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# Two dimensional general rate model¶

## Group /input/model/unit_XXX - UNIT_TYPE = GENERAL_RATE_MODEL_2D¶

For information on model equations, refer to Two Dimensional General rate model (GRM2D).

`UNIT_TYPE`

Specifies the type of unit operation model

Type:string

Range:\(\texttt{GENERAL_RATE_MODEL_2D}\)

Length:1

`NCOMP`

Number of chemical components in the chromatographic medium

Type:int

Range:\(\geq 1\)

Length:1

`ADSORPTION_MODEL`

Specifies the type of binding model of each particle type (or of all particle types if length is 1)

Type:string

Range:See Section Binding models

Length:\(1 / \texttt{NPARTYPE}\)

`ADSORPTION_MODEL_MULTIPLEX`

Multiplexing mode of \(\texttt{ADSORPTION_MODEL}\). If set to 0, each particle type has a different binding model and the length of \(\texttt{ADSORPTION_MODEL}\) is \(\texttt{NPARTYPE}\). If set to 1, all particle types share the same binding model and the length of \(\texttt{ADSORPTION_MODEL}\) is 1. This field is optional and inferred from the length of \(\texttt{ADSORPTION_MODEL}\) if left out.

Type:int

Range:\(\{0, 1\}\)

Length:1

`NBOUND`

Number of bound states for each component in each particle type in type-major ordering

Type:int

Range:\(\geq 0\)

Length:\(\texttt{NCOMP} / \texttt{NPARTYPE} \cdot \texttt{NCOMP}\)

`REACTION_MODEL_BULK`

Specifies the type of reaction model of the bulk volume. The model is configured in the subgroup \(\texttt{reaction_bulk}\).

Type:string

Range:See Section Reaction models

Length:1

`REACTION_MODEL_PARTICLES`

Specifies the type of reaction model of each particle type (or of all particle types if length is 1). The model is configured in the subgroup \(\texttt{reaction_particle}\), or \(\texttt{reaction_particle_XXX}\) in case of disabled multiplexing.

Type:string

Range:See Section Reaction models

Length:\(1 / \texttt{NPARTYPE}\)

`REACTION_MODEL_PARTICLES_MULTIPLEX`

Multiplexing mode of \(\texttt{REACTION_MODEL_PARTICLES}\). If set to 0, each particle type has a different reaction model and the length of \(\texttt{REACTION_MODEL_PARTICLES}\) is \(\texttt{NPARTYPE}\). If set to 1, all particle types share the same reaction model and the length of \(\texttt{REACTION_MODEL_PARTICLES}\) is 1. This field is optional and inferred from the length of \(\texttt{REACTION_MODEL_PARTICLES}\) if left out.

Type:int

Range:\(\{0, 1\}\)

Length:1

`INIT_C`

Initial concentrations for each component in all radial zones the bulk mobile phase (length \(\texttt{NCOMP}\)), or for each component in each radial zone (length \(\texttt{NCOMP} \cdot \texttt{NRAD}\), ordering radial-major)

Unit:\(\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\)

Type:double

Range:\(\geq 0\)

Length:\(\texttt{NCOMP} / \texttt{NCOMP} \cdot \texttt{NRAD}\)

`INIT_CP`

Initial concentrations for each component in the bead liquid phase (optional, \(\texttt{INIT_C}\) is used if left out). The length of this field can be \(\texttt{NCOMP}\) (same values for each radial zone and particle type), \(\texttt{NPARTYPE} \cdot \texttt{NCOMP}\) (same values for each radial zone), \(\texttt{RAD} \cdot \texttt{NCOMP}\) (same values for each particle type), or \(\texttt{NRAD} \cdot \texttt{NPARTYPE} \cdot \texttt{NCOMP}\). The ordering is radial-type-major. Values for each particle type can only be given when \(\texttt{ADSORPTION_MODEL_MULTIPLEX}\) is 0. In the radial-inhomogeneous case, the \(\texttt{SENS_REACTION}\) field is used for indexing the radial zone when specifying parameter sensitivities.

Unit:\(\mathrm{mol}\,\mathrm{m}_{\mathrm{MP}}^{-3}\)

Type:double

Range:\(\geq 0\)

`INIT_Q`

Initial concentrations for each bound state of each component in the bead solid phase. If \(\texttt{ADSORPTION_MODEL_MULTIPLEX}\) is 0, values for each particle type are required in type-component-major ordering (length is \(\texttt{NTOTALBND}\)). If \(\texttt{ADSORPTION_MODEL_MULTIPLEX}\) is 1, values for one particle type are required in component-major ordering (length is \(\sum_{i = 0}^{\texttt{NCOMP} - 1} \texttt{NBND}_i\)). Alternatively, values for each radial zone can be supplied. If \(\texttt{ADSORPTION_MODEL_MULTIPLEX}\) is 0, values for each radial zone and each particle type are required in radial-type-component-major ordering (length is \(\texttt{NRAD} \cdot \texttt{NTOTALBND}\)). If \(\texttt{ADSORPTION_MODEL_MULTIPLEX}\) is 1, values for each radial zone and all particle types are required in radial-component-major ordering (length is \(\texttt{NRAD} \cdot \sum_{i = 0}^{\texttt{NCOMP} - 1} \texttt{NBND}_i\)). In the radial-inhomogeneous case, the \(\texttt{SENS_REACTION}\) field is used for indexing the radial zone when specifying parameter sensitivities.

Unit:\(\mathrm{mol}\,\mathrm{m}_{\mathrm{SP}}^{-3}\)

Type:double

Range:\(\geq 0\)

`INIT_STATE`

Full state vector for initialization (optional, \(\texttt{INIT_C}\), \(\texttt{INIT_CP}\), and \(\texttt{INIT_Q}\) will be ignored; if length is \(2\texttt{NDOF}\), then the second half is used for time derivatives)

Unit:\(various\)

Type:double

Range:\(\mathbb{R}\)

Length:\(\texttt{NDOF} / 2\texttt{NDOF}\)

`COL_DISPERSION`

Axial dispersion coefficient. In case of a spatially inhomogeneous setting, the \(\texttt{SENS_PARTYPE}\) field is used for indexing the radial zone when specifying parameter sensitivities.

Unit:\(\mathrm{m}_{\mathrm{IV}}^{2}\,\mathrm{s}^{-1}\)

Type:double

Range:\(\geq 0\)

Length:see \(\texttt{COL_DISPERSION_MULTIPLEX}\)

`COL_DISPERSION_MULTIPLEX`

Multiplexing mode of \(\texttt{COL_DISPERSION}\). Determines whether \(\texttt{COL_DISPERSION}\) is treated as component-, radial-, and/or section-independent. This field is optional. When left out, multiplexing behavior is inferred from the length of \(\texttt{COL_DISPERSION}\). Valid modes are:

Component-independent, radial-independent, section-independent; length of \(\texttt{COL_DISPERSION}\) is 1

Component-independent, radial-dependent, section-independent; length of \(\texttt{COL_DISPERSION}\) is \(\texttt{NRAD}\)

Component-dependent, radial-independent, section-independent; length of \(\texttt{COL_DISPERSION}\) is \(\texttt{NCOMP}\)

Component-dependent, radial-dependent, section-independent; length of \(\texttt{COL_DISPERSION}\) is \(\texttt{NCOMP} \cdot \texttt{NRAD}\); ordering is radial-major

Component-independent, radial-independent, section-dependent; length of \(\texttt{COL_DISPERSION}\) is \(\texttt{NSEC}\)

Component-independent, radial-dependent, section-dependent; length of \(\texttt{COL_DISPERSION}\) is \(\texttt{NRAD} \cdot \texttt{NSEC}\); ordering is section-major

Component-dependent, radial-independent, section-independent; length of \(\texttt{COL_DISPERSION}\) is \(\texttt{NCOMP} \cdot \texttt{NSEC}\); ordering is section-major

Component-dependent, radial-dependent, section-dependent; length of \(\texttt{COL_DISPERSION}\) is \(\texttt{NCOMP} \cdot \texttt{NRAD} \cdot \texttt{NSEC}\); ordering is section-radial-major

Type:int

Range:\(\{0, \dots, 7 \}\)

Length:1

`COL_DISPERSION_RADIAL`

Radial dispersion coefficient. In case of a spatially inhomogeneous setting, the \(\texttt{SENS_PARTYPE}\) field is used for indexing the radial zone when specifying parameter sensitivities.

Unit:\(\mathrm{m}_{\mathrm{IV}}^{2}\,\mathrm{s}^{-1}\)

Type:double

Range:\(\geq 0\)

Length:see \(\texttt{COL_DISPERSION_RADIAL_MULTIPLEX}\)

`COL_DISPERSION_RADIAL_MULTIPLEX`

Multiplexing mode of \(\texttt{COL_DISPERSION_RADIAL}\). Determines whether \(\texttt{COL_DISPERSION_RADIAL}\) is treated as component-, radial-, and/or section-independent. This field is optional. When left out, multiplexing behavior is inferred from the length of \(\texttt{COL_DISPERSION_RADIAL}\). Valid modes are:

Component-independent, radial-independent, section-independent; length of \(\texttt{COL_DISPERSION_RADIAL}\) is 1

Component-independent, radial-dependent, section-independent; length of \(\texttt{COL_DISPERSION_RADIAL}\) is \(\texttt{NRAD}\)

Component-dependent, radial-independent, section-independent; length of \(\texttt{COL_DISPERSION_RADIAL}\) is \(\texttt{NCOMP}\)

Component-dependent, radial-dependent, section-independent; length of \(\texttt{COL_DISPERSION_RADIAL}\) is \(\texttt{NCOMP} \cdot \texttt{NRAD}\); ordering is radial-major

Component-independent, radial-independent, section-dependent; length of \(\texttt{COL_DISPERSION_RADIAL}\) is \(\texttt{NSEC}\)

Component-independent, radial-dependent, section-dependent; length of \(\texttt{COL_DISPERSION_RADIAL}\) is \(\texttt{NRAD} \cdot \texttt{NSEC}\); ordering is section-major

Component-dependent, radial-independent, section-independent; length of \(\texttt{COL_DISPERSION_RADIAL}\) is \(\texttt{NCOMP} \cdot \texttt{NSEC}\); ordering is section-major

Component-dependent, radial-dependent, section-dependent; length of \(\texttt{COL_DISPERSION_RADIAL}\) is \(\texttt{NCOMP} \cdot \texttt{NRAD} \cdot \texttt{NSEC}\); ordering is section-radial-major

Type:int

Range:\(\{0, \dots, 7 \}\)

Length:1

`COL_LENGTH`

Column length

Unit:\(\mathrm{m}\)

Type:double

Range:\(> 0\)

Length:1

`COL_RADIUS`

Column radius. This parameter is optional if

`CROSS_SECTION_AREA`

is provided.

Unit:\(\mathrm{m}\)

Type:double

Range:\(> 0\)

Length:1

`CROSS_SECTION_AREA`

Cross section area of the column. This parameter is optional and will be ignored if COL_RADIUS is provided.

Unit:\(\mathrm{m}^{2}\)

Type:double

Range:\(>0\)

Length:1

`COL_POROSITY`

Column porosity, either constant (length is 1) or for each radial zone (length is \(\texttt{NRAD}\)). In case of a spatially inhomogeneous setting, the \(\texttt{SENS_PARTYPE}\) field is used for indexing the radial zone when specifying parameter sensitivities.

Type:double

Range:\((0,1]\)

Length:\(1 / \texttt{NRAD}\)

`FILM_DIFFUSION`

Film diffusion coefficients for each component of each particle type

Unit:\(\mathrm{m}\,\mathrm{s}^{-1}\)

Type:double

Range:\(\geq 0\)

Length:see \(\texttt{FILM_DIFFUSION_MULTIPLEX}\)

`FILM_DIFFUSION_MULTIPLEX`

Multiplexing mode of \(\texttt{FILM_DIFFUSION}\). Determines whether \(\texttt{FILM_DIFFUSION}\) is treated as component-, type-, and/or section-independent. This field is optional. When left out, multiplexing behavior is inferred from the length of \(\texttt{FILM_DIFFUSION}\). Valid modes are:

Component-dependent, type-independent, section-independent; length of \(\texttt{FILM_DIFFUSION}\) is \(\texttt{NCOMP}\)

Component-dependent, type-independent, section-dependent; length of \(\texttt{FILM_DIFFUSION}\) is \(\texttt{NCOMP} \cdot \texttt{NSEC}\); ordering is section-major

Component-dependent, type-dependent, section-independent; length of \(\texttt{FILM_DIFFUSION}\) is \(\texttt{NCOMP} \cdot \texttt{NPARTYPE}\); ordering is type-major

Component-dependent, type-dependent, section-dependent; length of \(\texttt{FILM_DIFFUSION}\) is \(\texttt{NCOMP} \cdot \texttt{NPARTYPE} \cdot \texttt{NSEC}\); ordering is section-type-major

Type:int

Range:\(\{0, \dots, 3 \}\)

Length:1

`PAR_POROSITY`

Particle porosity of all particle types or for each particle type

Type:double

Range:\((0,1]\)

Length:\(1 / \texttt{NPARTYPE}\)

`PAR_RADIUS`

Particle radius of all particle types or for each particle type

Unit:\(\mathrm{m}\)

Type:double

Range:\(>0\)

Length:\(1 / \texttt{NPARTYPE}\)

`PAR_CORERADIUS`

Particle core radius of all particle types or for each particle type (optional, defaults to \(0~m\))

Unit:\(\mathrm{m}\)

Type:double

Range:\([0, \texttt{PAR_RADIUS})\)

Length:\(1 / \texttt{NPARTYPE}\)

`PORE_ACCESSIBILITY`

Pore accessibility factor of each component in each particle type (optional, defaults to 1). Note: Should not be used in combination with any binding model!

Type:double

Range:\((0, 1]\)

Length:see \(\texttt{PORE_ACCESSIBILITY_MULTIPLEX}\)

`PORE_ACCESSIBILITY_MULTIPLEX`

Multiplexing mode of \(\texttt{PORE_ACCESSIBILITY}\). Determines whether \(\texttt{PORE_ACCESSIBILITY}\) is treated as component-, type-, and/or section-independent. This field is optional. When left out, multiplexing behavior is inferred from the length of \(\texttt{PORE_ACCESSIBILITY}\). Valid modes are:

Component-dependent, type-independent, section-independent; length of \(\texttt{PORE_ACCESSIBILITY}\) is \(\texttt{NCOMP}\)

Component-dependent, type-independent, section-dependent; length of \(\texttt{PORE_ACCESSIBILITY}\) is \(\texttt{NCOMP} \cdot \texttt{NSEC}\); ordering is section-major

Component-dependent, type-dependent, section-independent; length of \(\texttt{PORE_ACCESSIBILITY}\) is \(\texttt{NCOMP} \cdot \texttt{NPARTYPE}\); ordering is type-major

Component-dependent, type-dependent, section-dependent; length of \(\texttt{PORE_ACCESSIBILITY}\) is \(\texttt{NCOMP} \cdot \texttt{NPARTYPE} \cdot \texttt{NSEC}\); ordering is section-type-major

Type:int

Range:\(\{0, \dots, 3 \}\)

Length:1

`PAR_DIFFUSION`

Effective particle diffusion coefficients of each component in each particle type

Unit:\(\mathrm{m}_{\mathrm{MP}}^{2}\,\mathrm{s}^{-1}\)

Type:double

Range:\(> 0\)

Length:see \(\texttt{PAR_DIFFUSION_MULTIPLEX}\)

`PAR_DIFFUSION_MULTIPLEX`

Multiplexing mode of \(\texttt{PAR_DIFFUSION}\). Determines whether \(\texttt{PAR_DIFFUSION}\) is treated as component-, type-, and/or section-independent. This field is optional. When left out, multiplexing behavior is inferred from the length of \(\texttt{PAR_DIFFUSION}\). Valid modes are:

Component-dependent, type-independent, section-independent; length of \(\texttt{PAR_DIFFUSION}\) is \(\texttt{NCOMP}\)

Component-dependent, type-independent, section-dependent; length of \(\texttt{PAR_DIFFUSION}\) is \(\texttt{NCOMP} \cdot \texttt{NSEC}\); ordering is section-major

Component-dependent, type-dependent, section-independent; length of \(\texttt{PAR_DIFFUSION}\) is \(\texttt{NCOMP} \cdot \texttt{NPARTYPE}\); ordering is type-major

Component-dependent, type-dependent, section-dependent; length of \(\texttt{PAR_DIFFUSION}\) is \(\texttt{NCOMP} \cdot \texttt{NPARTYPE} \cdot \texttt{NSEC}\); ordering is section-type-major

Type:int

Range:\(\{0, \dots, 3 \}\)

Length:1

`PAR_SURFDIFFUSION`

Particle surface diffusion coefficients of each bound state of each component in each particle type (optional, defaults to all \(0~m_{SP}^2 s^{-1}\))

Unit:\(\mathrm{m}_{\mathrm{SP}}^{2}\,\mathrm{s}^{-1}\)

Type:double

Range:\(\geq 0\)

Length:see \(\texttt{PAR_SURFDIFFUSION_MULTIPLEX}\)

`PAR_SURFDIFFUSION_MULTIPLEX`

Multiplexing mode of \(\texttt{PAR_SURFDIFFUSION}\). Determines whether \(\texttt{PAR_SURFDIFFUSION}\) is treated as component-, type-, and/or section-independent. This field is optional. When left out, multiplexing behavior is inferred from the length of \(\texttt{PAR_SURFDIFFUSION}\). Valid modes are:

Component-dependent, type-independent, section-independent; length of \(\texttt{PAR_SURFDIFFUSION}\) is \(\texttt{NBND}\); ordering is component-major

Component-dependent, type-independent, section-dependent; length of \(\texttt{PAR_SURFDIFFUSION}\) is \(\texttt{NBND} \cdot \texttt{NSEC}\); ordering is section-component-major

Component-dependent, type-dependent, section-independent; length of \(\texttt{PAR_SURFDIFFUSION}\) is \(\texttt{NTOTALBND}\); ordering is type-component-major

Component-dependent, type-dependent, section-dependent; length of \(\texttt{PAR_SURFDIFFUSION}\) is \(\texttt{NTOTALBND} \cdot \texttt{NSEC}\); ordering is section-type-component-major

Type:int

Range:\(\{0, \dots, 3 \}\)

Length:1

`VELOCITY`

Indicates flow direction in each radial zone (forward if value is positive, backward if value is negative), see Section Specification of flow rate / velocity and direction). In case of a spatially inhomogeneous setting, the \(\texttt{SENS_PARTYPE}\) field is used for indexing the radial cell when specifying parameter sensitivities.

Type:double

Range:\(\mathbb{R}\)

Length:see \(\texttt{VELOCITY_MULTIPLEX}\)

`VELOCITY_MULTIPLEX`

Multiplexing mode of \(\texttt{VELOCITY}\). Determines whether \(\texttt{VELOCITY}\) is treated as radial- and/or section-independent. This field is optional. When left out, multiplexing behavior is inferred from the length of \(\texttt{VELOCITY}\). Valid modes are:

Radial-independent, section-independent; length of \(\texttt{VELOCITY}\) is 1

Radial-dependent, section-independent; length of \(\texttt{VELOCITY}\) is \(\texttt{NRAD}\)

Section-dependent; length of \(\texttt{VELOCITY}\) is \(\texttt{NSEC}\)

Radial-dependent, section-dependent; length of \(\texttt{VELOCITY}\) is \(\texttt{NRAD} \cdot \texttt{NSEC}\); ordering is section-major

Type:int

Range:\(\{0, \dots, 3 \}\)

Length:1

`NPARTYPE`

Number of particle types. Optional, inferred from the length of \(\texttt{NPAR}\) or \(\texttt{NBOUND}\) if left out.

Type:int

Range:\(\geq 1\)

Length:1

`PAR_GEOM`

Specifies the particle geometry for all or each particle type. Valid values are \(\texttt{SPHERE}\), \(\texttt{CYLINDER}\), \(\texttt{SLAB}\). Optional, defaults to \(\texttt{SPHERE}\).

Type:string

Length:\(1\) / \(\texttt{NPARTYPE}\)

`PAR_TYPE_VOLFRAC`

Volume fractions of the particle types. The volume fractions can be set homogeneous or individually along both axes. For each cell, the volume fractions have to sum to 1. In case of a spatially inhomogeneous setting, the \(\texttt{SENS_SECTION}\) field is used for indexing the axial cell and the \(\texttt{SENS_REACTION}\) field is used for indexing the radial cell when specifying parameter sensitivities. This field is optional in case of only one particle type.

Type:double

Range:\([0,1]\)

Length:see \(\texttt{PAR_TYPE_VOLFRAC_MULTIPLEX}\)

`PAR_TYPE_VOLFRAC_MULTIPLEX`

Multiplexing mode of \(\texttt{PAR_TYPE_VOLFRAC}\). Determines whether \(\texttt{PAR_TYPE_VOLFRAC}\) is treated as radial- and/or section-independent. This field is optional. When left out, multiplexing behavior is inferred from the length of \(\texttt{PAR_TYPE_VOLFRAC}\). Valid modes are:

Radial-independent, axial-independent; length of \(\texttt{PAR_TYPE_VOLFRAC}\) is \(\texttt{NPARTYPE}\)

Radial-dependent, axial-independent; length of \(\texttt{PAR_TYPE_VOLFRAC}\) is \(\texttt{NRAD} \cdot \texttt{NPARTYPE}\); ordering is radial-major

Axial-dependent; length of \(\texttt{PAR_TYPE_VOLFRAC}\) is \(\texttt{NCOL} \cdot \texttt{NPARTYPE}\); ordering is axial-major

Radial-dependent, axial-dependent; length of \(\texttt{PAR_TYPE_VOLFRAC}\) is \(\texttt{NCOL} \cdot \texttt{NRAD} \cdot \texttt{NPARTYPE}\); ordering is axial-radial-major

Type:int

Range:\(\{0, \dots, 3 \}\)

Length:1

## Group /input/model/unit_XXX/discretization - UNIT_TYPE - GENERAL_RATE_MODEL_2D¶

`NCOL`

Number of axial column discretization cells

Type:int

Range:\(\geq 1\)

Length:1

`NRAD`

Number of radial column discretization cells

Type:int

Range:\(\geq 1\)

Length:1

`NPAR`

Number of particle (radial) discretization cells for each particle type

Type:int

Range:\(\geq 1\)

Length:\(1 / \texttt{NPARTYPE}\)

`RADIAL_DISC_TYPE`

Specifies the radial discretization scheme. Valid values are \(\texttt{EQUIDISTANT}\), \(\texttt{EQUIVOLUME}\), and \(\texttt{USER_DEFINED}\).

Type:string

Length:1

`RADIAL_COMPARTMENTS`

Coordinates for the radial compartment boundaries (ignored if \(\texttt{RADIAL_DISC_TYPE} \neq \texttt{USER_DEFINED}\)). The coordinates are absolute and have to include the endpoints 0 and \(\texttt{COLUMN_RADIUS}\). The values are expected in ascending order (i.e., 0 is the first and \(\texttt{COLUMN_RADIUS}\) the last value in the array).

Unit:\(\mathrm{m}\)

Type:double

Range:\([0,\texttt{COLUMN_RADIUS}]\)

Length:\(\texttt{NRAD} + 1\)

`PAR_DISC_TYPE`

Specifies the discretization scheme inside the particles for all or each particle type. Valid values are \(\texttt{EQUIDISTANT_PAR}\), \(\texttt{EQUIVOLUME_PAR}\), and \(\texttt{USER_DEFINED_PAR}\).

Type:string

Length:\(1 / \texttt{NPARTYPE}\)

`PAR_DISC_VECTOR`

Node coordinates for the cell boundaries (ignored if \(\texttt{PAR_DISC_TYPE} \neq \texttt{USER_DEFINED_PAR}\)). The coordinates are relative and have to include the endpoints 0 and 1. They are later linearly mapped to the true radial range \([r_{c,j}, r_{p,j}]\). The coordinates for each particle type are appended to one long vector in type-major ordering.

Type:double

Range:\([0,1]\)

Length:\(sum_i (\texttt{NPAR}_i + 1)\)

`PAR_BOUNDARY_ORDER`

Order of accuracy of outer particle boundary condition. Optional, defaults to 2.

Type:int

Range:\(\{ 1,2 \}\)

Length:1

`USE_ANALYTIC_JACOBIAN`

Determines whether analytically computed Jacobian matrix (faster) is used (value is 1) instead of Jacobians generated by algorithmic differentiation (slower, value is 0)

Type:int

Range:\(\{0, 1\}\)

Length:1

`LINEAR_SOLVER_BULK`

Linear solver used for the sparse column bulk block. This field is optional, the best available method is selected (i.e., sparse direct solver if possible). Valid values are:

\(\texttt{DENSE}\) Converts the sparse matrix into a banded matrix and uses regular LAPACK. Slow and memory intensive, but always available.

\(\texttt{UMFPACK}\) Uses the UMFPACK sparse direct solver (LU decomposition) from SuiteSparse. Fast, but has to be enabled when compiling and requires UMFPACK library.

\(\texttt{SUPERLU}\) Uses the SuperLU sparse direct solver (LU decomposition). Fast, but has to be enabled when compiling and requires SuperLU library.

Type:string

Range:\(\{\texttt{DENSE},\texttt{UMFPACK},\texttt{SUPERLU}\}\)

Length:1

`RECONSTRUCTION`

Type of reconstruction method for fluxes

Type:string

Range:\(\texttt{WENO}\)

Length:1

`GS_TYPE`

Type of Gram-Schmidt orthogonalization, see IDAS guide Section~4.5.7.3, p.~41f. A value of 0 enables classical Gram-Schmidt, a value of 1 uses modified Gram-Schmidt.

Type:int

Range:\(\{0, 1\}\)

Length:1

`MAX_KRYLOV`

Defines the size of the Krylov subspace in the iterative linear GMRES solver (0: \(\texttt{MAX_KRYLOV} = \texttt{NCOL} \cdot \texttt{NRAD} \cdot \texttt{NCOMP} \cdot \texttt{NPARTYPE}\))

Type:int

Range:\(\{0, \dots, \texttt{NCOL} \cdot \texttt{NRAD} \cdot \texttt{NCOMP} \cdot \texttt{NPARTYPE} \}\)

Length:1

`MAX_RESTARTS`

Maximum number of restarts in the GMRES algorithm. If lack of memory is not an issue, better use a larger Krylov space than restarts.

Type:int

Range:\(\geq 0\)

Length:1

`SCHUR_SAFETY`

Schur safety factor; Influences the tradeoff between linear iterations and nonlinear error control; see IDAS guide Section~2.1 and 5.

Type:double

Range:\(\geq 0\)

Length:1

For further discretization parameters, see also flux_restruction_methods, and Nonlinear solver for consistent initialization.