Revision 421e76f6667a2adabc54ddd03476ecaf8aca4596 authored by Dmitri Naumov on 15 September 2021, 19:53:50 UTC, committed by Dmitri Naumov on 16 September 2021, 11:04:03 UTC
1 parent cba1123
RichardsComponentTransportProcess.h
/**
* \file
* \copyright
* Copyright (c) 2012-2021, OpenGeoSys Community (http://www.opengeosys.org)
* Distributed under a Modified BSD License.
* See accompanying file LICENSE.txt or
* http://www.opengeosys.org/project/license
*
*/
#pragma once
#include "RichardsComponentTransportFEM.h"
#include "RichardsComponentTransportProcessData.h"
#include "NumLib/Extrapolation/LocalLinearLeastSquaresExtrapolator.h"
#include "ProcessLib/Process.h"
namespace ProcessLib
{
namespace RichardsComponentTransport
{
/**
* # RichardsComponentTransport process
*
* ## Governing Equations
*
* ### Richards Flow
*
* The flow process is described by
* \f[
* \phi \frac{\partial \rho_w}{\partial p} \frac{\partial p}{\partial t} S
* - \phi \rho_w \frac{\partial S}{\partial p_c}
* \frac{\partial p_c}{\partial t}
* - \nabla \cdot \left[\rho_w \frac{k_{\mathrm{rel}} \kappa}{\mu}
* \nabla \left( p + \rho_w g z \right)\right]
* - Q_p = 0,
* \f]
* where
* - \f$\phi\f$ is the porosity,
* - \f$S\f$ is the saturation,
* - \f$p\f$ is the pressure,
* - \f$k_{\mathrm{rel}}\f$ is the relative permeability (depending on \f$S\f$),
* - \f$\kappa\f$ is the specific permeability,
* - \f$\mu\f$ is viscosity of the fluid,
* - \f$\rho_w\f$ is the mass density of the fluid, and
* - \f$g\f$ is the gravitational acceleration.
*
* Here it is assumed, that
* - the porosity is constant and
* - the pressure of the gas phase is zero.
*
* The capillary pressure is given by
* \f[
* p_c = \frac{\rho_w g}{\alpha}
* \left[S_{\mathrm{eff}}^{-\frac{1}{m}} - 1\right]^{\frac{1}{n}}
* \f]
* and the effective saturation by
* \f[
* S_{\mathrm{eff}} = \frac{S-S_r}{S_{\max} - S_r}
* \f]
*
* ### Mass Transport
* The mass transport process is described by
* \f[
* \phi R \frac{\partial C}{\partial t}
+ \nabla \cdot \left(\vec{q} C - D \nabla C \right)
+ \phi R \vartheta C - Q_C = 0
* \f]
* where
* - \f$R\f$ is the retardation factor,
* - \f$C\f$ is the concentration,
* - \f$\vec{q} = \frac{k_{\mathrm{rel}} \kappa}{\mu(C)}
* \nabla \left( p + \rho_w g z \right)\f$ is the Darcy velocity,
* - \f$D\f$ is the hydrodynamic dispersion tensor,
* - \f$\vartheta\f$ is the decay rate.
*
* For the hydrodynamic dispersion tensor the relation
* \f[
* D = (\phi D_d + \beta_T \|\vec{q}\|) I + (\beta_L - \beta_T) \frac{\vec{q}
* \vec{q}^T}{\|\vec{q}\|}
* \f]
* is implemented, where \f$D_d\f$ is the molecular diffusion coefficient,
* \f$\beta_L\f$ the longitudinal dispersivity of chemical species, and
* \f$\beta_T\f$ the transverse dispersivity of chemical species.
*
* The implementation uses a monolithic approach, i.e., both processes
* are assembled within one global system of equations.
*
* ## Process Coupling
*
* The advective term of the concentration equation is given by the Richards
* flow process, i.e., the concentration distribution depends on
* darcy velocity of the Richards flow process. On the other hand the
* concentration dependencies of the viscosity and density in the groundwater
* flow couples the unsaturated H process to the C process.
*
* \note At the moment there is not any coupling by source or sink terms, i.e.,
* the coupling is implemented only by density changes due to concentration
* changes in the buoyance term in the groundwater flow. This coupling schema is
* referred to as the Boussinesq approximation.
* */
class RichardsComponentTransportProcess final : public Process
{
public:
RichardsComponentTransportProcess(
std::string name,
MeshLib::Mesh& mesh,
std::unique_ptr<ProcessLib::AbstractJacobianAssembler>&&
jacobian_assembler,
std::vector<std::unique_ptr<ParameterLib::ParameterBase>> const&
parameters,
unsigned const integration_order,
std::vector<std::vector<std::reference_wrapper<ProcessVariable>>>&&
process_variables,
RichardsComponentTransportProcessData&& process_data,
SecondaryVariableCollection&& secondary_variables,
bool const use_monolithic_scheme);
//! \name ODESystem interface
//! @{
bool isLinear() const override { return false; }
//! @}
private:
void initializeConcreteProcess(
NumLib::LocalToGlobalIndexMap const& dof_table,
MeshLib::Mesh const& mesh,
unsigned const integration_order) override;
void assembleConcreteProcess(const double t, double const dt,
std::vector<GlobalVector*> const& x,
std::vector<GlobalVector*> const& xdot,
int const process_id, GlobalMatrix& M,
GlobalMatrix& K, GlobalVector& b) override;
void assembleWithJacobianConcreteProcess(
const double t, double const dt, std::vector<GlobalVector*> const& x,
std::vector<GlobalVector*> const& xdot, const double dxdot_dx,
const double dx_dx, int const process_id, GlobalMatrix& M,
GlobalMatrix& K, GlobalVector& b, GlobalMatrix& Jac) override;
RichardsComponentTransportProcessData _process_data;
std::vector<
std::unique_ptr<RichardsComponentTransportLocalAssemblerInterface>>
_local_assemblers;
};
} // namespace RichardsComponentTransport
} // namespace ProcessLib
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