Compositional Transport step in a Finite Volume discretization for a adaptive 2D-grid.
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template<class TypeTag>
class Dumux::FV2dTransport2P2CAdaptive< TypeTag >
Compositional Transport step in a Finite Volume discretization for a adaptive 2D-grid.
The finite volume model for the solution of the transport equation for compositional two-phase flow.
\[ \frac{\partial C^\kappa}{\partial t} = - \nabla \cdot \left( \sum_{\alpha} X^{\kappa}_{\alpha} \varrho_{alpha} \bf{v}_{\alpha}\right) + q^{\kappa}, \]
where \( \bf{v}_{\alpha} = - \lambda_{\alpha} \bf{K} \left(\nabla p_{\alpha} + \rho_{\alpha} \bf{g} \right) \). \( p_{\alpha} \) denotes the phase pressure, \( \bf{K} \) the absolute permeability, \( \lambda_{\alpha} \) the phase mobility, \( \rho_{\alpha} \) the phase density and \( \bf{g} \) the gravity constant and \( C^{\kappa} \) the total Component concentration.
- Template Parameters
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| virtual void | update (const Scalar t, Scalar &dt, TransportSolutionType &updateVec, bool impes=false) |
| | Calculate the update vector and determine timestep size. More...
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| void | getMpfaFlux (Dune::FieldVector< Scalar, 2 > &, Dune::FieldVector< Scalar, 2 > &, const IntersectionIterator &, CellData &) |
| | Compute flux over an irregular interface using a mpfa method. More...
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| | FV2dTransport2P2CAdaptive (Problem &problem) |
| | Constructs a FV2dTransport2P2CAdaptive object. More...
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| virtual | ~FV2dTransport2P2CAdaptive () |
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| void | updateTransportedQuantity (TransportSolutionType &updateVector) |
| | Updates the transported quantity once an update is calculated. More...
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| void | updateTransportedQuantity (TransportSolutionType &updateVector, Scalar dt) |
| | Updates the transported quantity once an update is calculated. More...
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| void | updateConcentrations (TransportSolutionType &updateVector, Scalar dt) |
| | Updates the concentrations once an update is calculated. More...
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| void | getFlux (ComponentVector &fluxEntries, EntryType ×tepFlux, const Intersection &intersection, CellData &cellDataI) |
| | Get flux at an interface between two cells The flux through \( \gamma \) is calculated according to the underlying pressure field, calculated by the pressure model. More...
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| void | getFluxOnBoundary (ComponentVector &fluxEntries, EntryType ×tepFlux, const Intersection &intersection, const CellData &cellDataI) |
| | Get flux on Boundary. More...
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| void | evalBoundary (GlobalPosition globalPosFace, const Intersection &intersection, FluidState &BCfluidState, PhaseVector &pressBound) |
| | Evaluate the boundary conditions. More...
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| void | initialize () |
| | Set the initial values before the first pressure equation This method is called before first pressure equation is solved from IMPET. More...
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| template<class MultiWriter > |
| void | addOutputVtkFields (MultiWriter &writer) |
| | Write transport variables into the output files. More...
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| void | serializeEntity (std::ostream &outstream, const Element &element) |
| | Function needed for restart option of the transport model: Write out. More...
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| void | deserializeEntity (std::istream &instream, const Element &element) |
| | Function needed for restart option of the transport model: Read in. More...
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template<class TypeTag >
| void Dumux::FVTransport2P2C< TypeTag >::getFlux |
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ComponentVector & |
fluxEntries, |
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EntryType & |
timestepFlux, |
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const Intersection & |
intersection, |
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CellData & |
cellDataI |
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inherited |
Get flux at an interface between two cells The flux through \( \gamma \) is calculated according to the underlying pressure field, calculated by the pressure model.
\[ - A_{\gamma} \mathbf{n}^T_{\gamma} \mathbf{K} \sum_{\alpha} \varrho_{\alpha} \lambda_{\alpha} \mathbf{d}_{ij} \left( \frac{p_{\alpha,j}^t - p^{t}_{\alpha,i}}{\Delta x} + \varrho_{\alpha} \mathbf{g}^T \mathbf{d}_{ij} \right) \sum_{\kappa} X^{\kappa}_{\alpha} \]
Here, \( \mathbf{d}_{ij} \) is the normalized vector connecting the cell centers, and \( \mathbf{n}_{\gamma} \) represents the normal of the face \( \gamma \). Due to the nature of the primay Variable, the (volume-)specific total mass concentration, this represents a mass flux per cell volume.
- Parameters
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| fluxEntries | The flux entries, mass influx from cell \(j\) to \(i\). |
| timestepFlux | flow velocities for timestep estimation |
| intersection | The intersection |
| cellDataI | The cell data for cell \(i\) |
template<class TypeTag >
| void Dumux::FVTransport2P2C< TypeTag >::getFluxOnBoundary |
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ComponentVector & |
fluxEntries, |
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EntryType & |
timestepFlux, |
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const Intersection & |
intersection, |
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const CellData & |
cellDataI |
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inherited |
Get flux on Boundary.
The flux through \( \gamma \) is calculated according to the underlying pressure field, calculated by the pressure model.
\[ - A_{\gamma} \mathbf{n}^T_{\gamma} \mathbf{K} \mathbf{d}_{i-Boundary} \sum_{\alpha} \varrho_{\alpha} \lambda_{\alpha} \sum_{\kappa} X^{\kappa}_{\alpha} \left( \frac{p_{\alpha,Boundary}^t - p^{t}_{\alpha,i}}{\Delta x} + \varrho_{\alpha}\mathbf{g}^T \mathbf{d}_{i-Boundary}\right) \]
Here, \( \mathbf{u} \) is the normalized vector connecting the cell centers, and \( \mathbf{n}_{\gamma_{ij}} \) represents the normal of the face \( \gamma{ij} \).
- Parameters
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| fluxEntries | The flux entries, mass influx from cell \(j\) to \(i\). |
| timestepFlux | flow velocities for timestep estimation |
| intersection | The intersection |
| cellDataI | The cell data for cell \(i\) |
template<class TypeTag >
| void Dumux::FV2dTransport2P2CAdaptive< TypeTag >::getMpfaFlux |
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Dune::FieldVector< Scalar, 2 > & |
fluxEntries, |
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Dune::FieldVector< Scalar, 2 > & |
timestepFlux, |
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const IntersectionIterator & |
intersectionIterator, |
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CellData & |
cellDataI |
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) |
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Compute flux over an irregular interface using a mpfa method.
A mpfa l-method is applied to calculate fluxes near hanging nodes, using:
\[ - \sum_{\alpha} \varrho_{\alpha} \lambda_{\alpha} \left( \sum_k \tau_{2k} p^t_{\alpha,k} + \varrho_{\alpha} \sum_k \tau_{2k} \mathbf{g}^T \mathbf{x}_{k} \right) \sum_{\kappa} X^{\kappa}_{\alpha} \]
We provide two options: Calculating the flux expressed by twice the flux through the one unique interaction region on the hanging node if one halfedge is stored (eg on boundaries). Or using the second interaction region covering neighboring cells.
- Parameters
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| fluxEntries | The flux entries, mass influx from cell \(j\) to \(i\). |
| timestepFlux | flow velocities for timestep estimation |
| intersectionIterator | Iterator of the intersection between cell I and J |
| cellDataI | The cell data for cell \(i\) |
get geometrical Info, transmissibility matrix
Calculate the update vector and determine timestep size.
This method calculates the update vector \( u \) of the discretized equation
\[ C^{\kappa , new} = C^{\kappa , old} + u, \]
where \( u = \sum_{\gamma} \boldsymbol{v}_{\alpha} * \varrho_{\alpha} * X^{\kappa}_{\alpha} * \boldsymbol{n} * A_{\gamma} \), \( \boldsymbol{n} \) is the face normal and \( A_{\gamma} \) is the face area of face \( \gamma \). In addition to the update vector, the recommended time step size dt is calculated employing a CFL condition. This method uses a standard Tpfa method for regular fluxes, and a MPFA can be used near hanging nodes. The lengths of the vectors are resized to agree with the current grid resolution.
- Parameters
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| t | Current simulation time \(\mathrm{[s]}\) |
| [out] | dt | Time step size \(\mathrm{[s]}\) |
| [out] | updateVec | Update vector, or update estimate for secants, resp. Here in \(\mathrm{[kg/m^3]}\) |
| impet | Flag that determines if it is a real impet step or an update estimate for volume derivatives |
Reimplemented from Dumux::FVTransport2P2C< TypeTag >.
1.9.3