out, discretisation_option):
"""
The projection steps, returning a field to its original space
for an embedded DG advection scheme. For the case of the
recovered scheme, there are two options dependent on whether
the scheme is limited or not.
:arg x_out: the outgoing field.
:arg discretisation_option: string specifying which option to use.
"""
if discretisation_option == "embedded_dg":
self.Projector.project()
elif discretisation_option == "recovered":
if self.limiter is not None:
self.x_brok_interpolator.interpolate()
self.x_out_projector.project()
else:
self.Projector.project()
x_out.assign(self.x_projected)
@abstractproperty
def lhs(self):
return self.equation.mass_term(self.equation.trial)
@abstractproperty
def rhs(self):
return self.equation.mass_term(self.q1) - self.dt*self.equation.advection_term(self.q1)
def update_ubar(self, xn, xnp1, alpha):
un = xn.split()[0]
unp1 = xnp1.split()[0]
self.ubar.assign(un + alpha*(unp1-un))
@cached_property
def solver(self):
# setup solver using lhs and rhs defined in derived class
problem = LinearVariationalProblem(self.lhs, self.rhs, self.dq)
solver_name = self.field.name()+self.equation.__class__.__name__+self.__class__.__name__
return LinearVariationalSolver(problem, solver_parameters=self.solver_parameters, options_prefix=solver_name)
@abstractmethod
def apply(self, x_in, x_out):
"""
Function takes x as input, computes L(x) as defined by the equation,
and returns x_out as output.
:arg x: :class:`.Function` object, the input Function.
:arg x_out: :class:`.Function` object, the output Function.
"""
pass
def __init__(self, state):
super().__init__(state)
# obtain our fields
self.theta = state.fields('theta')
self.water_v = state.fields('water_v')
self.rain = state.fields('rain')
rho = state.fields('rho')
try:
water_c = state.fields('water_c')
water_l = self.rain + water_c
except NotImplementedError:
water_l = self.rain
# declare function space
Vt = self.theta.function_space()
# make rho variables
# we recover rho into theta space
if state.vertical_degree == 0 and state.horizontal_degree == 0:
boundary_method = Boundary_Method.physics
else:
boundary_method = None
Vt_broken = FunctionSpace(state.mesh, BrokenElement(Vt.ufl_element()))
rho_averaged = Function(Vt)
self.rho_recoverer = Recoverer(rho,
rho_averaged,
VDG=Vt_broken,
boundary_method=boundary_method)
# define some parameters as attributes
dt = state.timestepping.dt
R_d = state.parameters.R_d
cp = state.parameters.cp
cv = state.parameters.cv
c_pv = state.parameters.c_pv
c_pl = state.parameters.c_pl
c_vv = state.parameters.c_vv
R_v = state.parameters.R_v
# make useful fields
Pi = thermodynamics.pi(state.parameters, rho_averaged, self.theta)
T = thermodynamics.T(state.parameters,
self.theta,
Pi,
r_v=self.water_v)
p = thermodynamics.p(state.parameters, Pi)
L_v = thermodynamics.Lv(state.parameters, T)
R_m = R_d + R_v * self.water_v
c_pml = cp + c_pv * self.water_v + c_pl * water_l
c_vml = cv + c_vv * self.water_v + c_pl * water_l
# use Teten's formula to calculate w_sat
w_sat = thermodynamics.r_sat(state.parameters, T, p)
# expression for ventilation factor
a = Constant(1.6)
b = Constant(124.9)
c = Constant(0.2046)
C = a + b * (rho_averaged * self.rain)**c
# make appropriate condensation rate
f = Constant(5.4e5)
g = Constant(2.55e6)
h = Constant(0.525)
dot_r_evap = (((1 - self.water_v / w_sat) * C *
(rho_averaged * self.rain)**h) /
(rho_averaged * (f + g / (p * w_sat))))
# make evap_rate function, needs to be the same for all updates in one time step
evap_rate = Function(Vt)
# adjust evap rate so negative rain doesn't occur
self.lim_evap_rate = Interpolator(
conditional(
dot_r_evap < 0, 0.0,
conditional(self.rain < 0.0, 0.0,
min_value(dot_r_evap, self.rain / dt))), evap_rate)
# tell the prognostic fields what to update to
self.water_v_new = Interpolator(self.water_v + dt * evap_rate, Vt)
self.rain_new = Interpolator(self.rain - dt * evap_rate, Vt)
self.theta_new = Interpolator(
self.theta * (1.0 - dt * evap_rate *
(cv * L_v / (c_vml * cp * T) - R_v * cv * c_pml /
(R_m * cp * c_vml))), Vt)
def setup(self, equation, uadv=None, apply_bcs=True, *active_labels):
self.residual = equation.residual
if self.field_name is not None:
self.idx = equation.field_names.index(self.field_name)
self.fs = self.state.fields(self.field_name).function_space()
self.residual = self.residual.label_map(
lambda t: t.get(prognostic) == self.field_name,
lambda t: Term(
split_form(t.form)[self.idx].form,
t.labels),
drop)
bcs = equation.bcs[self.field_name]
else:
self.field_name = equation.field_name
self.fs = equation.function_space
self.idx = None
if type(self.fs.ufl_element()) is MixedElement:
bcs = [bc for _, bcs in equation.bcs.items() for bc in bcs]
else:
bcs = equation.bcs[self.field_name]
if len(active_labels) > 0:
self.residual = self.residual.label_map(
lambda t: any(t.has_label(time_derivative, *active_labels)),
map_if_false=drop)
options = self.options
# -------------------------------------------------------------------- #
# Routines relating to transport
# -------------------------------------------------------------------- #
if hasattr(self.options, 'ibp'):
self.replace_transport_term()
self.replace_transporting_velocity(uadv)
# -------------------------------------------------------------------- #
# Wrappers for embedded / recovery methods
# -------------------------------------------------------------------- #
if self.discretisation_option in ["embedded_dg", "recovered"]:
# construct the embedding space if not specified
if options.embedding_space is None:
V_elt = BrokenElement(self.fs.ufl_element())
self.fs = FunctionSpace(self.state.mesh, V_elt)
else:
self.fs = options.embedding_space
self.xdg_in = Function(self.fs)
self.xdg_out = Function(self.fs)
if self.idx is None:
self.x_projected = Function(equation.function_space)
else:
self.x_projected = Function(self.state.fields(self.field_name).function_space())
new_test = TestFunction(self.fs)
parameters = {'ksp_type': 'cg',
'pc_type': 'bjacobi',
'sub_pc_type': 'ilu'}
# -------------------------------------------------------------------- #
# Make boundary conditions
# -------------------------------------------------------------------- #
if not apply_bcs:
self.bcs = None
elif self.discretisation_option in ["embedded_dg", "recovered"]:
# Transfer boundary conditions onto test function space
self.bcs = [DirichletBC(self.fs, bc.function_arg, bc.sub_domain) for bc in bcs]
else:
self.bcs = bcs
# -------------------------------------------------------------------- #
# Modify test function for SUPG methods
# -------------------------------------------------------------------- #
if self.discretisation_option == "supg":
# construct tau, if it is not specified
dim = self.state.mesh.topological_dimension()
if options.tau is not None:
# if tau is provided, check that is has the right size
tau = options.tau
assert as_ufl(tau).ufl_shape == (dim, dim), "Provided tau has incorrect shape!"
else:
# create tuple of default values of size dim
default_vals = [options.default*self.dt]*dim
# check for directions is which the space is discontinuous
# so that we don't apply supg in that direction
if is_cg(self.fs):
vals = default_vals
else:
space = self.fs.ufl_element().sobolev_space()
if space.name in ["HDiv", "DirectionalH"]:
vals = [default_vals[i] if space[i].name == "H1"
else 0. for i in range(dim)]
else:
raise ValueError("I don't know what to do with space %s" % space)
tau = Constant(tuple([
tuple(
[vals[j] if i == j else 0. for i, v in enumerate(vals)]
) for j in range(dim)])
)
self.solver_parameters = {'ksp_type': 'gmres',
'pc_type': 'bjacobi',
'sub_pc_type': 'ilu'}
test = TestFunction(self.fs)
new_test = test + dot(dot(uadv, tau), grad(test))
if self.discretisation_option is not None:
# replace the original test function with one defined on
# the embedding space, as this is the space where the
# the problem will be solved
self.residual = self.residual.label_map(
all_terms,
map_if_true=replace_test_function(new_test))
if self.discretisation_option == "embedded_dg":
if self.limiter is None:
self.x_out_projector = Projector(self.xdg_out, self.x_projected,
solver_parameters=parameters)
else:
self.x_out_projector = Recoverer(self.xdg_out, self.x_projected)
if self.discretisation_option == "recovered":
# set up the necessary functions
self.x_in = Function(self.state.fields(self.field_name).function_space())
x_rec = Function(options.recovered_space)
x_brok = Function(options.broken_space)
# set up interpolators and projectors
self.x_rec_projector = Recoverer(self.x_in, x_rec, VDG=self.fs, boundary_method=options.boundary_method) # recovered function
self.x_brok_projector = Projector(x_rec, x_brok) # function projected back
self.xdg_interpolator = Interpolator(self.x_in + x_rec - x_brok, self.xdg_in)
if self.limiter is not None:
self.x_brok_interpolator = Interpolator(self.xdg_out, x_brok)
self.x_out_projector = Recoverer(x_brok, self.x_projected)
else:
self.x_out_projector = Projector(self.xdg_out, self.x_projected)
# setup required functions
self.dq = Function(self.fs)
self.q1 = Function(self.fs)
class TimeDiscretisation(object, metaclass=ABCMeta):
"""
Base class for time discretisation schemes.
:arg state: :class:`.State` object.
:arg field: field to be evolved
:arg equation: :class:`.Equation` object, specifying the equation
that field satisfies
:arg solver_parameters: solver_parameters
:arg limiter: :class:`.Limiter` object.
:arg options: :class:`.DiscretisationOptions` object
"""
def __init__(self, state, field_name=None, solver_parameters=None,
limiter=None, options=None):
self.state = state
self.field_name = field_name
self.dt = self.state.dt
self.limiter = limiter
self.options = options
if options is not None:
self.discretisation_option = options.name
else:
self.discretisation_option = None
# get default solver options if none passed in
if solver_parameters is None:
self.solver_parameters = {'ksp_type': 'cg',
'pc_type': 'bjacobi',
'sub_pc_type': 'ilu'}
else:
self.solver_parameters = solver_parameters
if logger.isEnabledFor(DEBUG):
self.solver_parameters["ksp_monitor_true_residual"] = None
def setup(self, equation, uadv=None, apply_bcs=True, *active_labels):
self.residual = equation.residual
if self.field_name is not None:
self.idx = equation.field_names.index(self.field_name)
self.fs = self.state.fields(self.field_name).function_space()
self.residual = self.residual.label_map(
lambda t: t.get(prognostic) == self.field_name,
lambda t: Term(
split_form(t.form)[self.idx].form,
t.labels),
drop)
bcs = equation.bcs[self.field_name]
else:
self.field_name = equation.field_name
self.fs = equation.function_space
self.idx = None
if type(self.fs.ufl_element()) is MixedElement:
bcs = [bc for _, bcs in equation.bcs.items() for bc in bcs]
else:
bcs = equation.bcs[self.field_name]
if len(active_labels) > 0:
self.residual = self.residual.label_map(
lambda t: any(t.has_label(time_derivative, *active_labels)),
map_if_false=drop)
options = self.options
# -------------------------------------------------------------------- #
# Routines relating to transport
# -------------------------------------------------------------------- #
if hasattr(self.options, 'ibp'):
self.replace_transport_term()
self.replace_transporting_velocity(uadv)
# -------------------------------------------------------------------- #
# Wrappers for embedded / recovery methods
# -------------------------------------------------------------------- #
if self.discretisation_option in ["embedded_dg", "recovered"]:
# construct the embedding space if not specified
if options.embedding_space is None:
V_elt = BrokenElement(self.fs.ufl_element())
self.fs = FunctionSpace(self.state.mesh, V_elt)
else:
self.fs = options.embedding_space
self.xdg_in = Function(self.fs)
self.xdg_out = Function(self.fs)
if self.idx is None:
self.x_projected = Function(equation.function_space)
else:
self.x_projected = Function(self.state.fields(self.field_name).function_space())
new_test = TestFunction(self.fs)
parameters = {'ksp_type': 'cg',
'pc_type': 'bjacobi',
'sub_pc_type': 'ilu'}
# -------------------------------------------------------------------- #
# Make boundary conditions
# -------------------------------------------------------------------- #
if not apply_bcs:
self.bcs = None
elif self.discretisation_option in ["embedded_dg", "recovered"]:
# Transfer boundary conditions onto test function space
self.bcs = [DirichletBC(self.fs, bc.function_arg, bc.sub_domain) for bc in bcs]
else:
self.bcs = bcs
# -------------------------------------------------------------------- #
# Modify test function for SUPG methods
# -------------------------------------------------------------------- #
if self.discretisation_option == "supg":
# construct tau, if it is not specified
dim = self.state.mesh.topological_dimension()
if options.tau is not None:
# if tau is provided, check that is has the right size
tau = options.tau
assert as_ufl(tau).ufl_shape == (dim, dim), "Provided tau has incorrect shape!"
else:
# create tuple of default values of size dim
default_vals = [options.default*self.dt]*dim
# check for directions is which the space is discontinuous
# so that we don't apply supg in that direction
if is_cg(self.fs):
vals = default_vals
else:
space = self.fs.ufl_element().sobolev_space()
if space.name in ["HDiv", "DirectionalH"]:
vals = [default_vals[i] if space[i].name == "H1"
else 0. for i in range(dim)]
else:
raise ValueError("I don't know what to do with space %s" % space)
tau = Constant(tuple([
tuple(
[vals[j] if i == j else 0. for i, v in enumerate(vals)]
) for j in range(dim)])
)
self.solver_parameters = {'ksp_type': 'gmres',
'pc_type': 'bjacobi',
'sub_pc_type': 'ilu'}
test = TestFunction(self.fs)
new_test = test + dot(dot(uadv, tau), grad(test))
if self.discretisation_option is not None:
# replace the original test function with one defined on
# the embedding space, as this is the space where the
# the problem will be solved
self.residual = self.residual.label_map(
all_terms,
map_if_true=replace_test_function(new_test))
if self.discretisation_option == "embedded_dg":
if self.limiter is None:
self.x_out_projector = Projector(self.xdg_out, self.x_projected,
solver_parameters=parameters)
else:
self.x_out_projector = Recoverer(self.xdg_out, self.x_projected)
if self.discretisation_option == "recovered":
# set up the necessary functions
self.x_in = Function(self.state.fields(self.field_name).function_space())
x_rec = Function(options.recovered_space)
x_brok = Function(options.broken_space)
# set up interpolators and projectors
self.x_rec_projector = Recoverer(self.x_in, x_rec, VDG=self.fs, boundary_method=options.boundary_method) # recovered function
self.x_brok_projector = Projector(x_rec, x_brok) # function projected back
self.xdg_interpolator = Interpolator(self.x_in + x_rec - x_brok, self.xdg_in)
if self.limiter is not None:
self.x_brok_interpolator = Interpolator(self.xdg_out, x_brok)
self.x_out_projector = Recoverer(x_brok, self.x_projected)
else:
self.x_out_projector = Projector(self.xdg_out, self.x_projected)
# setup required functions
self.dq = Function(self.fs)
self.q1 = Function(self.fs)
def pre_apply(self, x_in, discretisation_option):
"""
Extra steps to discretisation if using an embedded method,
which might be either the plain embedded method or the
recovered space scheme.
:arg x_in: the input set of prognostic fields.
:arg discretisation option: string specifying which scheme to use.
"""
if discretisation_option == "embedded_dg":
try:
self.xdg_in.interpolate(x_in)
except NotImplementedError:
self.xdg_in.project(x_in)
elif discretisation_option == "recovered":
self.x_in.assign(x_in)
self.x_rec_projector.project()
self.x_brok_projector.project()
self.xdg_interpolator.interpolate()
def post_apply(self, x_out, discretisation_option):
"""
The projection steps, returning a field to its original space
for an embedded DG scheme. For the case of the
recovered scheme, there are two options dependent on whether
the scheme is limited or not.
:arg x_out: the outgoing field.
:arg discretisation_option: string specifying which option to use.
"""
if discretisation_option == "recovered" and self.limiter is not None:
self.x_brok_interpolator.interpolate()
self.x_out_projector.project()
x_out.assign(self.x_projected)
@abstractproperty
def lhs(self):
l = self.residual.label_map(
lambda t: t.has_label(time_derivative),
map_if_true=replace_subject(self.dq, self.idx),
map_if_false=drop)
return l.form
@abstractproperty
def rhs(self):
r = self.residual.label_map(
all_terms,
map_if_true=replace_subject(self.q1, self.idx))
r = r.label_map(
lambda t: t.has_label(time_derivative),
map_if_false=lambda t: -self.dt*t)
return r.form
def replace_transport_term(self):
"""
This routine allows the default transport term to be replaced with a
different one, specified through the transport options.
This is necessary because when the prognostic equations are declared,
the whole transport
"""
# Extract transport term of equation
old_transport_term_list = self.residual.label_map(
lambda t: t.has_label(transport), map_if_false=drop)
# If there are more transport terms, extract only the one for this variable
if len(old_transport_term_list.terms) > 1:
raise NotImplementedError('Cannot replace transport terms when there are more than one')
# Then we should only have one transport term
old_transport_term = old_transport_term_list.terms[0]
# If the transport term has an ibp label, then it could be replaced
if old_transport_term.has_label(ibp_label) and hasattr(self.options, 'ibp'):
# Do the options specify a different ibp to the old transport term?
if old_transport_term.labels['ibp'] != self.options.ibp:
# Set up a new transport term
field = self.state.fields(self.field_name)
test = TestFunction(self.fs)
# Set up new transport term (depending on the type of transport equation)
if old_transport_term.labels['transport'] == TransportEquationType.advective:
new_transport_term = advection_form(self.state, test, field, ibp=self.options.ibp)
elif old_transport_term.labels['transport'] == TransportEquationType.conservative:
new_transport_term = continuity_form(self.state, test, field, ibp=self.options.ibp)
else:
raise NotImplementedError(f'Replacement of transport term not implemented yet for {old_transport_term.labels["transport"]}')
# Finally, drop the old transport term and add the new one
self.residual = self.residual.label_map(
lambda t: t.has_label(transport), map_if_true=drop)
self.residual += subject(new_transport_term, field)
def replace_transporting_velocity(self, uadv):
# replace the transporting velocity in any terms that contain it
if any([t.has_label(transporting_velocity) for t in self.residual]):
assert uadv is not None
if uadv == "prognostic":
self.residual = self.residual.label_map(
lambda t: t.has_label(transporting_velocity),
map_if_true=lambda t: Term(ufl.replace(
t.form, {t.get(transporting_velocity): split(t.get(subject))[0]}), t.labels)
)
else:
self.residual = self.residual.label_map(
lambda t: t.has_label(transporting_velocity),
map_if_true=lambda t: Term(ufl.replace(
t.form, {t.get(transporting_velocity): uadv}), t.labels)
)
self.residual = transporting_velocity.update_value(self.residual, uadv)
@cached_property
def solver(self):
# setup solver using lhs and rhs defined in derived class
problem = NonlinearVariationalProblem(self.lhs-self.rhs, self.dq, bcs=self.bcs)
solver_name = self.field_name+self.__class__.__name__
return NonlinearVariationalSolver(problem, solver_parameters=self.solver_parameters, options_prefix=solver_name)
@abstractmethod
def apply(self, x_in, x_out):
"""
Function takes x as input, computes L(x) as defined by the equation,
and returns x_out as output.
:arg x: :class:`.Function` object, the input Function.
:arg x_out: :class:`.Function` object, the output Function.
"""
pass
class Condensation(Physics):
"""
The process of condensation of water vapour
into liquid water and evaporation of liquid
water into water vapour, with the associated
latent heat changes. The parametrization follows
that used in Bryan and Fritsch (2002).
:arg state: :class:`.State.` object.
:arg iterations: number of iterations to do
of condensation scheme per time step.
"""
def __init__(self, state, iterations=1):
super().__init__(state)
self.iterations = iterations
# obtain our fields
self.theta = state.fields('theta')
self.water_v = state.fields('vapour_mixing_ratio')
self.water_c = state.fields('cloud_liquid_mixing_ratio')
rho = state.fields('rho')
try:
# TODO: use the phase flag for the tracers here
rain = state.fields('rain_mixing_ratio')
water_l = self.water_c + rain
except NotImplementedError:
water_l = self.water_c
# declare function space
Vt = self.theta.function_space()
# make rho variables
# we recover rho into theta space
h_deg = rho.function_space().ufl_element().degree()[0]
v_deg = rho.function_space().ufl_element().degree()[1]
if v_deg == 0 and h_deg == 0:
boundary_method = Boundary_Method.physics
else:
boundary_method = None
Vt_broken = FunctionSpace(state.mesh, BrokenElement(Vt.ufl_element()))
rho_averaged = Function(Vt)
self.rho_recoverer = Recoverer(rho, rho_averaged, VDG=Vt_broken, boundary_method=boundary_method)
# define some parameters as attributes
dt = state.dt
R_d = state.parameters.R_d
cp = state.parameters.cp
cv = state.parameters.cv
c_pv = state.parameters.c_pv
c_pl = state.parameters.c_pl
c_vv = state.parameters.c_vv
R_v = state.parameters.R_v
# make useful fields
exner = thermodynamics.exner_pressure(state.parameters, rho_averaged, self.theta)
T = thermodynamics.T(state.parameters, self.theta, exner, r_v=self.water_v)
p = thermodynamics.p(state.parameters, exner)
L_v = thermodynamics.Lv(state.parameters, T)
R_m = R_d + R_v * self.water_v
c_pml = cp + c_pv * self.water_v + c_pl * water_l
c_vml = cv + c_vv * self.water_v + c_pl * water_l
# use Teten's formula to calculate w_sat
w_sat = thermodynamics.r_sat(state.parameters, T, p)
# make appropriate condensation rate
dot_r_cond = ((self.water_v - w_sat)
/ (dt * (1.0 + ((L_v ** 2.0 * w_sat)
/ (cp * R_v * T ** 2.0)))))
# make cond_rate function, that needs to be the same for all updates in one time step
cond_rate = Function(Vt)
# adjust cond rate so negative concentrations don't occur
self.lim_cond_rate = Interpolator(conditional(dot_r_cond < 0,
max_value(dot_r_cond, - self.water_c / dt),
min_value(dot_r_cond, self.water_v / dt)), cond_rate)
# tell the prognostic fields what to update to
self.water_v_new = Interpolator(self.water_v - dt * cond_rate, Vt)
self.water_c_new = Interpolator(self.water_c + dt * cond_rate, Vt)
self.theta_new = Interpolator(self.theta
* (1.0 + dt * cond_rate
* (cv * L_v / (c_vml * cp * T)
- R_v * cv * c_pml / (R_m * cp * c_vml))), Vt)
def apply(self):
self.rho_recoverer.project()
for i in range(self.iterations):
self.lim_cond_rate.interpolate()
self.theta.assign(self.theta_new.interpolate())
self.water_v.assign(self.water_v_new.interpolate())
self.water_c.assign(self.water_c_new.interpolate())
class Evaporation(Physics):
"""
The process of evaporation of rain into water vapour
with the associated latent heat change. This
parametrization comes from Klemp and Wilhelmson (1978).
:arg state: :class:`.State.` object.
"""
def __init__(self, state):
super().__init__(state)
# obtain our fields
self.theta = state.fields('theta')
self.water_v = state.fields('vapour_mixing_ratio')
self.rain = state.fields('rain_mixing_ratio')
rho = state.fields('rho')
try:
water_c = state.fields('cloud_liquid_mixing_ratio')
water_l = self.rain + water_c
except NotImplementedError:
water_l = self.rain
# declare function space
Vt = self.theta.function_space()
# make rho variables
# we recover rho into theta space
h_deg = rho.function_space().ufl_element().degree()[0]
v_deg = rho.function_space().ufl_element().degree()[1]
if v_deg == 0 and h_deg == 0:
boundary_method = Boundary_Method.physics
else:
boundary_method = None
Vt_broken = FunctionSpace(state.mesh, BrokenElement(Vt.ufl_element()))
rho_averaged = Function(Vt)
self.rho_recoverer = Recoverer(rho, rho_averaged, VDG=Vt_broken, boundary_method=boundary_method)
# define some parameters as attributes
dt = state.dt
R_d = state.parameters.R_d
cp = state.parameters.cp
cv = state.parameters.cv
c_pv = state.parameters.c_pv
c_pl = state.parameters.c_pl
c_vv = state.parameters.c_vv
R_v = state.parameters.R_v
# make useful fields
exner = thermodynamics.exner_pressure(state.parameters, rho_averaged, self.theta)
T = thermodynamics.T(state.parameters, self.theta, exner, r_v=self.water_v)
p = thermodynamics.p(state.parameters, exner)
L_v = thermodynamics.Lv(state.parameters, T)
R_m = R_d + R_v * self.water_v
c_pml = cp + c_pv * self.water_v + c_pl * water_l
c_vml = cv + c_vv * self.water_v + c_pl * water_l
# use Teten's formula to calculate w_sat
w_sat = thermodynamics.r_sat(state.parameters, T, p)
# expression for ventilation factor
a = Constant(1.6)
b = Constant(124.9)
c = Constant(0.2046)
C = a + b * (rho_averaged * self.rain) ** c
# make appropriate condensation rate
f = Constant(5.4e5)
g = Constant(2.55e6)
h = Constant(0.525)
dot_r_evap = (((1 - self.water_v / w_sat) * C * (rho_averaged * self.rain) ** h)
/ (rho_averaged * (f + g / (p * w_sat))))
# make evap_rate function, needs to be the same for all updates in one time step
evap_rate = Function(Vt)
# adjust evap rate so negative rain doesn't occur
self.lim_evap_rate = Interpolator(conditional(dot_r_evap < 0,
0.0,
conditional(self.rain < 0.0,
0.0,
min_value(dot_r_evap, self.rain / dt))),
evap_rate)
# tell the prognostic fields what to update to
self.water_v_new = Interpolator(self.water_v + dt * evap_rate, Vt)
self.rain_new = Interpolator(self.rain - dt * evap_rate, Vt)
self.theta_new = Interpolator(self.theta
* (1.0 - dt * evap_rate
* (cv * L_v / (c_vml * cp * T)
- R_v * cv * c_pml / (R_m * cp * c_vml))), Vt)
def apply(self):
self.rho_recoverer.project()
self.lim_evap_rate.interpolate()
self.theta.assign(self.theta_new.interpolate())
self.water_v.assign(self.water_v_new.interpolate())
self.rain.assign(self.rain_new.interpolate())