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3.4
DUNE for Multi-{Phase, Component, Scale, Physics, ...} flow and transport in porous media
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3.4
DUNE for Multi-{Phase, Component, Scale, Physics, ...} flow and transport in porous media
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Everything flux related in DuMux More...
Everything flux related in DuMux
Modules | |
| Flux related to the box scheme | |
| Flux related to the box scheme. | |
| Flux related to the cell-centered schemes | |
| Flux related to the cell-centered schemes. | |
| Flux related to the cell-centered two-point flux approximation schemes | |
| Flux related to the cell-centered two-point flux approximation schemes. | |
| Flux related to the cell-centered multi-point flux approximation schemes | |
| Flux related to the cell-centered multi-point flux approximation schemes. | |
| Flux related to the pore network models | |
| Flux related to the pore newtwork models. | |
| Flux related to the staggered scheme | |
| Flux related to the staggered scheme. | |
| Flux related to the shallow water model | |
| Flux related to the shallow water model. | |
Files | |
| file | flux/darcyslaw.hh |
| Darcy's law specialized for different discretization schemes This file contains the data which is required to calculate volume and mass fluxes of fluid phases over a face of a finite volume by means of the Darcy approximation. Specializations are provided for the different discretization methods. | |
| file | effectivestresslaw.hh |
| The effective stress law specialized for different discretization schemes. This computes the stress tensor and surface forces resulting from poro-mechanical deformation. | |
| file | fickiandiffusioncoefficients.hh |
| Container storing the diffusion coefficients required by Fick's law. Uses the minimal possible container size and provides unified access. | |
| file | flux/fickslaw.hh |
| Fick's law specilized for different discretization schemes. This file contains the data which is required to calculate diffusive mass fluxes due to molecular diffusion with Fick's law. | |
| file | fluxvariablesbase.hh |
| Base class for the flux variables living on a sub control volume face. | |
| file | fluxvariablescaching.hh |
| Classes related to flux variables caching. | |
| file | forchheimerslaw.hh |
| Forchheimer's law specialized for different discretization schemes This file contains the data which is required to calculate volume and mass fluxes of fluid phases over a face of a finite volume by means of the Forchheimer approximation. Specializations are provided for the different discretization methods. | |
| file | flux/fourierslaw.hh |
| Fourier's law specialized for different discretization schemes This file contains the data which is required to calculate diffusive mass fluxes due to molecular diffusion with Fourier's law. | |
| file | fourierslawnonequilibrium.hh |
| This file contains the data which is required to calculate diffusive mass fluxes due to molecular diffusion with Fourier's law. | |
| file | hookeslaw.hh |
| Hooke's law specialized for different discretization schemes. This computes the stress tensor and surface forces resulting from mechanical deformation. | |
| file | maxwellstefandiffusioncoefficients.hh |
| Container storing the diffusion coefficients required by the Maxwell- Stefan diffusion law. Uses the minimal possible container size and provides unified access. | |
| file | maxwellstefanslaw.hh |
| This file contains the data which is required to calculate diffusive mass fluxes due to molecular diffusion with Fick's law. | |
| file | referencesystemformulation.hh |
| The reference frameworks and formulations available for splitting total fluxes into a advective and diffusive part. | |
| file | shallowwaterflux.hh |
| file | shallowwaterviscousflux.hh |
| file | stationaryvelocityfield.hh |
| Constant velocity advective law for transport models. This file contains the data which is required to calculate volume and mass fluxes of fluid phases over a face of a finite volume. A stationary velocity field is given by the user for use in tracer models. | |
| file | flux/traits.hh |
| Defines the flux traits. | |
| file | flux/upwindscheme.hh |
| Base class for the upwind scheme. | |
Classes | |
| class | Dumux::EffectiveStressLaw< StressType, GridGeometry, dm > |
| This computes the stress tensor and surface forces resulting from poro-mechanical deformation. More... | |
| class | Dumux::FickianDiffusionCoefficients< Scalar, numPhases, numComponents > |
| Container storing the diffusion coefficients required by Fick's law. Uses the minimal possible container size and provides unified access. More... | |
| class | Dumux::FluxVariablesBase< Problem, FVElementGeometry, ElementVolumeVariables, ElementFluxVariablesCache > |
| Base class for the flux variables living on a sub control volume face. More... | |
| struct | Dumux::FluxVariablesCaching::EmptyAdvectionCache |
| Empty caches to use in a constitutive flux law/process, e.g. Darcy's law. More... | |
| class | Dumux::HookesLaw< Scalar, GridGeometry, dm > |
| This computes the stress tensor and surface forces resulting from mechanical deformation. More... | |
| class | Dumux::MaxwellStefanDiffusionCoefficients< Scalar, numPhases, numComponents > |
| Container storing the diffusion coefficients required by the Maxwell- Stefan diffusion law. Uses the minimal possible container size and provides unified access. More... | |
| class | Dumux::ShallowWaterFlux< NumEqVector > |
| Computes the shallow water flux by solving a riemann problem. More... | |
| class | Dumux::ShallowWaterViscousFlux< PrimaryVariables, NumEqVector, > |
| Computes the shallow water viscous momentum flux due to (turbulent) viscosity by adding all surrounding shear stresses. For now implemented strictly for 2D depth-averaged models (i.e. 3 equations) More... | |
| class | Dumux::StationaryVelocityField< Scalar > |
| Evaluates a user given velocity field. More... | |
| struct | Dumux::HasStationaryVelocityField< AdvectionType > |
| Trait of an advection type stating whether it implements a stationary velocity field. More... | |
| struct | Dumux::FluxTraits< FluxVariables > |
| Traits of a flux variables type. More... | |
Typedefs | |
| template<class TypeTag > | |
| using | Dumux::DarcysLaw = DarcysLawImplementation< TypeTag, GetPropType< TypeTag, Properties::GridGeometry >::discMethod > |
| Evaluates the normal component of the Darcy velocity on a (sub)control volume face. More... | |
| template<class TypeTag , ReferenceSystemFormulation referenceSystem = ReferenceSystemFormulation::massAveraged> | |
| using | Dumux::FicksLaw = FicksLawImplementation< TypeTag, GetPropType< TypeTag, Properties::GridGeometry >::discMethod, referenceSystem > |
| Evaluates the diffusive mass flux according to Fick's law. More... | |
| template<class TypeTag > | |
| using | Dumux::ForchheimersLaw = ForchheimersLawImplementation< TypeTag, GetPropType< TypeTag, Properties::GridGeometry >::discMethod > |
| Evaluates the normal component of the Forchheimer velocity on a (sub)control volume face. More... | |
| template<class TypeTag > | |
| using | Dumux::FouriersLaw = FouriersLawImplementation< TypeTag, GetPropType< TypeTag, Properties::GridGeometry >::discMethod > |
| Evaluates the heat conduction flux according to Fouriers's law. More... | |
| template<class TypeTag > | |
| using | Dumux::FouriersLawNonEquilibrium = FouriersLawNonEquilibriumImplementation< TypeTag, GetPropType< TypeTag, Properties::GridGeometry >::discMethod > |
| Evaluates the heat conduction flux according to Fouriers's law. More... | |
| template<class TypeTag , ReferenceSystemFormulation referenceSystem = ReferenceSystemFormulation::massAveraged> | |
| using | Dumux::MaxwellStefansLaw = MaxwellStefansLawImplementation< TypeTag, GetPropType< TypeTag, Properties::GridGeometry >::discMethod, referenceSystem > |
| Evaluates the diffusive mass flux according to Maxwell Stafan's law. More... | |
| template<class GridGeometry > | |
| using | Dumux::UpwindScheme = UpwindSchemeImpl< GridGeometry, GridGeometry::discMethod > |
| The upwind scheme used for the advective fluxes. This depends on the chosen discretization method. More... | |
Enumerations | |
| enum class | Dumux::ReferenceSystemFormulation { Dumux::ReferenceSystemFormulation::massAveraged , Dumux::ReferenceSystemFormulation::molarAveraged } |
| The formulations available for Fick's law related to the reference system. More... | |
Functions | |
| template<class VolumeVariables > | |
| VolumeVariables::PrimaryVariables::value_type | Dumux::massOrMolarDensity (const VolumeVariables &volVars, ReferenceSystemFormulation referenceSys, const int phaseIdx) |
| evaluates the density to be used in Fick's law based on the reference system More... | |
| template<class VolumeVariables > | |
| VolumeVariables::PrimaryVariables::value_type | Dumux::massOrMoleFraction (const VolumeVariables &volVars, ReferenceSystemFormulation referenceSys, const int phaseIdx, const int compIdx) |
| returns the mass or mole fraction to be used in Fick's law based on the reference system More... | |
| template<class Problem , class FVElementGeometry , class ElementVolumeVariables > | |
| static NumEqVector | Dumux::ShallowWaterFlux< NumEqVector >::flux (const Problem &problem, const typename FVElementGeometry::GridGeometry::GridView::template Codim< 0 >::Entity &element, const FVElementGeometry &fvGeometry, const ElementVolumeVariables &elemVolVars, const typename FVElementGeometry::SubControlVolumeFace &scvf) |
| Prepares the Riemann problem for the advective flux for the 2D shallow water model. The actual model uses an exact Riemann solver after Torro and the reconstruction after Audusse and a flux limiter for small water depths. More... | |
| template<class Problem , class FVElementGeometry , class ElementVolumeVariables > | |
| static NumEqVector | Dumux::ShallowWaterViscousFlux< PrimaryVariables, NumEqVector, >::flux (const Problem &problem, const typename FVElementGeometry::GridGeometry::GridView::template Codim< 0 >::Entity &element, const FVElementGeometry &fvGeometry, const ElementVolumeVariables &elemVolVars, const typename FVElementGeometry::SubControlVolumeFace &scvf) |
| Compute the viscous momentum flux contribution from the interface shear stress. More... | |
| using Dumux::DarcysLaw = typedef DarcysLawImplementation<TypeTag, GetPropType<TypeTag, Properties::GridGeometry>::discMethod> |
Evaluates the normal component of the Darcy velocity on a (sub)control volume face.
| using Dumux::FicksLaw = typedef FicksLawImplementation<TypeTag, GetPropType<TypeTag, Properties::GridGeometry>::discMethod, referenceSystem> |
Evaluates the diffusive mass flux according to Fick's law.
| using Dumux::ForchheimersLaw = typedef ForchheimersLawImplementation<TypeTag, GetPropType<TypeTag, Properties::GridGeometry>::discMethod> |
Evaluates the normal component of the Forchheimer velocity on a (sub)control volume face.
| using Dumux::FouriersLaw = typedef FouriersLawImplementation<TypeTag, GetPropType<TypeTag, Properties::GridGeometry>::discMethod> |
Evaluates the heat conduction flux according to Fouriers's law.
| using Dumux::FouriersLawNonEquilibrium = typedef FouriersLawNonEquilibriumImplementation<TypeTag, GetPropType<TypeTag, Properties::GridGeometry>::discMethod> |
Evaluates the heat conduction flux according to Fouriers's law.
| using Dumux::MaxwellStefansLaw = typedef MaxwellStefansLawImplementation<TypeTag, GetPropType<TypeTag, Properties::GridGeometry>::discMethod, referenceSystem> |
Evaluates the diffusive mass flux according to Maxwell Stafan's law.
| using Dumux::UpwindScheme = typedef UpwindSchemeImpl<GridGeometry, GridGeometry::discMethod> |
The upwind scheme used for the advective fluxes. This depends on the chosen discretization method.
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strong |
The formulations available for Fick's law related to the reference system.
This means that the diffusive fluxes are calculated with the mass fraction gradients and the unit of the fluxes is kg/s. It is also possible to use a molar-averaged reference system, which can be beneficial, e.g., when it is known that the molar-averaged advective velocity would be zero. When using a molar-averaged reference velocity, Fick's law is formulated with mole fraction gradients and the unit of the flux is moles/s. This means that depending on the reference system, the units of the fluxes need to be adapted to be used in mass or mole balances.
| Enumerator | |
|---|---|
| massAveraged | |
| molarAveraged | |
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inlinestatic |
Prepares the Riemann problem for the advective flux for the 2D shallow water model. The actual model uses an exact Riemann solver after Torro and the reconstruction after Audusse and a flux limiter for small water depths.
The computed water flux of the Riemann solver is given in m^2/s, the momentum fluxes are given in m^3/s^2. The Riemann flux is multiplied by scvf.area() (given in m for a 2D domain) to get the flux over the face.
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inlinestatic |
Compute the viscous momentum flux contribution from the interface shear stress.
The viscous momentum flux
\[ \int \int_{V} \mathbf{\nabla} \cdot \nu_t h \mathbf{\nabla} \mathbf{u} dV \]
is re-written using Gauss' divergence theorem to:
\[ \int_{S_f} \nu_t h \mathbf{\nabla} \mathbf{u} \cdot \mathbf{n_f} dS \]
The vertical (Elder-like) contribution to the turbulent viscosity scales with water depth
\[ h \]
and shear velocity
\[ u_{*} \]
:
\[ \nu_t^v = c^v \frac{\kappa}{6} u_{*} h \]
The horizontal (Smagorinsky-like) contribution to the turbulent viscosity scales with the water depth (squared) and the magnitude of the stress (rate-of-strain) tensor:
\[ nu_t^h = (c^h h)^2 \sqrt{ 2\left(\frac{\partial u}{\partial x}\right)^2 + \left(\frac{\partial u}{\partial y} + \frac{\partial v}{\partial x}\right)^2 + 2\left(\frac{\partial v}{\partial y}\right)^2 } \]
However, based on the velocity vectors in the direct neighbours of the volume face, it is not possible to compute all components of the stress tensor. Only the gradients of u and v in the direction of the vector between the cell centres is available. To avoid the reconstruction of the full velocity gradient tensor based on a larger stencil, the horizontal contribution to the eddy viscosity (in the mixing-length model) is computed using only the velocity gradients normal to the face:
\[ \frac{\partial u}{\partial n} , \frac{\partial v}{\partial n} \]
In other words, the present approximation of the horizontal contribution to the turbulent viscosity reduces to:
\[ nu_t^h = (c^h h)^2 \sqrt{ 2\left(\frac{\partial u}{\partial n}\right)^2 + 2\left(\frac{\partial v}{\partial n}\right)^2 } \]
It should be noted that this simplified approach is formally inconsistent and will result in a turbulent viscosity that is dependent on the grid (orientation).
| VolumeVariables::PrimaryVariables::value_type Dumux::massOrMolarDensity | ( | const VolumeVariables & | volVars, |
| ReferenceSystemFormulation | referenceSys, | ||
| const int | phaseIdx | ||
| ) |
evaluates the density to be used in Fick's law based on the reference system
| VolumeVariables::PrimaryVariables::value_type Dumux::massOrMoleFraction | ( | const VolumeVariables & | volVars, |
| ReferenceSystemFormulation | referenceSys, | ||
| const int | phaseIdx, | ||
| const int | compIdx | ||
| ) |
returns the mass or mole fraction to be used in Fick's law based on the reference system
1.9.3