"""
================================================================
Discretization (:mod:`CADETProcess.processModel.discretization`)
================================================================
The following module is a collection of classes that define different discretization
schemes for :mod:`UnitOperations <CADETProcess.processModel.unitOperation>` for the
CADETProcess software package.
The :class:`~CADETProcess.processModel.DiscretizationParametersBase` class is the base
class for all other classes in this module and defines some common parameters.
Specific parameters for each scheme are defined as attributes of each class.
"""
from CADETProcess.dataStructure import Structure
from CADETProcess.dataStructure import (
Bool, Switch,
RangedInteger, UnsignedInteger, UnsignedFloat,
SizedRangedList
)
__all__ = [
'NoDiscretization',
'LRMDiscretizationFV', 'LRMDiscretizationDG',
'LRMPDiscretizationFV', 'LRMPDiscretizationDG',
'GRMDiscretizationFV', 'GRMDiscretizationDG',
'WenoParameters', 'ConsistencySolverParameters',
'DGMixin'
]
[docs]
class DiscretizationParametersBase(Structure):
"""Base class for storing discretization parameters.
Attributes
----------
dimensionality : dict
Dimensionality of the parameters
weno_parameters : WenoParameters
Parameters for the WENO scheme.
consistency_solver: ConsistencySolverParameters
Consistency solver parameters for Cadet.
"""
_dimensionality = []
def __init__(self):
"""Initialize a new DiscretizationParametersBase instance."""
self.weno_parameters = WenoParameters()
self.consistency_solver = ConsistencySolverParameters()
super().__init__()
@property
def dimensionality(self):
"""dict: Dimensionality of the parameters."""
dim = {}
for d in self._dimensionality:
v = getattr(self, d)
if v is None:
continue
dim[d] = v
return dim
@property
def parameters(self):
"""dict: Dictionary with parameter values."""
parameters = super().parameters
parameters['weno'] = self.weno_parameters.parameters
parameters['consistency_solver'] = self.consistency_solver.parameters
return parameters
@parameters.setter
def parameters(self, parameters):
try:
self.weno_parameters.parameters = parameters.pop('weno')
except KeyError:
pass
try:
self.consistency_solver.parameters \
= parameters.pop('consistency_solver')
except KeyError:
pass
super(DiscretizationParametersBase, self.__class__).parameters.fset(
self, parameters
)
[docs]
class NoDiscretization(DiscretizationParametersBase):
"""Class for unit operations without spatial discretization."""
pass
[docs]
class DGMixin(DiscretizationParametersBase):
pass
[docs]
class LRMDiscretizationFV(DiscretizationParametersBase):
"""Discretization parameters of the FV version of the LRM.
This class stores parameters for the Lax-Richtmyer-Morton (LRM) flux-based
finite volume discretization.
Attributes
----------
ncol : UnsignedInteger, optional
Number of axial column discretization cells. Default is 100.
use_analytic_jacobian : Bool, optional
If True, use analytically computed Jacobian matrix (faster).
If False, use Jacobians generated by algorithmic differentiation (slower).
Default is True.
reconstruction : Switch, optional
Method for spatial reconstruction. Valid values are 'WENO' (Weighted
Essentially Non-Oscillatory). Default is 'WENO'.
"""
ncol = UnsignedInteger(default=100)
use_analytic_jacobian = Bool(default=True)
reconstruction = Switch(default='WENO', valid=['WENO'])
_parameters = DiscretizationParametersBase._parameters + [
'ncol', 'use_analytic_jacobian', 'reconstruction',
]
_dimensionality = ['ncol']
[docs]
class LRMDiscretizationDG(DGMixin):
"""Discretization parameters of the DG version of the LRM.
Attributes
----------
ncol : UnsignedInteger, optional
Number of axial column discretization cells. Default is 16.
use_analytic_jacobian : Bool, optional
If True, use analytically computed Jacobian matrix (faster).
If False, use Jacobians generated by algorithmic differentiation (slower).
Default is True.
reconstruction : Switch, optional
Method for spatial reconstruction. Valid values are 'WENO' (Weighted
Essentially Non-Oscillatory). Default is 'WENO'.
polynomial_degree : UnsignedInteger, optional
Degree of the polynomial used for axial discretization. Default is 3.
polydeg : UnsignedInteger, optional
Degree of the polynomial used for axial discretization. Default is 3.
exact_integration : Bool, optional
Whether to use exact integration for the axial discretization.
Default is False.
See Also
--------
CADETProcess.processModel.LRMPDiscretizationFV
CADETProcess.processModel.LumpedRateModelWithPores
"""
ncol = UnsignedInteger(default=16)
use_analytic_jacobian = Bool(default=True)
reconstruction = Switch(default='WENO', valid=['WENO'])
polynomial_degree = UnsignedInteger(default=3)
polydeg = polynomial_degree
exact_integration = Bool(default=False)
_parameters = DiscretizationParametersBase._parameters + [
'ncol', 'use_analytic_jacobian', 'reconstruction',
'polydeg', 'exact_integration'
]
_dimensionality = ['axial_dof']
@property
def axial_dof(self):
"""int: Number of degrees of freedom in the axial discretization."""
return self.ncol * (self.polynomial_degree + 1)
[docs]
class LRMPDiscretizationFV(DiscretizationParametersBase):
"""Discretization parameters of the FV version of the LRMP.
Attributes
----------
ncol : UnsignedInteger, optional
Number of axial column discretization cells. Default is 100.
par_geom : Switch, optional
The geometry of the particles in the model.
Valid values are 'SPHERE', 'CYLINDER', and 'SLAB'.
Default is 'SPHERE'.
use_analytic_jacobian : Bool, optional
If True, use analytically computed Jacobian matrix (faster).
If False, use Jacobians generated by algorithmic differentiation (slower).
Default is True.
reconstruction : Switch, optional
Method for spatial reconstruction. Valid values are 'WENO' (Weighted
Essentially Non-Oscillatory). Default is 'WENO'.
gs_type : Bool, optional
Type of Gram-Schmidt orthogonalization.
If 0, use classical Gram-Schmidt.
If 1, use modified Gram-Schmidt.
The default is 1.
max_krylov : UnsignedInteger, optional
Size of the Krylov subspace in the iterative linear GMRES solver.
If 0, max_krylov = NCOL * NCOMP * NPARTYPE is used.
The default is 0.
max_restarts : UnsignedInteger, optional
Maximum number of restarts to use for the GMRES method. Default is 10.
schur_safety : UnsignedFloat, optional
Safety factor for the Schur complement solver. Default is 1.0e-8.
See Also
--------
CADETProcess.processModel.LRMPDiscretizationDG
CADETProcess.processModel.LumpedRateModelWithPores
"""
ncol = UnsignedInteger(default=100)
par_geom = Switch(
default='SPHERE',
valid=['SPHERE', 'CYLINDER', 'SLAB']
)
use_analytic_jacobian = Bool(default=True)
reconstruction = Switch(default='WENO', valid=['WENO'])
gs_type = Bool(default=True)
max_krylov = UnsignedInteger(default=0)
max_restarts = UnsignedInteger(default=10)
schur_safety = UnsignedFloat(default=1.0e-8)
_parameters = DiscretizationParametersBase._parameters + [
'ncol', 'par_geom',
'use_analytic_jacobian', 'reconstruction',
'gs_type', 'max_krylov', 'max_restarts', 'schur_safety'
]
_dimensionality = ['ncol']
[docs]
class LRMPDiscretizationDG(DGMixin):
"""Discretization parameters of the DG version of the LRMP.
Attributes
----------
ncol : UnsignedInteger, optional
Number of axial column discretization cells. Default is 16.
par_geom : Switch, optional
The geometry of the particles in the model.
Valid values are 'SPHERE', 'CYLINDER', and 'SLAB'.
Default is 'SPHERE'.
use_analytic_jacobian : Bool, optional
If True, use analytically computed Jacobian matrix (faster).
If False, use Jacobians generated by algorithmic differentiation (slower).
Default is True.
reconstruction : Switch, optional
Method for spatial reconstruction. Valid values are 'WENO' (Weighted
Essentially Non-Oscillatory). Default is 'WENO'.
polynomial_degree : UnsignedInteger, optional
Degree of the polynomial used for spatial discretization. Default is 3.
polydeg : UnsignedInteger, optional
Alias for polynomial_degree.
exact_integration : Bool, optional
Whether to use exact integration for the spatial discretization.
Default is False.
gs_type : Bool, optional
Type of Gram-Schmidt orthogonalization.
If 0, use classical Gram-Schmidt.
If 1, use modified Gram-Schmidt.
The default is 1.
max_krylov : UnsignedInteger, optional
Size of the Krylov subspace in the iterative linear GMRES solver.
If 0, max_krylov = NCOL * NCOMP * NPARTYPE is used.
The default is 0.
max_restarts : UnsignedInteger, optional
Maximum number of restarts to use for the GMRES method. Default is 10.
schur_safety : UnsignedFloat, optional
Safety factor for the Schur complement solver. Default is 1.0e-8.
See Also
--------
CADETProcess.processModel.LRMPDiscretizationFV
CADETProcess.processModel.LumpedRateModelWithPores
"""
ncol = UnsignedInteger(default=16)
par_geom = Switch(
default='SPHERE',
valid=['SPHERE', 'CYLINDER', 'SLAB']
)
use_analytic_jacobian = Bool(default=True)
reconstruction = Switch(default='WENO', valid=['WENO'])
polynomial_degree = UnsignedInteger(default=3)
polydeg = polynomial_degree
exact_integration = Bool(default=False)
gs_type = Bool(default=True)
max_krylov = UnsignedInteger(default=0)
max_restarts = UnsignedInteger(default=10)
schur_safety = UnsignedFloat(default=1.0e-8)
_parameters = DiscretizationParametersBase._parameters + [
'ncol', 'par_geom',
'use_analytic_jacobian', 'reconstruction',
'polydeg', 'exact_integration',
'gs_type', 'max_krylov', 'max_restarts', 'schur_safety'
]
_dimensionality = ['axial_dof']
@property
def axial_dof(self):
"""int: Number of axial degrees of freedom in the spatial discretization."""
return self.ncol * (self.polynomial_degree + 1)
[docs]
class GRMDiscretizationFV(DiscretizationParametersBase):
"""Discretization parameters of the FV version of the LRMP.
Attributes
----------
ncol : UnsignedInteger, optional
Number of axial column discretization cells. Default is 100.
npar : UnsignedInteger, optional
Number of discretization cells in the radial direction. Default is 5.
par_geom : Switch, optional
The geometry of the particles in the model.
Valid values are 'SPHERE', 'CYLINDER', and 'SLAB'.
Default is 'SPHERE'.
par_disc_type : Switch, optional
Discretization scheme inside the particles for all or each particle type.
Valid values are 'EQUIDISTANT_PAR', 'EQUIVOLUME_PAR', and 'USER_DEFINED_PAR'.
Default is 'EQUIDISTANT_PAR'.
par_disc_vector : SizedRangedList, optional
Node coordinates for the cell boundaries
(ignored if `par_disc_type` != `USER_DEFINED_PAR).
The coordinates are relative and have to include the endpoints `0` and `1`.
They are later linearly mapped to the true radial range.
The coordinates for each particle type are appended to one long vector in
type-major ordering.
Default is a uniformly spaced vector with `npar+1` points between 0 and 1.
par_boundary_order : RangedInteger, optional
The order of the boundary scheme used to discretize the particles.
Valid values are 1 (first order) and 2 (second order).
Default is 2.
use_analytic_jacobian : Bool, optional
If True, use analytically computed Jacobian matrix (faster).
If False, use Jacobians generated by algorithmic differentiation (slower).
Default is True.
reconstruction : Switch, optional
Method for spatial reconstruction. Valid values are 'WENO' (Weighted
Essentially Non-Oscillatory). Default is 'WENO'.
gs_type : Bool, optional
Type of Gram-Schmidt orthogonalization.
If 0, use classical Gram-Schmidt.
If 1, use modified Gram-Schmidt.
The default is 1.
max_krylov : UnsignedInteger, optional
Size of the Krylov subspace in the iterative linear GMRES solver.
If 0, max_krylov = ncol * ncomp * npar is used, where ncomp is the
number of components in the model.
Default is 0.
max_restarts : UnsignedInteger, optional
Maximum number of restarts to use for the GMRES method. Default is 10.
schur_safety : UnsignedFloat, optional
Safety factor for the Schur complement solver. Default is 1.0e-8.
fix_zero_surface_diffusion : Bool, optional
If True, fix the surface diffusion coefficient of particles with zero
surface diffusion to a small positive value. Default is False.
See Also
--------
CADETProcess.processModel.LRMPDiscretizationDG
CADETProcess.processModel.LumpedRateModelWithPores
"""
ncol = UnsignedInteger(default=100)
npar = UnsignedInteger(default=5)
par_geom = Switch(
default='SPHERE',
valid=['SPHERE', 'CYLINDER', 'SLAB']
)
par_disc_type = Switch(
default='EQUIDISTANT_PAR',
valid=['EQUIDISTANT_PAR', 'EQUIVOLUME_PAR', 'USER_DEFINED_PAR']
)
par_disc_vector = SizedRangedList(
lb=0, ub=1, size='par_disc_vector_length', is_optional=True
)
par_boundary_order = RangedInteger(lb=1, ub=2, default=2)
use_analytic_jacobian = Bool(default=True)
reconstruction = Switch(default='WENO', valid=['WENO'])
gs_type = Bool(default=True)
max_krylov = UnsignedInteger(default=0)
max_restarts = UnsignedInteger(default=10)
schur_safety = UnsignedFloat(default=1.0e-8)
fix_zero_surface_diffusion = Bool(default=False)
_parameters = DiscretizationParametersBase._parameters + [
'ncol', 'npar',
'par_geom', 'par_disc_type', 'par_disc_vector', 'par_boundary_order',
'use_analytic_jacobian', 'reconstruction',
'gs_type', 'max_krylov', 'max_restarts', 'schur_safety',
'fix_zero_surface_diffusion',
]
_required_parameters = [
'ncol', 'npar',
'par_geom', 'par_disc_type', 'par_boundary_order',
'use_analytic_jacobian', 'reconstruction',
'gs_type', 'max_krylov', 'max_restarts', 'schur_safety',
'fix_zero_surface_diffusion',
]
_dimensionality = ['ncol', 'npar']
@property
def par_disc_vector_length(self):
"""int: Number of entries in the particle discretization vector."""
return self.npar + 1
[docs]
class GRMDiscretizationDG(DGMixin):
"""Discretization parameters of the DG version of the GRM.
Attributes
----------
ncol : UnsignedInteger, optional
Number of axial column discretization cells. Default is 16.
npar : UnsignedInteger, optional
Number of particle (radial) discretization cells for each particle type.
Default is 1.
nparcell : UnsignedInteger, optional
Alias for npar
par_geom : Switch, optional
The geometry of the particles in the model.
Valid values are 'SPHERE', 'CYLINDER', and 'SLAB'.
Default is 'SPHERE'.
use_analytic_jacobian : Bool, optional
If True, use analytically computed Jacobian matrix (faster).
If False, use Jacobians generated by algorithmic differentiation (slower).
Default is True.
reconstruction : Switch, optional
Method for spatial reconstruction. Valid values are 'WENO' (Weighted
Essentially Non-Oscillatory). Default is 'WENO'.
polynomial_degree : UnsignedInteger, optional
Degree of the polynomial used for axial discretization. Default is 3.
polydeg : UnsignedInteger, optional
Alias for polynomial_degree.
polynomial_degree_particle : UnsignedInteger, optional
Degree of the polynomial used for particle radial discretization. Default is 3.
exact_integration : Bool, optional
Whether to use exact integration for the axial discretization.
Default is False.
exact_integration : Bool, optional
Whether to use exact integration for the particle radial discretization.
Default is False.
gs_type : Bool, optional
Type of Gram-Schmidt orthogonalization.
If 0, use classical Gram-Schmidt.
If 1, use modified Gram-Schmidt.
The default is 1.
max_krylov : UnsignedInteger, optional
Size of the Krylov subspace in the iterative linear GMRES solver.
If 0, max_krylov = NCOL * NCOMP * NPARTYPE is used.
The default is 0.
max_restarts : UnsignedInteger, optional
Maximum number of restarts to use for the GMRES method. Default is 10.
schur_safety : UnsignedFloat, optional
Safety factor for the Schur complement solver. Default is 1.0e-8.
fix_zero_surface_diffusion : Bool, optional
Whether to fix zero surface diffusion for particles. Default is False.
If True, the parameters must not become non-zero during this or subsequent
simulation runs. The internal data structures are optimized for a more efficient
simulation.
Default is False (optimization disabled in favor of flexibility).
See Also
--------
CADETProcess.processModel.GRMDiscretizationDG
CADETProcess.processModel.GeneralRateModel
"""
ncol = UnsignedInteger(default=16)
npar = UnsignedInteger(default=1)
nparcell = npar
par_geom = Switch(
default='SPHERE',
valid=['SPHERE', 'CYLINDER', 'SLAB']
)
par_disc_type = Switch(
default='EQUIDISTANT_PAR',
valid=['EQUIDISTANT_PAR', 'EQUIVOLUME_PAR', 'USER_DEFINED_PAR']
)
par_disc_vector = SizedRangedList(
lb=0, ub=1, size='par_disc_vector_length'
)
par_boundary_order = RangedInteger(lb=1, ub=2, default=2)
use_analytic_jacobian = Bool(default=True)
reconstruction = Switch(default='WENO', valid=['WENO'])
polynomial_degree = UnsignedInteger(default=3)
polydeg = polynomial_degree
polynomial_degree_particle = UnsignedInteger(default=3)
parpolydeg = polynomial_degree_particle
exact_integration = Bool(default=False)
exact_integration_particle = Bool(default=True)
par_exact_integration = exact_integration_particle
gs_type = Bool(default=True)
max_krylov = UnsignedInteger(default=0)
max_restarts = UnsignedInteger(default=10)
schur_safety = UnsignedFloat(default=1.0e-8)
fix_zero_surface_diffusion = Bool(default=False)
_parameters = DiscretizationParametersBase._parameters + [
'ncol', 'nparcell',
'par_geom', 'par_disc_type', 'par_disc_vector', 'par_boundary_order',
'use_analytic_jacobian', 'reconstruction',
'polydeg', 'parpolydeg',
'exact_integration', 'par_exact_integration',
'gs_type', 'max_krylov', 'max_restarts', 'schur_safety',
'fix_zero_surface_diffusion',
]
_dimensionality = ['axial_dof', 'par_dof']
@property
def axial_dof(self):
"""int: Number of axial degrees of freedom in the axial discretization."""
return self.ncol * (self.polynomial_degree + 1)
@property
def par_dof(self):
"""int: Number of particle degrees of freedom in the axial discretization."""
return self.ncol * (self.polynomial_degree_particle + 1)
@property
def par_disc_vector_length(self):
"""int: Number of entries in the particle discretization vector."""
return self.npar + 1
[docs]
class WenoParameters(Structure):
"""Discretization parameters for the WENO scheme.
Attributes
----------
boundary_model : Switch, optional
Specifies the method for dealing with boundary cells.
Valid values are:
0: Lower WENO order (stable)
1: Zero weights (unstable for small `D_ax`)
2: Zero weights for p != 0 (stable?)
3: Large ghost points
Default is 0.
weno_eps : UnsignedFloat, optional
A small positive number used to avoid division by zero in the WENO scheme.
Default is 1e-10.
weno_order : UnsignedInteger, optional
Order of the WENO scheme. Valid values are:
1: Standard upwind scheme (order 1)
2: WENO 2 (order 3)
3: WENO 3 (order 5)
Default is 3.
See Also
--------
Structure
"""
boundary_model = UnsignedInteger(default=0, ub=3)
weno_eps = UnsignedFloat(default=1e-10)
weno_order = UnsignedInteger(default=3, ub=3)
_parameters = ['boundary_model', 'weno_eps', 'weno_order']
[docs]
class ConsistencySolverParameters(Structure):
"""A class for defining the consistency solver parameters for Cadet.
Parameters
----------
solver_name : Switch, optional
Name of the solver.
Valid values are 'LEVMAR', 'ATRN_RES', 'ATRN_ERR', and 'COMPOSITE'.
The default is 'LEVMAR'
init_damping : UnsignedFloat, optional
The initial damping parameter. Default is 0.01.
min_damping : UnsignedFloat, optional
The minimum damping parameter. Default is 0.0001.
max_iterations : UnsignedFloat, optional
The maximum number of iterations. Default is 50.
subsolvers : Switch, optional
Vector with names of solvers for the composite solver
(only required for composite solver).
Valid values are 'LEVMAR', 'ATRN_RES', 'ATRN_ERR', and 'COMPOSITE'.
The default is 'LEVMAR'
See Also
--------
Structure
"""
solver_name = Switch(
default='LEVMAR',
valid=['LEVMAR', 'ATRN_RES', 'ARTN_ERR', 'COMPOSITE']
)
init_damping = UnsignedFloat(default=0.01)
min_damping = UnsignedFloat(default=0.0001)
max_iterations = UnsignedInteger(default=50)
subsolvers = Switch(
default='LEVMAR',
valid=['LEVMAR', 'ATRN_RES', 'ARTN_ERR']
)
_parameters = [
'solver_name', 'init_damping', 'min_damping',
'max_iterations', 'subsolvers'
]
