biot_tools.h

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/*
 * Copyright (c) 2019-2020:  G-CSC, Goethe University Frankfurt
 * Author: Arne Naegel
 *
 * This file is part of UG4.
 *
 * UG4 is free software: you can redistribute it and/or modify it under the
 * terms of the GNU Lesser General Public License version 3 (as published by the
 * Free Software Foundation) with the following additional attribution
 * requirements (according to LGPL/GPL v3 §7):
 *
 * (1) The following notice must be displayed in the Appropriate Legal Notices
 * of covered and combined works: "Based on UG4 (www.ug4.org/license)".
 *
 * (2) The following notice must be displayed at a prominent place in the
 * terminal output of covered works: "Based on UG4 (www.ug4.org/license)".
 *
 * (3) The following bibliography is recommended for citation and must be
 * preserved in all covered files:
 * "Reiter, S., Vogel, A., Heppner, I., Rupp, M., and Wittum, G. A massively
 *   parallel geometric multigrid solver on hierarchically distributed grids.
 *   Computing and visualization in science 16, 4 (2013), 151-164"
 * "Vogel, A., Reiter, S., Rupp, M., Nägel, A., and Wittum, G. UG4 -- a novel
 *   flexible software system for simulating pde based models on high performance
 *   computers. Computing and visualization in science 16, 4 (2013), 165-179"
 *
 * 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 Lesser General Public License for more details.
 */
 
#ifndef __BIOT_TOOLS_H__
#define __BIOT_TOOLS_H__
 
 
// std libs.
#include <string.h>
#include <vector>
 
// Boost
#include <boost/math/special_functions/bessel.hpp>
 
// UG4 dependencies.
#include "lib_disc/spatial_disc/domain_disc.h"
#include "lib_disc/spatial_disc/elem_disc/elem_disc_interface.h"
#include "lib_disc/spatial_disc/user_data/linker/scale_add_linker.h"
 
 
// Plugin dependencies.
#include "../ConvectionDiffusion/fe/convection_diffusion_fe.h"
#include "../ConvectionDiffusion/fe/convection_diffusion_stab_fe.h"
#include "../ConvectionDiffusion/fv1/convection_diffusion_fv1.h"
#include "../SmallStrainMechanics/small_strain_mech.h"
#include "../SmallStrainMechanics/material_laws/hooke.h"
 
#ifdef UG_JSON
#include <nlohmann/json.hpp>
#endif
 
namespace ug {
namespace Poroelasticity {
 
double BesselJ0(double x);
double BesselJ1(double x);
 
 
 
 
struct BiotDiscConfig
{
  BiotDiscConfig(const char* uCmp, const char *pCmp)
  : m_uCmp(uCmp), m_pCmp(pCmp), m_uOrder(2), m_pOrder(1), m_dStab(0.0),
   m_bSteadyStateMechanics(true), m_identityFlow(false)
  {}
  BiotDiscConfig(const char* uCmp, const char *pCmp) {…}
 
  BiotDiscConfig(const char* uCmp, int uorder, const char *pCmp, int porder)
  : m_uCmp(uCmp), m_pCmp(pCmp), m_uOrder(uorder), m_pOrder(porder), m_dStab(0.0),
   m_bSteadyStateMechanics(true), m_identityFlow(false)  {}
  BiotDiscConfig(const char* uCmp, int uorder, const char *pCmp, int porder) {…}
 
  BiotDiscConfig(const char* uCmp, int uorder, const char *pCmp, int porder, double dStab)
  : m_uCmp(uCmp), m_pCmp(pCmp), m_uOrder(uorder), m_pOrder(porder), m_dStab(dStab), 
  m_bSteadyStateMechanics(true), m_identityFlow(false) {}
  BiotDiscConfig(const char* uCmp, int uorder, const char *pCmp, int porder, double dStab) {…}
 
  BiotDiscConfig(const char* uCmp, int uorder, const char *pCmp, int porder, bool bSteadyStateMechanics)
  : m_uCmp(uCmp), m_pCmp(pCmp), m_uOrder(uorder), m_pOrder(porder), m_dStab(0.0), 
  m_bSteadyStateMechanics(bSteadyStateMechanics), m_identityFlow(false) {}
  BiotDiscConfig(const char* uCmp, int uorder, const char *pCmp, int porder, bool bSteadyStateMechanics) {…}
 
 
  void set_stabilization(double dStab)
  { m_dStab = dStab; }
  void set_stabilization(double dStab) {…}
 
  int get_porder() const {return m_pOrder;}
  int get_uorder() const {return m_uOrder;}
 
  std::string m_uCmp, m_pCmp;
  int m_uOrder, m_pOrder;
  double m_dStab;
 
  bool m_bSteadyStateMechanics;
  bool m_identityFlow;
};
struct BiotDiscConfig {…};
 
/*
 *
 *
 {
 
  {"alpha":1.0,"beta":2.799999999999999e-06,"kappa":0.01,"lambda":142857.1428571429,"mu":35714.28571428572,"phi":0.0,"subsets":"INNER"}
 } */
class BiotSubsetParameters
{
public:
 
  BiotSubsetParameters() {}
 
  BiotSubsetParameters(const char *s, number alpha, number kappa, number phi, number lambda, number mu, number beta)
  : m_subsets(s), m_alpha(alpha), m_kappa(kappa), m_phi(phi), m_lambda(lambda), m_mu(mu), m_beta_uzawa(beta)
  {}
  BiotSubsetParameters(const char *s, number alpha, number kappa, number phi, number lambda, number mu, number beta) {…}
 
  std::string get_subsets() const { return m_subsets; }
  void set_subsets(std::string subset) { m_subsets = subset; }
 
  number get_alpha() const { return m_alpha; }
  void set_alpha(number alpha)  { m_alpha = alpha; }
 
  number get_phi() const { return m_phi; }
  void set_phi(number phi) { m_phi = phi; }
 
  number get_kappa() const { return m_kappa; }
  void set_kappa(number kappa) { m_kappa = kappa; }
 
  number get_lambda() const { return m_lambda; }
  void set_lambda(number lambda) { m_lambda = lambda; }
 
  number get_mu() const { return m_mu; }
  void set_mu(number mu) { m_mu = mu; }
 
  number get_beta() const { return m_beta_uzawa; }
  void set_beta(number beta) { m_beta_uzawa = beta; }
 
#ifdef UG_JSON
  friend void from_json(const nlohmann::json& j, BiotSubsetParameters& p);
#endif
 
protected:
  std::string m_subsets;
 
  number m_alpha;
  number m_kappa;
 
  number m_phi;
  number m_lambda;
  number m_mu;
 
  number m_beta_uzawa;
};
class BiotSubsetParameters {…};
 
#ifdef UG_JSON
void to_json(nlohmann::json &j, const BiotSubsetParameters &p);
void from_json(const nlohmann::json &j, BiotSubsetParameters &p);
#endif
 
 
 
double DefaultCharTime(const BiotSubsetParameters& p, double length=1.0);
 
// Container for data (TODO: Extend to real IElemDisc?)
template <typename TDomain>
class BiotElemDisc
{
public:
  static const int dim = TDomain::dim;
  typedef IElemDisc<TDomain> TElemDisc;
  typedef SmallStrainMechanics::SmallStrainMechanicsElemDisc<TDomain> TSmallStrainMechanics;
  typedef ConvectionDiffusionPlugin::ConvectionDiffusionFE<TDomain> TConvectionDiffusion;
  typedef ScaleAddLinker<number, dim, number> TScaleAddLinkerNumber;
 
  BiotElemDisc()
  : flowEqDisc(SPNULL), displacementEqDisc(SPNULL) {}
  BiotElemDisc() {…}
 
  BiotElemDisc(SmartPtr<TConvectionDiffusion> pDisc, SmartPtr<TSmallStrainMechanics> uDisc)
  : flowEqDisc(pDisc), displacementEqDisc(uDisc) {}
  BiotElemDisc(SmartPtr<TConvectionDiffusion> pDisc, SmartPtr<TSmallStrainMechanics> uDisc) {…}
 
  // SmartPtr<TConvectionDiffusion> pressure_disc()
  SmartPtr<TElemDisc> pressure_disc()
  {return flowEqDisc; }
  SmartPtr<TElemDisc> pressure_disc() {…}
 
  // SmartPtr<TSmallStrainMechanics> displacement_disc()
  SmartPtr<TElemDisc> displacement_disc()
  {return displacementEqDisc; }
  SmartPtr<TElemDisc> displacement_disc() {…}
 
  ConstSmartPtr<TScaleAddLinkerNumber> compression_linker()
  {return compressionLinker; }
  ConstSmartPtr<TScaleAddLinkerNumber> compression_linker() {…}
 
  ConstSmartPtr<TScaleAddLinkerNumber> divergence()
  {return divLinker; }
  ConstSmartPtr<TScaleAddLinkerNumber> divergence() {…}
 
protected:
  // Container data.
  SmartPtr<TConvectionDiffusion> flowEqDisc;
  SmartPtr<TSmallStrainMechanics> displacementEqDisc;
 
 
  SmartPtr<TScaleAddLinkerNumber> divLinker;
  SmartPtr<TScaleAddLinkerNumber> compressionLinker;
 
public:
  void CreateElemDiscs(const BiotSubsetParameters &param,
             const BiotDiscConfig &config)
  {
    CreateElemDiscs(param, config.m_uCmp.c_str(), config.m_uOrder,
                 config.m_pCmp.c_str(), config.m_pOrder,
                 config.m_bSteadyStateMechanics);
  }
  void CreateElemDiscs(const BiotSubsetParameters &param, {…}
  // This is the main function for constructing from a parameter set.
  void CreateElemDiscs(const BiotSubsetParameters &param,
              const char *ucmps, int uorder,
              const char *pcmp, int porder,
              bool bSteadyStateMechanics=true)
    {
 
      // Create main objects.
      flowEqDisc = make_sp(new TConvectionDiffusion(pcmp, param.get_subsets().c_str()));
      displacementEqDisc = make_sp(new TSmallStrainMechanics(ucmps, param.get_subsets().c_str()));
 
       // Do not scale with tau?
      displacementEqDisc->set_stationary(bSteadyStateMechanics);
 
      // A) Specify displacement eq (for u)
      // (Note: This corresponds to plane strain in 2D)
      auto matLaw = make_sp(new SmallStrainMechanics::HookeLaw<TDomain>());
      matLaw->set_hooke_elasticity_tensor(param.get_lambda(), param.get_mu());
 
      displacementEqDisc->set_material_law(matLaw);
      displacementEqDisc->set_mass_scale(0.0);
 
      // Add divergence.
      divLinker = make_sp(new TScaleAddLinkerNumber());
      divLinker->add(param.get_alpha(), flowEqDisc->value());
      displacementEqDisc->set_div_factor(divLinker);
 
      // B) Specify flow eq (for p).
      compressionLinker = make_sp(new TScaleAddLinkerNumber());
      compressionLinker->add(param.get_alpha(), displacementEqDisc->divergence());
 
      flowEqDisc->set_mass(compressionLinker);
      flowEqDisc->set_mass_scale(param.get_phi());   //  Storativity 1.0/M = S ‰
      flowEqDisc->set_diffusion((number) param.get_kappa());
 
      // TODO: Adjust quadrature order
      if (dim==2) {
 
        if (porder==1) { flowEqDisc->set_quad_order(4); }
        if (uorder==2) { displacementEqDisc->set_quad_order(4); }
 
      }
      else if (dim == 3) {
 
        if (uorder == 1) {
            // displacementEqDisc->set_quad_order(2);
        } else if (uorder == 2) {
            displacementEqDisc->set_quad_order(5);
            flowEqDisc->set_quad_order(3);
        }
      }
 
      // Print info.
      // UG_LOG(flowEqDisc->config_string());
      UG_LOG(displacementEqDisc->config_string());
 
 
    }
  void CreateElemDiscs(const BiotSubsetParameters &param, {…}
 
    void SetPressureDiscIdentity()
    {
      flowEqDisc->set_mass(0.0);
      flowEqDisc->set_mass_scale(1.0); 
      flowEqDisc->set_diffusion(0.0);
      //flowEqDisc->set_flux(ConstUserVector<dim>(0.0));
      //flowEqDisc->set_velocity(ConstUserVector<dim>(0.0));
      flowEqDisc->set_reaction_rate(0.0);
      flowEqDisc->set_reaction(0.0);
      flowEqDisc->set_source(0.0);
 
    }
    void SetPressureDiscIdentity() {…}
 
 
 
 
 
};
class BiotElemDisc {…};
 
template <typename TDomain>
class BiotElemDiscFactory{
public:
  static const int dim = TDomain::dim;
  typedef BiotElemDisc<TDomain> TBiotDisc;
 
  BiotElemDiscFactory(const char *ucmps, int uorder, const char *pcmp, int porder,
      bool bSteadyStateMechanics=true)
  : m_config(ucmps, uorder, pcmp, porder, bSteadyStateMechanics){}
  BiotElemDiscFactory(const char *ucmps, int uorder, const char *pcmp, int porder, {…}
 
  BiotElemDiscFactory(const BiotDiscConfig& config) : m_config(config) {}
 
  // Create new disc container.
  SmartPtr<TBiotDisc> create_elem_discs(const BiotSubsetParameters &param) const
  {
    SmartPtr<TBiotDisc>  biot = make_sp(new TBiotDisc ());
    biot->CreateElemDiscs(param, m_config);
 
    if (m_config.m_identityFlow) 
    { biot->SetPressureDiscIdentity(); }
    return biot;
  }
  SmartPtr<TBiotDisc> create_elem_discs(const BiotSubsetParameters &param) const {…}
 
  // Create new disc container. Pressure disc is identity.
  SmartPtr<TBiotDisc> create_elem_discs_for_consistency(const BiotSubsetParameters &param) const
  {
    SmartPtr<TBiotDisc>  biot = make_sp(new TBiotDisc ());
    biot->CreateElemDiscs(param, m_config);
    biot->SetPressureDiscIdentity();
    return biot;
  }
  SmartPtr<TBiotDisc> create_elem_discs_for_consistency(const BiotSubsetParameters &param) const {…}
  
protected:
  // BiotDiscConfig& config() {return m_config;}
  const BiotDiscConfig& config() {return m_config;} const
  BiotDiscConfig m_config;
 
};
class BiotElemDiscFactory {…};
 
/* JSON object representation
{
  "discretization" = {
    "ucmp" = "ux, uy, uz"
    "uorder" = 2,
 
    "pcmp" = "p"
    "porder" = 1,
 
    "stab" = 1.0
  }
 
 
  "gridname" = "mygrid"
 
 
  "params" : [
      { "subset" = "subset1", "alpha" = 1.0, "mu" =   },
      { "subset" = "subset2", "alpha" = 1.0 },
  ]
}
*/
 
 
template <typename TDomain, typename TAlgebra>
class BiotProblem
{
public:
  static const int dim = TDomain::dim;
  typedef IElemDisc<TDomain> TElemDisc;
  typedef DomainDiscretization<TDomain, TAlgebra> TDomainDisc;
  typedef GridFunction<TDomain,TAlgebra> TGridFunction;
protected:
  typedef ConvectionDiffusionPlugin::ConvectionDiffusionStabFE<TDomain> TConvectionDiffusionStab;
  typedef ConvectionDiffusionPlugin::ConvectionDiffusionFV1<TDomain> TConvectionDiffusionFV1;
public:
 
  BiotProblem(const char* uCmp, const char *pCmp, const char *gridname)
  : m_config(uCmp, pCmp), m_gridname(gridname) {}
  BiotProblem(const char* uCmp, const char *pCmp, const char *gridname) {…}
 
  BiotProblem(const BiotDiscConfig& config, const char *gridname)
  : m_config(config), m_gridname(gridname)  {}
  BiotProblem(const BiotDiscConfig& config, const char *gridname) {…}
 
  virtual ~BiotProblem() {}
 
  // get grid name
  const char* get_gridname() const { return m_gridname.c_str();}
 
  void add_subset_parameters(const BiotSubsetParameters &p)
  { m_params.push_back(p); }
  void add_subset_parameters(const BiotSubsetParameters &p) {…}
 
#ifdef UG_JSON
  void add_subset_parameters(const char* &json_string)
  {
    std::stringstream ss;
    ss << json_string;
 
    nlohmann::json json;
    ss >> json;
 
    BiotSubsetParameters _p = json; // implicit use of from_json!
    m_params.push_back(_p);
  }
#endif
 
 
 
  virtual double get_char_time()
  {
    std::vector<BiotSubsetParameters>::const_iterator it= m_params.begin();
    double tchar = 0.0;
 
    for(it = m_params.begin(); it != m_params.end(); it++)  {
      tchar=std::max(tchar, DefaultCharTime(*it));
    }
 
    return tchar;
  }
  virtual double get_char_time() {…}
 
  virtual double start_time()
  { return 0.0; }
  virtual double start_time() {…}
 
  virtual double end_time()
  { return 2.0*get_char_time(); }
  virtual double end_time() {…}
 
 
  void add_elem_discs_general(SmartPtr<TDomainDisc> dd, bool bSteadyStateMechanics=true, bool bIdentityFlow=false)
  {
    // Using factory to create elem discs.
    typedef BiotElemDiscFactory<TDomain> TBiotElemDiscFactory;
    typedef BiotElemDisc<TDomain> TBiotElemDisc;
 
    BiotDiscConfig conf = config();
    conf.m_bSteadyStateMechanics = bSteadyStateMechanics;
    conf.m_identityFlow = bIdentityFlow;
 
    BiotElemDiscFactory<TDomain> elemDiscFactory(conf);
 
    // Iterate over parameter sets.
    std::vector<BiotSubsetParameters>::iterator it;
    for(it = m_params.begin(); it != m_params.end(); it++)    
    {
      // Create elem discs and add
      SmartPtr<TBiotElemDisc> biot = elemDiscFactory.create_elem_discs(*it);
      dd->add(biot->displacement_disc().template cast_dynamic<TElemDisc>());
      dd->add(biot->pressure_disc().template cast_dynamic<TElemDisc>());
    }
  }
  void add_elem_discs_general(SmartPtr<TDomainDisc> dd, bool bSteadyStateMechanics=true, bool bIdentityFlow=false) {…}
 
 
  virtual void add_elem_discs(SmartPtr<TDomainDisc> dd, bool bSteadyStateMechanics=true)
  { add_elem_discs_general(dd,bSteadyStateMechanics); }
  virtual void add_elem_discs(SmartPtr<TDomainDisc> dd, bool bSteadyStateMechanics=true) {…}
 
  virtual void add_elem_discs_with_static_pressure(SmartPtr<TDomainDisc> dd)
  { add_elem_discs_general(dd, true, true); }
  virtual void add_elem_discs_with_static_pressure(SmartPtr<TDomainDisc> dd) {…}
 
 
 
protected:
  virtual void add_stab_discs(SmartPtr<TDomainDisc> dd, bool bSteadyStateMechanics=true)
  {
    UG_ASSERT(bSteadyStateMechanics == true, "ERROR: Only implemented for Mass matrix!");
 
    if (config().m_dStab <= 0.0) return;
 
    SmartPtr<TElemDisc> pDiscStab;
    std::vector<BiotSubsetParameters>::iterator it;
    for(it = m_params.begin(); it != m_params.end(); it++) {
      double gamma = it->get_lambda() + 2.0*it->get_mu();
        pDiscStab = make_sp(new TConvectionDiffusionStab(config().m_pCmp.c_str(), it->get_subsets().c_str(), config().m_dStab/gamma));
        dd->add(pDiscStab.template cast_dynamic<TElemDisc>());
    }
  }
  virtual void add_stab_discs(SmartPtr<TDomainDisc> dd, bool bSteadyStateMechanics=true) {…}
 
public:
  virtual void add_uzawa_discs(SmartPtr<TDomainDisc> dd, bool bSteadyStateMechanics=true)
  {
 
    UG_ASSERT(bSteadyStateMechanics == true, "ERROR: Only implemented for Mass matrix!");
 
    SmartPtr<TConvectionDiffusionFV1> pDiscUzawa;
    std::vector<BiotSubsetParameters>::iterator it;
    for(it = m_params.begin(); it != m_params.end(); it++) {
      pDiscUzawa = make_sp(new TConvectionDiffusionFV1(config().m_pCmp.c_str(), it->get_subsets().c_str()));
      pDiscUzawa->set_mass_scale(it->get_beta());
      dd->add(pDiscUzawa.template cast_static<TElemDisc>());
      }
 
  }
  virtual void add_uzawa_discs(SmartPtr<TDomainDisc> dd, bool bSteadyStateMechanics=true) {…}
 
  
  virtual void add_boundary_conditions_u(SmartPtr<TDomainDisc> dd) = 0;
  
  virtual void add_boundary_conditions_p(SmartPtr<TDomainDisc> dd) = 0;
 
  virtual void add_boundary_conditions(SmartPtr<TDomainDisc> dd, bool bSteadyStateMechanics=true)
  {
    add_boundary_conditions_u(dd);
    add_boundary_conditions_p(dd);
  }
  virtual void add_boundary_conditions(SmartPtr<TDomainDisc> dd, bool bSteadyStateMechanics=true) {…}
 
 
  virtual void interpolate_start_values(SmartPtr<TGridFunction> u, double t0)
  {}
  virtual void interpolate_start_values(SmartPtr<TGridFunction> u, double t0) {…}
 
  virtual bool post_processing(SmartPtr<TGridFunction> u, size_t step, double time) {return true; }
 
 
 
  const BiotDiscConfig& config() const { return m_config; }
  int get_porder() const {return config().m_pOrder;}
  int get_uorder() const {return config().m_uOrder;}
 
protected:
  BiotDiscConfig m_config;
  std::vector<BiotSubsetParameters> m_params;
  const std::string m_gridname;
};
class BiotProblem {…};
 
 
#ifdef UG_JSON
template <typename TDomain, typename TAlgebra>
void to_json(nlohmann::json &j, const BiotProblem<TDomain,TAlgebra> &p);
 
template <typename TDomain, typename TAlgebra>
void from_json(const nlohmann::json &j, BiotProblem<TDomain,TAlgebra> &p);
#endif
 
 
} // namespace Poroelasticity
} // namespace ug
 
#endif