model.hh File Reference

Large-deformation poroelastic model with volumetric-isochoric split. More...

#include <tuple>
#include <dumux/common/properties.hh>
#include <dumux/common/properties/model.hh>
#include <dumux/discretization/defaultgridvariables.hh>
#include "localresidual.hh"
#include "variables.hh"

Go to the source code of this file.

Description

Physical model

Three-field mixed formulation \((\mathbf{d}, p_s, p_f)\) for a saturated hyperelastic porous medium undergoing finite deformations.

Kinematics

\[ \mathbf{F} = \mathbf{I} + \nabla_X \mathbf{d}, \quad J = \det\mathbf{F}, \quad \mathbf{C} = \mathbf{F}^\top\mathbf{F}. \]

Governing equations

Momentum (displacement \(\mathbf{d}\)):

\[ -\nabla_X \cdot \mathbf{P} = \mathbf{f}, \qquad \mathbf{P} = \mathbf{P}_\text{iso}(\mathbf{F}) + (p_s - \alpha_B p_f)\, J\, \mathbf{F}^{-\top}, \]

where the isochoric part of the drained skeleton stress \(\mathbf{P}_\text{iso}\) is supplied by the problem via isochoricFirstPiolaKirchhoffStressTensor(F, elemDisc, ipGlobal) and the body force \(\mathbf{f}\) via the problem's source.

Solid pressure ( \(p_s\), algebraic):

\[ p_s^{\mathrm{eq}}(J) - p_s = 0 \]

(volumetric constitutive law; \(p_s^{\mathrm{eq}}\) supplied by the problem via volumetricPressure(J)).

Fluid mass balance ( \(p_f\), transient):

\[ \frac{\partial}{\partial t}\!\left(\alpha_B J + S_p p_f\right) - \nabla_X \cdot \!\left(J\,\frac{\kappa}{\mu_f}\,\mathbf{C}^{-1} \nabla_X p_f\right) = q, \]

with the Biot coefficient \(\alpha_B\), the storage coefficient \(S_p = 1/M\) (inverse Biot modulus, \(S_p = 0\) for incompressible constituents) and the fluid source \(q\) given by the problem's source. In the small-strain limit \(J \approx 1 + \nabla \cdot \mathbf{d}\) this is Biot's storage equation.

The spatial parameters provide biotCoefficient(element, elemDisc, ipGlobal), storageCoefficient(element, elemDisc, ipGlobal), permeability(element, elemDisc, ipGlobal, J) and fluidViscosity(element, elemDisc).

The type tags PoroElasticLargeDefMomentumModel, PoroElasticLargeDefSolidPressureModel and PoroElasticLargeDefFluidPressureModel are coupled via PoroElasticLargeDefCouplingManager and assembled with Experimental::MultiStageMultiDomainAssembler.

Classes
struct	Dumux::PoroElasticLargeDefMomentumIndices< dim >
	Index set for the momentum subdomain. More...
struct	Dumux::PoroElasticLargeDefMomentumModelTraits< dim >
	Model traits for the momentum subdomain ( \(\dim\) displacement DOFs per node). More...
struct	Dumux::PoroElasticLargeDefMomentumVVTraits< PV, MT >
struct	Dumux::PoroElasticLargeDefSolidPressureIndices
	Index set for the solid pressure subdomain. More...
struct	Dumux::PoroElasticLargeDefSolidPressureModelTraits
	Model traits for the solid pressure subdomain (1 pressure DOF per node). More...
struct	Dumux::PoroElasticLargeDefSolidPressureVVTraits< PV, MT >
struct	Dumux::PoroElasticLargeDefFluidPressureIndices
	Index set for the fluid pressure subdomain. More...
struct	Dumux::PoroElasticLargeDefFluidPressureModelTraits
	Model traits for the fluid pressure subdomain (1 fluid pressure DOF per node). More...
struct	Dumux::PoroElasticLargeDefFluidPressureVVTraits< PV, MT >
struct	Dumux::Properties::TTag::PoroElasticLargeDefMomentumModel
struct	Dumux::Properties::TTag::PoroElasticLargeDefSolidPressureModel
struct	Dumux::Properties::TTag::PoroElasticLargeDefFluidPressureModel
struct	Dumux::Properties::ModelTraits< TypeTag, TTag::PoroElasticLargeDefMomentumModel >
struct	Dumux::Properties::LocalResidual< TypeTag, TTag::PoroElasticLargeDefMomentumModel >
struct	Dumux::Properties::Variables< TypeTag, TTag::PoroElasticLargeDefMomentumModel >
struct	Dumux::Properties::VolumeVariables< TypeTag, TTag::PoroElasticLargeDefMomentumModel >
	Code asking for the volume variables gets the variables per local dof. More...
struct	Dumux::Properties::GridVariables< TypeTag, TTag::PoroElasticLargeDefMomentumModel >
	The grid variables, with the cache selected depending on the discretization scheme. More...
struct	Dumux::Properties::ModelTraits< TypeTag, TTag::PoroElasticLargeDefSolidPressureModel >
struct	Dumux::Properties::LocalResidual< TypeTag, TTag::PoroElasticLargeDefSolidPressureModel >
struct	Dumux::Properties::Variables< TypeTag, TTag::PoroElasticLargeDefSolidPressureModel >
struct	Dumux::Properties::VolumeVariables< TypeTag, TTag::PoroElasticLargeDefSolidPressureModel >
	Code asking for the volume variables gets the variables per local dof. More...
struct	Dumux::Properties::GridVariables< TypeTag, TTag::PoroElasticLargeDefSolidPressureModel >
	The grid variables, with the cache selected depending on the discretization scheme. More...
struct	Dumux::Properties::ModelTraits< TypeTag, TTag::PoroElasticLargeDefFluidPressureModel >
struct	Dumux::Properties::LocalResidual< TypeTag, TTag::PoroElasticLargeDefFluidPressureModel >
struct	Dumux::Properties::Variables< TypeTag, TTag::PoroElasticLargeDefFluidPressureModel >
struct	Dumux::Properties::VolumeVariables< TypeTag, TTag::PoroElasticLargeDefFluidPressureModel >
	Code asking for the volume variables gets the variables per local dof. More...
struct	Dumux::Properties::GridVariables< TypeTag, TTag::PoroElasticLargeDefFluidPressureModel >
	The grid variables, with the cache selected depending on the discretization scheme. More...

Namespaces
namespace	Dumux
namespace	Dumux::Properties
	The energy balance equation for a porous solid.
namespace	Dumux::Properties::TTag
	Type tag for numeric models.