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3.3.0
DUNE for Multi-{Phase, Component, Scale, Physics, ...} flow and transport in porous media
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3.3.0
DUNE for Multi-{Phase, Component, Scale, Physics, ...} flow and transport in porous media
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Sequential two-phase, two-component Darcy flow. More...
Sequential two-phase, two-component Darcy flow.
Provides a Finite Volume implementation for the pressure equation of a compressible system with two components. An IMPES-like method is used for the sequential solution of the problem. Diffusion is neglected, capillarity can be regarded. Isothermal conditions and local thermodynamic equilibrium are assumed. Gravity is included.
\[ c_{total}\frac{\partial p}{\partial t} + \sum_{\kappa} \frac{\partial v_{total}}{\partial C^{\kappa}} \nabla \cdot \left( \sum_{\alpha} X^{\kappa}_{\alpha} \varrho_{\alpha} \bf{v}_{\alpha}\right) = \sum_{\kappa} \frac{\partial v_{total}}{\partial C^{\kappa}} q^{\kappa}, \]
where \(\bf{v}_{\alpha} = - \lambda_{\alpha} \bf{K} \left(\nabla p_{\alpha} + \rho_{\alpha} \bf{g} \right) \). \( c_{total} \) represents the total compressibility, for constant porosity this yields \( - \frac{\partial V_{total}}{\partial p_{\alpha}} \), \(p_{\alpha} \) 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. See paper SPE 99619 or "Analysis of a Compositional Model for Fluid Flow in Porous Media" by Chen, Qin and Ewing for derivation.
The pressure base class FVPressure assembles the matrix and right-hand-side vector and solves for the pressure vector, whereas this class provides the actual entries for the matrix and RHS vector. The partial derivatives of the actual fluid volume \( v_{total} \) are gained by using a secant method.
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. The whole flux contribution for each cell is subdivided into a storage term, a flux term and a source term. Corresponding functions (getFlux() and getFluxOnBoundary()) are provided, internal sources are directly treated.
| TypeTag | The Type Tag |
Files | |
| file | adaptiveproperties.hh |
| Defines the properties required for the adaptive sequential 2p2c models. | |
| file | 2p2c/sequential/celldata.hh |
| Storage container for discretized data of the constitutive relations for one element. | |
| file | c/sequential/celldataadaptive.hh |
| Class including the variables and data of discretized data of the constitutive relations for one element. | |
| file | celldatamultiphysics.hh |
| Storage container for discretized data for multi-physics models. | |
| file | 2p2c/sequential/fluxdata.hh |
| Class including the variables and data of discretized data of the constitutive relations. | |
| file | fv2dpressureadaptive.hh |
| Finite Volume Diffusion Model. | |
| file | fv2dtransportadaptive.hh |
| Finite volume discretization of the component transport equation. | |
| file | fv3dpressureadaptive.hh |
| Finite volume diffusion model. | |
| file | fv3dtransportadaptive.hh |
| Finite volume discretization of the component transport equation. | |
| file | fvmpfal3dinteractionvolumecontaineradaptive.hh |
| Interaction volume container for compositional adaptive 3-d (using MPFA L-method). | |
| file | fvpressure.hh |
| Finite volume 2p2c pressure model. | |
| file | fvpressurecompositional.hh |
| Base class for compositional pressure equations. | |
| file | fvpressuremultiphysics.hh |
| Finite volume 2p2c pressure model with multi-physics. | |
| file | fvtransport.hh |
| Finite volume discretization of the component transport equation. | |
| file | fvtransportmultiphysics.hh |
| Finite volume discretization of the component transport equation. | |
| file | porousmediumflow/2p2c/sequential/problem.hh |
| Base class for sequential 2p2c compositional problems. | |
| file | porousmediumflow/2p2c/sequential/properties.hh |
| Defines the properties required for the sequential 2p2c models. | |
| file | 2p2c/sequential/variableclassadaptive.hh |
| Base class holding the variables for sequential models. | |
Classes | |
| struct | Dumux::SequentialTwoPTwoCIndicesAdaptive< TypeTag > |
| Missing indices to the mpfa2p model. More... | |
| class | Dumux::CellData2P2C< TypeTag > |
| Storage container for discretized data of the constitutive relations for one element. More... | |
| class | Dumux::CellData2P2CAdaptive< TypeTag > |
| Class including the data of a grid cell needed if an adaptive grid is used. More... | |
| class | Dumux::CellData2P2CMultiPhysics< TypeTag > |
| Storage container for discretized data for multiphysics models. More... | |
| class | Dumux::FluxData2P2C< TypeTag > |
| Class including the variables and data of discretized data of the constitutive relations. More... | |
| class | Dumux::FV2dPressure2P2CAdaptive< TypeTag > |
| The finite volume model for the solution of the compositional pressure equation. More... | |
| class | Dumux::FV2dTransport2P2CAdaptive< TypeTag > |
| Compositional Transport step in a Finite Volume discretization for a adaptive 2D-grid. More... | |
| class | Dumux::FV3dPressure2P2CAdaptive< TypeTag > |
| The finite volume model for the solution of the compositional pressure equation. More... | |
| class | Dumux::FV3dTransport2P2CAdaptive< TypeTag > |
| Compositional transport step in a finite volume discretization. More... | |
| class | Dumux::FvMpfaL3d2P2CInteractionVolumeContainerAdaptive< TypeTag > |
| Interaction volume container for compositional adaptive 3-d (using MPFA L-method) Model. More... | |
| class | Dumux::FVPressure2P2C< TypeTag > |
| The finite volume model for the solution of the compositional pressure equation. More... | |
| class | Dumux::FVPressureCompositional< TypeTag > |
| The finite volume model for the solution of the compositional pressure equation. More... | |
| class | Dumux::FVPressure2P2CMultiPhysics< TypeTag > |
| The finite volume model for the solution of the compositional pressure equation. More... | |
| class | Dumux::FVTransport2P2C< TypeTag > |
| Compositional transport step in a Finite Volume discretization. More... | |
| class | Dumux::FVTransport2P2CMultiPhysics< TypeTag > |
| Compositional transport step in a finite volume discretization. More... | |
| class | Dumux::IMPETProblem2P2C< TypeTag > |
| Base class for all compositional 2-phase problems which use an impet algorithm. More... | |
| class | Dumux::VariableClass2P2CAdaptive< TypeTag > |
| Class holding additionally mpfa data of adaptive compositional models. More... | |
1.9.3