BatteryElectricDiffusionDiscretization.h

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#ifndef _BATTERYELECTRICDIFFUSIONDISCRETIZATION_H_
#define _BATTERYELECTRICDIFFUSIONDISCRETIZATION_H_

#include "CRMatrix.h"
#include "Field.h"
#include "MultiField.h"
#include "MultiFieldMatrix.h"
#include "Mesh.h"
#include "Discretization.h"
#include "StorageSite.h"
#include "DiagonalMatrix.h"
#include "Gradient.h"
#include "DiagonalTensor.h"
/*
  template<class T>
  inline T harmonicAverage(const T& x0, const T& x1)
  {
  const T sum = x0+x1;
  if (x0+x1 != NumTypeTraits<T>::getZero())
  return 2.0*x0*x1/sum;
  else
  return sum;
  }
*/
  
template<class X, class Diag, class OffDiag>
  class BatteryElectricDiffusionDiscretization : public Discretization
  {
  public:

    typedef typename NumTypeTraits<X>::T_Scalar T_Scalar;
  
    typedef CRMatrix<Diag,OffDiag,X> CCMatrix;
    typedef typename CCMatrix::DiagArray DiagArray;
    typedef typename CCMatrix::PairWiseAssembler CCAssembler;

    typedef Gradient<X> XGrad;
    typedef Array<int> IntArray;
  
    typedef Array<X> XArray;
    typedef Array<T_Scalar> TArray;
    typedef Vector<T_Scalar,3> VectorT3;
    typedef Array<VectorT3> VectorT3Array;

    typedef Array<XGrad> GradArray;
  
  BatteryElectricDiffusionDiscretization(const MeshList& meshes,
                                         const GeomFields& geomFields,
                                         Field& varField,
                                         const Field& diffusivityField,
                                         const Field& concField,
                                         const Field& concGradientField,
                                         const int ElectrolyteMeshID) :
    Discretization(meshes),
      _geomFields(geomFields),
      _varField(varField),
      _diffusivityField(diffusivityField),
      _concField(concField),
      _concGradientField(concGradientField),
      _ElectrolyteMeshID(ElectrolyteMeshID)
      {}

    void discretize(const Mesh& mesh, MultiFieldMatrix& mfmatrix,
                    MultiField& xField, MultiField& rField)
    {
      if (mesh.getID() == _ElectrolyteMeshID)
        {
          // electric potential variables
          const StorageSite& cells = mesh.getCells();
   
          const MultiField::ArrayIndex cVarIndex(&_varField,&cells);

          //CCMatrix& matrix = dynamic_cast<CCMatrix&>(mfmatrix.getMatrix(cVarIndex,cVarIndex));    
 
          const VectorT3Array& cellCentroid =
            dynamic_cast<const VectorT3Array&>(_geomFields.coordinate[cells]);
          const TArray& cellVolume =
            dynamic_cast<const TArray&>(_geomFields.volume[cells]);
 
          //DiagArray& diag = matrix.getDiag();

          //const XArray& xCell = dynamic_cast<const XArray&>(xField[cVarIndex]); // may not need here
          XArray& rCell = dynamic_cast<XArray&>(rField[cVarIndex]);
      
          // lnspeciesConcentration variables
          const TArray& lnSpecConcCell = dynamic_cast<const TArray&>(_concField[cells]);

          const GradArray& lnSpecConcGradCell =
            dynamic_cast<const GradArray&>(_concGradientField[cells]);

          const TArray& diffCell =
            dynamic_cast<const TArray&>(_diffusivityField[cells]);

          const IntArray& ibType = dynamic_cast<const IntArray&>(_geomFields.ibType[cells]);


          foreach(const FaceGroupPtr fgPtr, mesh.getAllFaceGroups())
            {
              const FaceGroup& fg = *fgPtr;

              const StorageSite& faces = fg.site;
              const int nFaces = faces.getCount();
              const CRConnectivity& faceCells = mesh.getFaceCells(faces);
              const VectorT3Array& faceArea =
                dynamic_cast<const VectorT3Array&>(_geomFields.area[faces]);    
              const TArray& faceAreaMag =
                dynamic_cast<const TArray&>(_geomFields.areaMag[faces]);
              const VectorT3Array& faceCentroid =
                dynamic_cast<const VectorT3Array&>(_geomFields.coordinate[faces]);
              //CCAssembler& assembler = matrix.getPairWiseAssembler(faceCells);
              for(int f=0; f<nFaces; f++)
                {
                  const int c0 = faceCells(f,0);
                  const int c1 = faceCells(f,1);

                  T_Scalar vol0 = cellVolume[c0];
                  T_Scalar vol1 = cellVolume[c1];
        
                  VectorT3 ds=cellCentroid[c1]-cellCentroid[c0];

                  // for ib faces ignore the solid cell and use the face centroid for diff metric
                  if (((ibType[c0] == Mesh::IBTYPE_FLUID)
                       && (ibType[c1] == Mesh::IBTYPE_BOUNDARY)) ||
                      ((ibType[c1] == Mesh::IBTYPE_FLUID)
                       && (ibType[c0] == Mesh::IBTYPE_BOUNDARY)))
                    {
                      if (ibType[c0] == Mesh::IBTYPE_FLUID)
                        {
                          vol1 = 0.;
                          ds = faceCentroid[f]-cellCentroid[c0];
                        }
                      else
                        {
                          vol0 = 0.;
                          ds = cellCentroid[c1]-faceCentroid[f];
                        }
                    }
        
                  T_Scalar faceDiffusivity(1.0);
                  if (vol0 == 0.)
                    faceDiffusivity = diffCell[c1];
                  else if (vol1 == 0.)
                    faceDiffusivity = diffCell[c0];
                  else
                    faceDiffusivity = harmonicAverage(diffCell[c0],diffCell[c1]);

                  //convert diffusivity for ln term in battery equation
                  const T_Scalar transportNumber = 0.4;
                  const T_Scalar R = 8.314;
                  const T_Scalar F = 96485.0;
                  const T_Scalar Temp = 300.0;            
                  faceDiffusivity = faceDiffusivity*(-2.0)*R*Temp/F*(1.0-transportNumber);
             
                  const T_Scalar diffMetric = faceAreaMag[f]*faceAreaMag[f]/dot(faceArea[f],ds);
                  const T_Scalar diffCoeff = faceDiffusivity*diffMetric;
                  const VectorT3 secondaryCoeff = faceDiffusivity*(faceArea[f]-ds*diffMetric);
        
                  const XGrad gradF = (lnSpecConcGradCell[c0]*vol0+lnSpecConcGradCell[c1]*vol1)/(vol0+vol1);

                  const X dFluxSecondary = gradF*secondaryCoeff;
        
                  const X dFlux = diffCoeff*(lnSpecConcCell[c1]-lnSpecConcCell[c0]) + dFluxSecondary;

                  rCell[c0] += dFlux;
                  rCell[c1] -= dFlux;

                  //assembler.getCoeff01(f) +=diffCoeff;
                  //assembler.getCoeff10(f) +=diffCoeff;

                  //diag[c0] -= diffCoeff;
                  //diag[c1] -= diffCoeff;

                  //cout <<"dflux" << dFlux << endl;
                  /*
                    cout << " c0 and c1 " << c0 << " " << c1 << endl;
                    cout << " diffcell " << diffCell[c0] << " " << diffCell[c1] << " " << faceDiffusivity << endl;
                    cout << " diffmetric  " << diffMetric << endl;
                    cout << "diffCoeff  " << diffCoeff << endl;
                  */
        
              

                }
            }
        }
    }
  private:
    const GeomFields& _geomFields;
    Field& _varField;
    const Field& _diffusivityField; 
    const Field& _concField;
    const Field& _concGradientField;
    const int _ElectrolyteMeshID;
  };

#endif