transport_dg.hh

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/*!
 *
 * Copyright (C) 2015 Technical University of Liberec.  All rights reserved.
 * 
 * This program is free software; you can redistribute it and/or modify it under
 * the terms of the GNU General Public License version 3 as published by the
 * Free Software Foundation. (http://www.gnu.org/licenses/gpl-3.0.en.html)
 * 
 * This program is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
 * FOR A PARTICULAR PURPOSE.  See the GNU General Public License for more details.
 *
 * 
 * @file    transport_dg.hh
 * @brief   Discontinuous Galerkin method for equation of transport with dispersion.
 * @author  Jan Stebel
 */
 
#ifndef TRANSPORT_DG_HH_
#define TRANSPORT_DG_HH_
 
#include <math.h>                              // for fabs
#include <string.h>                            // for memcpy
#include <algorithm>                           // for max
 
#include <string>                              // for operator<<
#include <vector>                              // for vector
#include <armadillo>
#include "fem/update_flags.hh"                 // for operator|
#include "fem/mapping_p1.hh"
#include "fields/field_values.hh"              // for FieldValue<>::Scalar
#include "fields/field.hh"
#include "fields/multi_field.hh"
#include "la/vector_mpi.hh"
#include "fields/equation_output.hh"
#include "la/linsys.hh"
#include "input/accessors.hh"                  // for ExcAccessorForNullStorage
#include "input/accessors_impl.hh"             // for Record::val
#include "input/storage.hh"                    // for ExcStorageTypeMismatch
#include "input/type_base.hh"                  // for Array
#include "input/type_generic.hh"               // for Instance
#include "input/type_record.hh"                // for Record::ExcRecordKeyNo...
#include "mesh/long_idx.hh"                    // for LongIdx
#include "mesh/accessors.hh"                   // for ElementAccessor
#include "mesh/elements.h"                     // for Element::dim, Element:...
#include "mesh/neighbours.h"                   // for Neighbour::element
#include "mesh/side_impl.hh"                   // for Side::cond, Side::cond...
#include "mesh/sides.h"                        // for SideIter
#include "mpi.h"                               // for MPI_Comm_rank
#include "petscmat.h"                          // for Mat, MatDestroy
#include "petscvec.h"                          // for Vec, VecDestroy, VecSc...
#include "transport/concentration_model.hh"    // for ConcentrationTransport...
#include "transport/heat_model.hh"             // for HeatTransferModel, Hea...
 
class DiscreteSpace;
class Distribution;
class OutputTime;
class DOFHandlerMultiDim;
template<unsigned int dim, unsigned int spacedim> class FEValuesBase;
template<unsigned int dim> class FiniteElement;
template<unsigned int dim, unsigned int spacedim> class Mapping;
template<unsigned int dim> class Quadrature;
namespace Input { namespace Type { class Selection; } }
 
 
 
/**
 * Auxiliary container class for Finite element and related objects of all dimensions.
 * Its purpose is to provide templated access to these objects, applicable in
 * the assembling methods.
 */
class FEObjects {
public:
 
    FEObjects(Mesh *mesh_, unsigned int fe_order);
    ~FEObjects();
 
    template<unsigned int dim>
    inline FiniteElement<dim> *fe();
 
    template<unsigned int dim>
    inline FiniteElement<dim> *fe_rt();
 
    template<unsigned int dim>
    inline Quadrature<dim> *q();
 
    template<unsigned int dim>
    inline MappingP1<dim,3> *mapping();
 
    inline std::shared_ptr<DOFHandlerMultiDim> dh();
 
private:
 
    /// Finite elements for the solution of the advection-diffusion equation.
    FiniteElement<0> *fe0_;
    FiniteElement<1> *fe1_;
    FiniteElement<2> *fe2_;
    FiniteElement<3> *fe3_;
 
    /// Finite elements for the water velocity field.
    FiniteElement<1> *fe_rt1_;
    FiniteElement<2> *fe_rt2_;
    FiniteElement<3> *fe_rt3_;
 
    /// Quadratures used in assembling methods.
    Quadrature<0> *q0_;
    Quadrature<1> *q1_;
    Quadrature<2> *q2_;
    Quadrature<3> *q3_;
 
    /// Auxiliary mappings of reference elements.
    MappingP1<1,3> *map1_;
    MappingP1<2,3> *map2_;
    MappingP1<3,3> *map3_;
    
        std::shared_ptr<DiscreteSpace> ds_;
 
    /// Object for distribution of dofs.
    std::shared_ptr<DOFHandlerMultiDim> dh_;
};
 
 
 
/**
 * @brief Transport with dispersion implemented using discontinuous Galerkin method.
 *
 * TransportDG implements the discontinuous Galerkin method for the transport and diffusion of substances.
 * The concentration @f$ c_i ~[kg/m^3]@f$ of the i-th substance is governed by the advection-diffusion equation
 * @f[
 *      \partial_t c_i + \mathbf v\cdot\nabla c_i - \mathrm{div}(D\nabla c_i) = F \mbox{ in }\Omega^d,
 * @f]
 * where @f$\mathbf v@f$ is the fluid velocity and @f$\Omega^d@f$ the @f$d@f$-dimensional domain, respectively.
 * The hydrodynamic dispersivity tensor @f$\mathbf D ~[m^2/s]@f$ is given by:
 * @f[
 *      \mathbf D = D_m\mathbf I + |\mathbf v|\left(\alpha_T\mathbf I + (\alpha_L-\alpha_T)\frac{\mathbf v\otimes\mathbf v}{|\mathbf v|^2}\right).
 * @f]
 * The molecular dispersivity @f$D_m~[m^2/s]@f$, as well as the longitudal and transversal dispersivity @f$\alpha_L,~\alpha_T~[m]@f$ are input parameters of the model.
 *
 * For lower dimensions @f$d=1,2@f$ the advection-diffusion equation is multiplied by the fracture cross-cut @f$\delta^d~[m^{3-d}]@f$.
 *
 * The boundary @f$\partial\Omega^d@f$ is divided into three disjoint parts @f$\Gamma^d_D\cup\Gamma^d_N\cup\Gamma^d_F@f$.
 * We prescribe the following boundary conditions:
 * @f{eqnarray*}{
 *      c_i^d &= c_{iD}^d &\mbox{ on }\Gamma^d_D \mbox{ (Dirichlet)},\\
 *      \mathbf D^d\nabla c_i^d\cdot\mathbf n &= 0 &\mbox{ on }\Gamma^d_N \mbox{ (Neumann)},
 * @f}
 * The transfer of mass through fractures is described by the transmission conditions on @f$\Gamma^d_F@f$:
 * @f[
 *      -\mathbf D^d\nabla c_i^d\cdot\mathbf n = \sigma(c_i^d-c_i^{d-1}) + \left\{\begin{array}{cl}0 &\mbox{ if }\mathbf v^d\cdot\mathbf n\ge 0\\\mathbf v^d\cdot\mathbf n(c_i^{d-1}-c_i^d) & \mbox{ if }\mathbf v^d\cdot\mathbf n<0\end{array}\right.,\qquad
 *      F^{d-1} = (\sigma + |\mathbf v^d\cdot\mathbf n|)(c_i^d-c_i^{d-1}).
 * @f]
 * Here @f$\mathbf n@f$ stands for the unit outward normal vector to @f$\partial\Omega^d@f$.
 * The coefficient @f$\sigma@f$ determines the transfer of mass through fractures due to diffusion.
 *
 * @ingroup transport_mod
 *
 */
template<class Model>
class TransportDG : public Model
{
public:
 
    class EqData : public Model::ModelEqData {
    public:
 
        EqData();
 
        MultiField<3, FieldValue<3>::Scalar> fracture_sigma;    ///< Transition parameter for diffusive transfer on fractures (for each substance).
        MultiField<3, FieldValue<3>::Scalar> dg_penalty;        ///< Penalty enforcing inter-element continuity of solution (for each substance).
        Field<3, FieldValue<3>::Scalar> region_id;
        Field<3, FieldValue<3>::Scalar> subdomain;
 
        EquationOutput output_fields;
 
    };
 
 
 
    enum DGVariant {
        // Non-symmetric weighted interior penalty DG
        non_symmetric = -1,
 
        // Incomplete weighted interior penalty DG
        incomplete = 0,
 
        // Symmetric weighted interior penalty DG
        symmetric = 1
    };
 
    /**
     * @brief Constructor.
     * @param init_mesh         computational mesh
     * @param in_rec            input record
     */
    TransportDG(Mesh &init_mesh, const Input::Record in_rec);
    /**
 
     * @brief Declare input record type for the equation TransportDG.
     */
    static const Input::Type::Record & get_input_type();
 
    /**
     * @brief Input type for the DG variant selection.
     */
    static const Input::Type::Selection & get_dg_variant_selection_input_type();
 
    /**
     * @brief Initialize solution in the zero time.
     */
    void zero_time_step() override;
    
    bool evaluate_time_constraint(double &time_constraint)
    { return false; }
 
    /**
     * @brief Computes the solution in one time instant.
     */
    void update_solution() override;
 
    /**
     * @brief Postprocesses the solution and writes to output file.
     */
    void output_data();
 
    /**
     * @brief Destructor.
     */
    ~TransportDG();
 
    void initialize() override;
 
    void calculate_cumulative_balance();
 
    const Vec &get_solution(unsigned int sbi)
    { return ls[sbi]->get_solution(); }
 
    double **get_concentration_matrix()
    { return solution_elem_; }
 
    void calculate_concentration_matrix();
 
    void update_after_reactions(bool solution_changed);
 
    void get_par_info(LongIdx * &el_4_loc, Distribution * &el_ds);
 
    LongIdx *get_row_4_el();
 
 
 
 
private:
    /// Registrar of class to factory
    static const int registrar;
 
    inline typename Model::ModelEqData &data() { return data_; }
 
    void preallocate();
 
    /**
     * @brief Assembles the mass matrix.
     *
     * The routine just calls templated method assemble_mass_matrix() for each
     * space dimension.
     */
    void assemble_mass_matrix();
 
    /**
     * @brief Assembles the mass matrix for the given dimension.
     */
    template<unsigned int dim>
    void assemble_mass_matrix();
 
    /**
     * @brief Assembles the stiffness matrix.
     *
     * This routine just calls assemble_volume_integrals(), assemble_fluxes_boundary(),
     * assemble_fluxes_element_element() and assemble_fluxes_element_side() for each
     * space dimension.
     */
    void assemble_stiffness_matrix();
 
    /**
     * @brief Assembles the volume integrals into the stiffness matrix.
    */
    template<unsigned int dim>
    void assemble_volume_integrals();
 
    /**
     * @brief Assembles the right hand side due to volume sources.
     *
     * This method just calls set_sources() for each space dimension.
     */
    void set_sources();
 
    /**
     * @brief Assembles the right hand side vector due to volume sources.
     */
    template<unsigned int dim>
    void set_sources();
 
    /**
     * @brief Assembles the fluxes on the boundary.
     */
    template<unsigned int dim>
    void assemble_fluxes_boundary();
 
    /**
     * @brief Assembles the fluxes between elements of the same dimension.
     */
    template<unsigned int dim>
    void assemble_fluxes_element_element();
 
    /**
     * @brief Assembles the fluxes between elements of different dimensions.
     */
    template<unsigned int dim>
    void assemble_fluxes_element_side();
 
 
    /**
     * @brief Assembles the r.h.s. components corresponding to the Dirichlet boundary conditions.
     *
     * The routine just calls templated method set_boundary_condition() for each space dimension.
     */
    void set_boundary_conditions();
 
    /**
     * @brief Assembles the r.h.s. components corresponding to the Dirichlet boundary conditions
     * for a given space dimension.
     */
    template<unsigned int dim>
    void set_boundary_conditions();
 
    /**
     * @brief Calculates the velocity field on a given @p dim dimensional cell.
     *
     * @param cell     The cell.
     * @param velocity The computed velocity field (at quadrature points).
     * @param fv       The FEValues class providing the quadrature points
     *                 and the shape functions for velocity.
     */
    template<unsigned int dim>
    void calculate_velocity(const ElementAccessor<3> &cell, std::vector<arma::vec3> &velocity, FEValuesBase<dim,3> &fv);
 
    /**
     * @brief Calculates the dispersivity (diffusivity) tensor from the velocity field.
     *
     * @param K        The computed dispersivity tensor.
     * @param velocity The velocity field (at quadrature points).
     * @param Dm       Molecular diffusivities.
     * @param alphaL   Longitudal dispersivities.
     * @param alphaT   Transversal dispersivities.
     * @param porosity  Porosities.
     * @param cross_cut Cross-cuts of higher dimension.
     */
//  void calculate_dispersivity_tensor(arma::mat33 &K, const arma::vec3 &velocity,
//          double Dm, double alphaL, double alphaT, double porosity,
//          double cross_cut);
 
    /**
     * @brief Sets up some parameters of the DG method for two sides of an edge.
     *
     * @param edg               The edge.
     * @param s1                Side 1.
     * @param s2                Side 2.
     * @param K_size            Size of vector of tensors K.
     * @param K1                Dispersivity tensors on side s1 (in quadrature points).
     * @param K2                Dispersivity tensors on side s2 (in quadrature points).
     * @param normal_vector     Normal vector to side 0 of the neighbour
     *                          (assumed constant along the side).
     * @param alpha1, alpha2    Penalty parameter that influences the continuity
     *                          of the solution (large value=more continuity).
     * @param gamma             Computed penalty parameters.
     * @param omega             Computed weights.
     * @param transport_flux    Computed flux from side s1 to side s2.
     */
    void set_DG_parameters_edge(const Edge &edg,
            const int s1,
            const int s2,
            const int K_size,
            const std::vector<arma::mat33> &K1,
            const std::vector<arma::mat33> &K2,
            const std::vector<double> &fluxes,
            const arma::vec3 &normal_vector,
            const double alpha1,
            const double alpha2,
            double &gamma,
            double *omega,
            double &transport_flux);
 
    /**
     * @brief Sets up parameters of the DG method on a given boundary edge.
     *
     * Assumption is that the edge consists of only 1 side.
     * @param side              The boundary side.
     * @param K_size            Size of vector of tensors K.
     * @param K                 Dispersivity tensor.
     * @param ad_vector         Advection vector.
     * @param normal_vector     Normal vector (assumed constant along the edge).
     * @param alpha             Penalty parameter that influences the continuity
     *                          of the solution (large value=more continuity).
     * @param gamma             Computed penalty parameters.
     */
    void set_DG_parameters_boundary(const SideIter side,
                const int K_size,
                const std::vector<arma::mat33> &K,
                const double flux,
                const arma::vec3 &normal_vector,
                const double alpha,
                double &gamma);
 
 
    /**
     * @brief Sets the initial condition.
     */
    void set_initial_condition();
 
    /**
     * @brief Assembles the auxiliary linear system to calculate the initial solution
     * as L^2-projection of the prescribed initial condition.
     */
    template<unsigned int dim>
    void prepare_initial_condition();
 
 
 
    /// @name Physical parameters
    // @{
 
    /// Field data for model parameters.
    EqData data_;
 
    // @}
 
 
    /// @name Parameters of the numerical method
    // @{
 
    /// Finite element objects
    FEObjects *feo;
 
    /// Penalty parameters.
    std::vector<std::vector<double> > gamma;
 
    /// DG variant ((non-)symmetric/incomplete
    int dg_variant;
 
    /// Polynomial order of finite elements.
    unsigned int dg_order;
 
    // @}
 
 
 
    /// @name Solution of algebraic system
    // @{
 
    /// Vector of right hand side.
    std::vector<Vec> rhs;
 
    /// The stiffness matrix.
    std::vector<Mat> stiffness_matrix;
 
    /// The mass matrix.
    std::vector<Mat> mass_matrix;
    
    /// Mass from previous time instant (necessary when coefficients of mass matrix change in time).
    std::vector<Vec> mass_vec;
    
    /// Auxiliary vectors for calculation of sources in balance due to retardation (e.g. sorption).
    std::vector<Vec> ret_vec;
 
    /// Linear algebra system for the transport equation.
    LinSys **ls;
 
    /// Linear algebra system for the time derivative (actually it is used only for handling the matrix structures).
    LinSys **ls_dt;
 
    /// Element averages of solution (the array is passed to reactions in operator splitting).
    double **solution_elem_;
 
    // @}
 
 
    /// @name Output to file
    // @{
 
    /// Array for storing the output solution data.
    //vector<double*> output_solution;
 
    /// Vector of solution data.
    vector<VectorMPI> output_vec;
 
    /// Record with input specification.
    Input::Record input_rec;
 
 
    // @}
 
 
    /// @name Auxiliary fields used during assembly
    // @{
 
    /// Mass matrix coefficients.
    vector<double> mm_coef;
    /// Retardation coefficient due to sorption.
    vector<vector<double> > ret_coef;
    /// Temporary values of increments due to retardation (e.g. sorption)
    vector<double> ret_sources, ret_sources_prev;
    /// Advection coefficients.
    vector<vector<arma::vec3> > ad_coef;
    /// Diffusion coefficients.
    vector<vector<arma::mat33> > dif_coef;
    /// Advection coefficients on edges.
    vector<vector<vector<arma::vec3> > > ad_coef_edg;
    /// Diffusion coefficients on edges.
    vector<vector<vector<arma::mat33> > > dif_coef_edg;
 
    // @}
 
 
 
 
    /// @name Other
    // @{
 
    /// Indicates whether matrices have been preallocated.
    bool allocation_done;
 
    // @}
};
 
 
 
 
 
 
#endif /* TRANSPORT_DG_HH_ */