Hemker_Wide_VMS.h

// Navier-Stokes coupled with conformation stress tensor problem, Benchmark problem


void ExampleFile()
{
  OutPut("Example: Hemker_Wide_VMS" << endl) ;
}

#define __BENCH__


#include <Joint.h>
#include <BoundEdge.h>
#include <BoundComp.h>
#include <FE2D.h>
#include <FEDesc2D.h>

#include <MainUtilities.h>


#include <MacroCell.h>
#include <BoundEdge.h>
#include <IsoBoundEdge.h>
#include <gridgen.h>
#include <IsoInterfaceJoint.h>
#include <BdLine.h>
#include <BdCircle.h>
#include <GridCell.h>

#include <QuadAffin.h>
#include <QuadBilinear.h>
#include <QuadIsoparametric.h>
#include <TriaAffin.h>
#include <TriaIsoparametric.h>

extern "C"
{
  void triangulate(char*, struct triangulateio*,
                   struct triangulateio*, struct triangulateio*);
}

// ========================================================================
// exact solution
// ========================================================================
void ExactU1(double x, double y, double *values)
{
  values[0] = 0;
  values[1] = 0;
  values[2] = 0;
  values[3] = 0;
}

void ExactU2(double x, double y, double *values)
{
  values[0] = 0;
  values[1] = 0;
  values[2] = 0;
  values[3] = 0;
}

void ExactP(double x, double y, double *values)
{
  values[0] = 0;
  values[1] = 0;
  values[2] = 0;
  values[3] = 0;
}

// ========================================================================
// boundary conditions
// ========================================================================
void BoundCondition(int i, double t, BoundCond &cond)
{
      cond = DIRICHLET;
}

void U1BoundValue(int BdComp, double Param, double &value)
{
  switch(BdComp)
  {
    case 0: value = 0;
            break;
    case 1: value=1.5*(1.0 - (pow(-8+16*Param,2))/64.0);
            break;
    case 2: value = 0;
            break;
    case 3: value=1.5*(1.0 - (pow(8-16*Param,2))/64.0) ;
            break;
    case 4: value=0;
            break;
    default: cout << "wrong boundary part number: " << BdComp << endl;
  }
}

void U2BoundValue(int BdComp, double Param, double &value)
{
  value = 0;
  if(BdComp>4) cout << "wrong boundary part number: " << BdComp << endl;
}

// ========================================================================
// coefficients for Stokes form: A, B1, B2, f1, f2
// ========================================================================
void LinCoeffs(int n_points, double *x, double *y,
               double **parameters, double **coeffs)
{
  double eps = 1.0/TDatabase::ParamDB->RE_NR, beta = TDatabase::ParamDB->P3;
  int i;
  double *coeff, nondim;
 
  nondim = beta*eps;

  for(i=0;i<n_points;i++)
  {
    coeff = coeffs[i];

    coeff[0] = nondim;
    coeff[1] = 0; // f1
    coeff[2] = 0; // f2
  }
}

// ========================================================================
// exact solution
// ========================================================================
void ExactS1(double x, double y, double *values)
{
    values[0] = 0;
    values[1] = 0;
    values[2] = 0;
    values[3] = 0;
}

void ExactS2(double x, double y, double *values)
{
    values[0] = 0;
    values[1] = 0;
    values[2] = 0;
    values[3] = 0;
}

void ExactS3(double x, double y, double *values)
{
  values[0] = 0;
  values[1] = 0;
  values[2] = 0;
  values[3] = 0;
}

// ========================================================================
// boundary conditions
// ========================================================================
void BoundCondition_CST(int i, double t, BoundCond &cond)
{
  switch(i)
  {
    case 0:
    case 1: 
    case 2:
    case 4:
      cond = NEUMANN;
      break;
    case 3:
  cond = DIRICHLET;
  break;
  }
}

void S1BoundValue(int BdComp, double Param, double &value)
{
  double Wei = TDatabase::ParamDB->WEI_NR;
  switch(BdComp)
  {
    case 0: value=0.0;
            break;
//     case 1: value= (pow(1.5*Wei*(1-2*Param),2) * 2.0 )+1.0;
//             break;
    case 1: value=0.0;
            break;  
    case 2: value=0.0;
            break;
    case 3: value=(pow(0.375*Wei*(-1+2*Param),2) * 2.0 )+1.0;
            break;
    case 4: value=0.0;
            break;

  }
}

void S2BoundValue(int BdComp, double Param, double &value)
{
  double Wei = TDatabase::ParamDB->WEI_NR;
  switch(BdComp)
  {
    case 0: value=0;
            break;
//     case 1: value=1.5*Wei*(1-2*Param);
//             break;
            case 1: value=0.0;
            break;  
    case 2: value=0;
            break;
    case 3: value=0.375*Wei*(-1+2*Param);
            break;
    case 4: value=0;
            break;

  }
  return;
}



void S3BoundValue(int BdComp, double Param, double &value)
{
  switch(BdComp)
  {
    case 0: value=0.0;
            break;
//     case 1: value=1.0;
//             break;
            case 1: value=0.0;
            break;  
    case 2: value=0.0;
            break;
    case 3: value=1.0;
            break;
    case 4: value=0.0;
            break;

  }
  return;
}

void LinCoeffs_CST(int n_points, double *X, double *Y,
               double **parameters, double **coeffs)
{
  double nu=1./TDatabase::ParamDB->WEI_NR;

  int i;
  double *coeff;

  for(i=0;i<n_points;i++)
  {
    coeff = coeffs[i];
  
    coeff[0] = nu;
    coeff[1] = nu;   //f1
    coeff[2] = 0.0;  //f2
    coeff[3] = nu;   //f3
    

  }
}


void GetCdCl(TFEFunction2D *u1fct, TFEFunction2D *u2fct,
             TFEFunction2D *pfct, TFEFunction2D *tau1fct,
             TFEFunction2D *tau2fct, TFEFunction2D *tau3fct,
             double &cd, double &cl)
{
  int i,j,k,l, N_;
  int N_Points,N_Edges,comp,ed_nr;
  double *weights, *xi, *eta;
  double X[MaxN_QuadPoints_2D];
  double Y[MaxN_QuadPoints_2D];
  double AbsDetjk[MaxN_QuadPoints_2D];
  int N_LocalUsedElements;
  FE2D LocalUsedElements[3], CurrentElement;
  int *DOF;
  double **OrigFEValues, *Orig;
  bool SecondDer[3] = { FALSE, FALSE, FALSE };
  double *u1, *u2, *p, *tau1, *tau2, *tau3;
  TFESpace2D *USpace, *PSpace, *TauSpace;
  int *UGlobalNumbers, *UBeginIndex;
  int *PGlobalNumbers, *PBeginIndex;
  int *TauGlobalNumbers, *TauBeginIndex;
  int *N_BaseFunct, N_Cells;
  BaseFunct2D BaseFunct, *BaseFuncts;
  TCollection *Coll;
  TBaseCell *cell;
  double value, value1, value2, value3, value4, value5, value6;
  double FEFunctValues[MaxN_BaseFunctions2D];
  double FEFunctValues1[MaxN_BaseFunctions2D];
  double FEFunctValues2[MaxN_BaseFunctions2D];
  double FEFunctValues3[MaxN_BaseFunctions2D];
  double FEFunctValues4[MaxN_BaseFunctions2D];
  double FEFunctValues5[MaxN_BaseFunctions2D];
  double FEFunctValues6[MaxN_BaseFunctions2D];
  
  int N_DerivativesU = 3;
  double *Derivatives[MaxN_BaseFunctions2D];
  MultiIndex2D NeededDerivatives[3] = { D00, D10, D01 };
  TFEFunction2D *vfct;
  double *v, nu = 1/TDatabase::ParamDB->RE_NR;
  double wei = 1/TDatabase::ParamDB->WEI_NR, beta = TDatabase::ParamDB->P3;
  double *Der, *aux;
  TJoint *joint;
  TBoundEdge *boundedge;
  TBoundComp *BoundComp;
  TFE2D *eleCell;
  FE2D FEEle;
  TFEDesc2D *FEDesc;
  int N_DOF_Circ, *DOF_Circ;
  char VString[] = "v";

  u1 = u1fct->GetValues();
  u2 = u2fct->GetValues();
  p = pfct->GetValues();
  tau1 = tau1fct->GetValues();
  tau2 = tau2fct->GetValues();
  tau3 = tau3fct->GetValues();

  USpace = u1fct->GetFESpace2D();
  PSpace = pfct->GetFESpace2D();
  TauSpace = tau1fct->GetFESpace2D();

  UGlobalNumbers = USpace->GetGlobalNumbers();
  UBeginIndex = USpace->GetBeginIndex();

  PGlobalNumbers = PSpace->GetGlobalNumbers();
  PBeginIndex = PSpace->GetBeginIndex();
  
  TauGlobalNumbers = TauSpace->GetGlobalNumbers();
  TauBeginIndex = TauSpace->GetBeginIndex();

  BaseFuncts = TFEDatabase2D::GetBaseFunct2D_IDFromFE2D();
  N_BaseFunct = TFEDatabase2D::GetN_BaseFunctFromFE2D();

  aux = new double [MaxN_QuadPoints_2D*13];
  for(j=0;j<MaxN_QuadPoints_2D;j++)
    Derivatives[j] = aux + j*13;

  N_ = u1fct->GetLength();
  v = new double[N_];
  memset(v,0,N_*SizeOfDouble);
  vfct = new TFEFunction2D(USpace, VString, VString, v, N_);

// ########################################################################
// loop over all cells
// ########################################################################
  Coll = USpace->GetCollection(); // all spaces use same Coll
  N_Cells = Coll->GetN_Cells();
 
  for(i=0;i<N_Cells;i++)
  {
    cell = Coll->GetCell(i);
    N_Edges=cell->GetN_Edges();
    for(j=0;j<N_Edges;j++)              // loop over all edges of cell
    {
      joint=cell->GetJoint(j);
      if ((joint->GetType() == BoundaryEdge)||
          (joint->GetType() == IsoBoundEdge)) // boundary edge 
      {
        
        boundedge=(TBoundEdge *)joint;  
        BoundComp=boundedge->GetBoundComp();  // get boundary component
        comp=BoundComp->GetID();              // boundary id 
        if (comp==4) 
          {
            FEEle = USpace->GetFE2D(i,cell);   // finite element of cell
            eleCell =  TFEDatabase2D::GetFE2D(FEEle); 
            FEDesc = eleCell->GetFEDesc2D();   // fe descriptor
            N_DOF_Circ = FEDesc->GetN_JointDOF(); // # local dofs on joints
            DOF_Circ = FEDesc->GetJointDOF(j); // local dofs on joint j
            DOF = UGlobalNumbers + UBeginIndex[i]; // pointer to global dofs
            for (k=0;k<N_DOF_Circ;k++)         // set fe on circle to 1 
              v[DOF[DOF_Circ[k]]] = 1;
          }
      }      
    }
  }
  
  cd = 0;
  cl = 0;

// ########################################################################
// loop over all cells
// ########################################################################
  Coll = USpace->GetCollection(); // all spaces use same Coll
  N_Cells = Coll->GetN_Cells();
  for(i=0;i<N_Cells;i++)
  {
    cell = Coll->GetCell(i);

    // ####################################################################
    // find local used elements on this cell
    // ####################################################################
    N_LocalUsedElements = 3;
    LocalUsedElements[0] = USpace->GetFE2D(i, cell);
    LocalUsedElements[1] = PSpace->GetFE2D(i, cell);
    LocalUsedElements[2] = TauSpace->GetFE2D(i, cell);

    // ####################################################################
    // calculate values on original element
    // ####################################################################
    TFEDatabase2D::GetOrig(N_LocalUsedElements, LocalUsedElements, Coll, cell, SecondDer, N_Points, xi, eta, weights, X, Y, AbsDetjk);

    // calculate all needed values of p 
    CurrentElement = LocalUsedElements[1];
    BaseFunct = BaseFuncts[CurrentElement];
    N_ = N_BaseFunct[CurrentElement];

    DOF = PGlobalNumbers + PBeginIndex[i];
    for(l=0;l<N_;l++)
      FEFunctValues[l] = p[DOF[l]];

    OrigFEValues = TFEDatabase2D::GetOrigElementValues(BaseFunct, D00);

    for(j=0;j<N_Points;j++)
    {
      Orig = OrigFEValues[j];
      value = 0;
      for(l=0;l<N_;l++)
        value += FEFunctValues[l] * Orig[l];

      Derivatives[j][0] = value;
    }

    // calculate all needed values of u1, u2 
    CurrentElement = LocalUsedElements[0];
    BaseFunct = BaseFuncts[CurrentElement];
    N_ = N_BaseFunct[CurrentElement];

    DOF = UGlobalNumbers + UBeginIndex[i];
    for(l=0;l<N_;l++)
    {
      FEFunctValues1[l] = u1[DOF[l]];
      FEFunctValues2[l] = u2[DOF[l]];
      FEFunctValues3[l] = v[DOF[l]];
    }

    for(k=0;k<N_DerivativesU;k++)
    {
      OrigFEValues = TFEDatabase2D::GetOrigElementValues(BaseFunct,
                                      NeededDerivatives[k]);
      for(j=0;j<N_Points;j++)
      {
        Orig = OrigFEValues[j];
        value1 = 0;
        value2 = 0;
        value3 = 0;
        for(l=0;l<N_;l++)
        {
          value1 += FEFunctValues1[l] * Orig[l];
          value2 += FEFunctValues2[l] * Orig[l];
          value3 += FEFunctValues3[l] * Orig[l];
        } // endfor l
        Derivatives[j][k+1] = value1;
        Derivatives[j][k+4] = value2;
        Derivatives[j][k+7] = value3;
      } // endfor j
    } // endfor k

    
    // calculate all needed values of tau1, tau2, tau3 
    CurrentElement = LocalUsedElements[2];
    BaseFunct = BaseFuncts[CurrentElement];
    N_ = N_BaseFunct[CurrentElement];

    DOF = TauGlobalNumbers + TauBeginIndex[i];
    for(l=0;l<N_;l++)
    {  
      FEFunctValues4[l] = tau1[DOF[l]];
      FEFunctValues5[l] = tau2[DOF[l]];
      FEFunctValues6[l] = tau3[DOF[l]];
      
    }
    OrigFEValues = TFEDatabase2D::GetOrigElementValues(BaseFunct, D00);

    for(j=0;j<N_Points;j++)
    {
      Orig = OrigFEValues[j];
        value4 = 0;
        value5 = 0;
        value6 = 0;
        for(l=0;l<N_;l++)
        {
          value4 += FEFunctValues4[l] * Orig[l];
          value5 += FEFunctValues5[l] * Orig[l];
          value6 += FEFunctValues6[l] * Orig[l];
        } // endfor l
      Derivatives[j][10] = value4;
      Derivatives[j][11] = value5;
      Derivatives[j][12] = value6;
    }
    

 
    
    // calculation
    for(j=0;j<N_Points;j++)
    {
      Der = Derivatives[j];
      
      // beta*nu * (u1_x*v_x, u1_y*v_y), v= (v,0)
       value1  = beta*nu*(Der[2]*Der[8]+Der[3]*Der[9]);
      // (u1 * u1_x + u2* u1_y) * (1,0)
 //     value1 += (Der[1]*Der[2]+Der[4]*Der[3])*Der[7];
      // pressure times divergence of test function (1,0)
       value1 -= Der[0]*Der[8];
//       // (1-beta)*nu*wei* (tau1*v_x + tau2*v_y)
        value1 += (1.0-beta)*nu*wei*(Der[10]*Der[8] + Der[11]*Der[9]);

//       value2  = beta*nu*(Der[5]*Der[8]+Der[6]*Der[9]);
//    //   value2 += (Der[1]*Der[5]+Der[4]*Der[6])*Der[7];
//       value2 -= Der[0]*Der[9];
//       value2 += (1.0-beta)*nu*wei*(Der[11]*Der[8] + Der[12]*Der[9]);

      cd += AbsDetjk[j]*weights[j] * value1;
      cl += AbsDetjk[j]*weights[j] * value2;
    }

  } // endfor i

   cd *= -1;
   cl *= -1;

  delete Derivatives[0];
  delete vfct;
  delete v;
}

// **************************************************************************
// Triangular Mesh Generation
// **************************************************************************

void  TriaReMeshGen(TDomain *&Domain)
{
  int j, ID, k, N_G, *PartMarker, *PointNeighb, maxEpV=0;
  int a, b, len1, len2, Neighb_tmp, BDpart;
  int i, temp, N_Cells, N_RootCells, CurrVertex, N_Joints, N_Vertices;
  int N_Interface_Vert, N_Verti, N_Hori, N_SlipBound_Vert, N_BDVertices;
  int CurrComp, In_Index, *Triangles, Neib[2], CurrNeib;
  
  double deviation, hi, x0, y0, x, y, phi1, phi2;
  double T_a, T_b, C_x, C_y, s, theta;  
  double dt, area = TDatabase::ParamDB->Area;
  double *Coordinates, *Hole_List;  
  
  double Xi[4] = {-40., 40., 40.,-40.};
  double Yi[4] = {-8.,-8., 8., 8.}; 

  TBaseCell **CellTree, *cell;
  TBoundPart *BoundPart;
  TJoint *Joint;
  TCollection *coll;
  TVertex **VertexDel, **NewVertices;  
  TBdLine *UpdateBound[12];
  TBdCircle *UpdateIntface;

  
  boolean AllowEdgeRef = (boolean) TDatabase::ParamDB->MESHGEN_ALLOW_EDGE_REF;
  
  struct triangulateio In, Out;
  std::ostringstream opts;
  opts << " ";
  
  Out.pointlist = NULL;
  Out.pointattributelist = NULL;
  Out.pointmarkerlist = NULL;
  Out.trianglelist = NULL;
  Out.triangleattributelist = NULL;
  Out.trianglearealist = NULL;
  Out.neighborlist = NULL;
  Out.segmentlist = NULL;
  Out.segmentmarkerlist = NULL;
  Out.holelist = NULL;
  Out.regionlist = NULL;
  Out.edgelist = NULL;
  Out.edgemarkerlist = NULL;
  Out.normlist = NULL;

  opts.seekp(std::ios::beg); 
  

  BoundPart = Domain->GetBdPart(0);
  UpdateBound[0]  = (TBdLine*)BoundPart->GetBdComp(0);
  UpdateBound[1]  = (TBdLine*)BoundPart->GetBdComp(1);
  UpdateBound[2]  = (TBdLine*)BoundPart->GetBdComp(2);
  UpdateBound[3]  = (TBdLine*)BoundPart->GetBdComp(3);
  BoundPart = Domain->GetBdPart(1);
  UpdateIntface = (TBdCircle*)BoundPart->GetBdComp(0);
  
  
//OutPut("MESHGEN_REF_QUALIT " << TDatabase::ParamDB->MESHGEN_REF_QUALITY << endl);

  opts<<'p'; // Constrained Delaunay Triangulation:
           // initial values - only points defined on the boundary of the domain;
           // triangulation near boundary may variate from Delaunay criterion
  opts<<"q"<<  TDatabase::ParamDB->MESHGEN_REF_QUALITY;
              // Quality mesh generation with no angles smaller than 20 degrees;
  opts<<"a"<< area; // Imposes a maximum triangle area.
  opts<<'e'; // Outputs a list of edges of the triangulation
  opts<<'z'; // Numbers if items starting from 0
  //opts<<"VVVV"; // Gives detailed information about what Triangle is doing
  opts<<'Q'; // Supress all explanation of what Triangle is doing, unless an error occurs
//   opts<<'Y'; // Supress adding vertices on boundary edges
  opts<<ends;
  
  N_Interface_Vert = int (TDatabase::ParamDB->P6);    //Freesurf except end point
  N_Hori  = 300;      // number of horrizontal BD vertices
  N_Verti = 50;       // number of vertical BD vertices
  N_SlipBound_Vert = 2*N_Hori + 2*N_Verti;  

  N_BDVertices = N_Interface_Vert+N_SlipBound_Vert;
  In.numberofpoints = N_BDVertices;
  In.pointlist = new double[2*In.numberofpoints];
  In.pointmarkerlist = new int[In.numberofpoints];
  In.numberofpointattributes = 0;

  In.numberofsegments = In.numberofpoints;
  In.segmentlist = new int[2*In.numberofsegments];
  In.segmentmarkerlist = new int[In.numberofsegments]; 
  In.numberofregions = 0;
  In.regionlist = NULL;
  
  In.numberofholes = 1;
  In.holelist = NULL;

  Hole_List = new double[2* In.numberofholes];
  Hole_List[0] = 0.;
  Hole_List[1] = 0.;
  In.holelist = Hole_List;
    
  In_Index = 0;
  CurrComp = 1;  
  
  hi = (Xi[1] - Xi[0])/(double)N_Hori;
  x0 = Xi[0];
  y0 = Yi[0];
  x  = Xi[0];  
  
  // points and segments on the horizontal boundary (marker=1)
  for(i=0;i<N_Hori;i++) // without last point
   {
    x = x0 + (double)i*hi;
    In.pointlist[2*In_Index] = x;
    In.pointlist[2*In_Index+1] = y0;
//     cout<<" x : "<< In.pointlist[2*In_Index] << " y : "<< In.pointlist[2*In_Index+1] <<endl;
    In.pointmarkerlist[In_Index] = CurrComp;
    In.segmentlist[2*In_Index] = In_Index;
    In.segmentlist[2*In_Index+1] = In_Index+1;
    In.segmentmarkerlist[In_Index] = CurrComp;
    In_Index++;
   }
   
  CurrComp++;  
  
  hi = (Yi[2] - Yi[1])/(double)N_Verti;
  x0 = Xi[1];
  y0 = Yi[1];
  y  = Yi[1];
  // points and segments on the horizontal boundary (marker=1)
  for(i=0;i<N_Verti;i++) // without last point
   {
    y = y0 + (double)i*hi; 
    In.pointlist[2*In_Index] = x0;
    In.pointlist[2*In_Index+1] = y;
//     cout<<" x : "<< In.pointlist[2*In_Index] << " y : "<< In.pointlist[2*In_Index+1] <<endl;
    In.pointmarkerlist[In_Index] = CurrComp;
    In.segmentlist[2*In_Index] = In_Index;
    In.segmentlist[2*In_Index+1] = In_Index+1;
    In.segmentmarkerlist[In_Index] = CurrComp;
    In_Index++;

   }
   
  CurrComp++;  
//   cout<<endl;

  hi = (Xi[3] - Xi[2])/(double)N_Hori;
  x0 = Xi[2];
  y0 = Yi[2];
  x  = Xi[2];
  // points and segments on the horizontal boundary (marker=1)
 for(i=0;i<N_Hori;i++) // without last point
   {
    x = x0 + (double)i*hi;
    In.pointlist[2*In_Index] = x;
    In.pointlist[2*In_Index+1] = y0;
//     cout<<" x : "<< In.pointlist[2*In_Index] << " y : "<< In.pointlist[2*In_Index+1] <<endl;
    In.pointmarkerlist[In_Index] = CurrComp;
    In.segmentlist[2*In_Index] = In_Index;
    In.segmentlist[2*In_Index+1] = In_Index+1;
    In.segmentmarkerlist[In_Index] = CurrComp;
    In_Index++;

   }
   
  CurrComp++;
//   cout<<endl;

  hi = (Yi[0] - Yi[3])/(double)N_Verti;
  x0 = Xi[3];
  y0 = Yi[3];
  y  = Yi[3];
  // points and segments on the horizontal boundary (marker=1)
 for(i=0;i<N_Verti;i++) // without last point
   {
    y = y0 + (double)i*hi;     
    In.pointlist[2*In_Index] = x0;
    In.pointlist[2*In_Index+1] = y;
//     cout<<" x : "<< In.pointlist[2*In_Index] << " y : "<< In.pointlist[2*In_Index+1] <<endl;
    In.pointmarkerlist[In_Index] = CurrComp;
    In.segmentlist[2*In_Index] = In_Index;
    In.segmentlist[2*In_Index+1] = In_Index+1;
    In.segmentmarkerlist[In_Index] = CurrComp;
    In_Index++;
 
   }
  CurrComp++;  
  
  In.segmentlist[2*(In_Index-1)+1] = 0;
  temp=In_Index;
 
  
  T_a = TDatabase::ParamDB->P1; // x axis value in ellipse
  T_b = TDatabase::ParamDB->P2; // y axis value in ellipse !!! set in modifyGausscoord funct also
//   deviation = fabs( T_a - T_b);  


   C_x = 0.0;  // center of the inner phase
   C_y = 0.0, // center of the inner phase
   phi1 = 0.000000E+0000; // end degree value of interface
   phi2 = 2.*Pi;
 
//   C_x = 0.0;  // center of the inner phase
//   C_y = 0.0, // center of the inner phase
  s = (phi2- phi1)/(double)N_Interface_Vert; 
 
  // points and segments on the interface (marker=2)
//   theta = 0.;
//   t0 = theta;
  
   for(i=0;i<N_Interface_Vert;i++)
    {
      theta = phi1 + (double)i*s;       
//      cout<<" theta : "<< theta <<endl;
      
//       if(fabs(I_FaceX[i]) < 1e-10 ) I_FaceX[i] = 0.0;
      In.pointlist[2*In_Index] =   T_a*cos(theta);;
      In.pointlist[2*In_Index+1] =  T_b*sin(theta);

//       if(i==0) 
//        {
//         FreeBD_X = I_FaceX[i];   FreeBD_Y = I_FaceY[i]; 
//        cout << " sorting " << FreeBD_X << ' ' << FreeBD_Y<<endl;
//        }

//       if(i==1)
//        {
//         h_interface = sqrt((I_FaceX[i-1]-I_FaceX[i])*(I_FaceX[i-1]-I_FaceX[i]) +
//                             (I_FaceY[i-1]-I_FaceY[i])*(I_FaceY[i-1]-I_FaceY[i]) );
//         OutPut("h_interface " <<h_interface << endl);
//        }
//       cout<<(180./Pi)*theta<< " x : "<< In.pointlist[2*In_Index] << " y : "<< In.pointlist[2*In_Index+1] <<endl;

      In.pointmarkerlist[In_Index] = CurrComp;
      In.segmentlist[2*In_Index] = In_Index;
      In.segmentlist[2*In_Index+1] = In_Index+1;
      In.segmentmarkerlist[In_Index] = CurrComp;
      In_Index++;
    }

  In.segmentlist[2*(In_Index-1)+1] = temp;  
  
//  exit(0);
 
  if(Out.pointlist!=NULL) {
    free(Out.pointlist); Out.pointlist = NULL;}
  if(Out.pointattributelist!=NULL) {
    free(Out.pointattributelist); Out.pointattributelist = NULL;}
  if(Out.pointmarkerlist!=NULL) {
    free(Out.pointmarkerlist); Out.pointmarkerlist = NULL;}
  if(Out.trianglelist!=NULL) {
    free(Out.trianglelist); Out.trianglelist = NULL;}
  if(Out.triangleattributelist!=NULL) {
    free(Out.triangleattributelist); Out.triangleattributelist = NULL;}
  if(Out.trianglearealist!=NULL) {
    free(Out.trianglearealist); Out.trianglearealist = NULL;}
  if(Out.neighborlist!=NULL) {
    free(Out.neighborlist); Out.neighborlist = NULL;}
  if(Out.segmentlist!=NULL) {
    free(Out.segmentlist); Out.segmentlist = NULL;}
  if(Out.segmentmarkerlist!=NULL) {
    free(Out.segmentmarkerlist); Out.segmentmarkerlist = NULL;}
  if(Out.holelist!=NULL) {
    free(Out.holelist); Out.holelist = NULL;}
  if(Out.regionlist!=NULL) {
    free(Out.regionlist); Out.regionlist = NULL;}
  if(Out.edgelist!=NULL) {
    free(Out.edgelist); Out.edgelist = NULL;}
  if(Out.edgemarkerlist!=NULL) {
    free(Out.edgemarkerlist); Out.edgemarkerlist = NULL;}
  if(Out.normlist!=NULL) {
    free(Out.normlist); Out.normlist = NULL;}

  // call triangle
  triangulate((char*)opts.str().c_str(), &In, &Out, (struct triangulateio *)NULL);
  
  
  Domain->GetTreeInfo(CellTree, N_RootCells);
  coll = Domain->GetCollection(It_Finest, 0);
  N_Cells = coll->GetN_Cells();
  
  // remove all existing vertices and joints
  VertexDel = new TVertex*[3*N_RootCells];
  
   CurrVertex = 0;

  for(i=0;i<N_Cells;i++)
    {
      cell = coll->GetCell(i);
      N_Joints = cell->GetN_Joints();
      N_Vertices = cell->GetN_Vertices();
      for(j=0;j<N_Joints;j++)
        {
         if(CurrVertex==0)
          {
              VertexDel[CurrVertex] = cell->GetVertex(j);
              CurrVertex++;
           }
          else
           {
            ID = 0;
            for(k=0;k<CurrVertex;k++)
            if(VertexDel[k]==cell->GetVertex(j))
             {
              ID = 1; break;
             }
            if(ID!=1)
             {
              VertexDel[CurrVertex] = cell->GetVertex(j);
              CurrVertex++;
             }
           } // else if(CurrVertex==0)

          ID = 0;
          for(k=0;k<CurrVertex;k++)
          if(VertexDel[k]==cell->GetVertex((j+1)%N_Vertices))
           {
            ID = 1; break;
           }
            if(ID!=1)
           {
            VertexDel[CurrVertex] = cell->GetVertex((j+1)%N_Vertices);
            CurrVertex++;
           }
        } // for j
    } // for i
  for(i=0;i<CurrVertex;i++)
    delete VertexDel[i];

  delete []VertexDel;
  OutPut(CurrVertex<<" vertices were deleted"<<endl);

 // remove all existing cells and joints
  for(i=0;i<N_RootCells;i++)
    delete (TGridCell*)CellTree[i];
  OutPut(N_RootCells<<" cells were deleted"<<endl);
   delete CellTree;
   delete coll;

   
   
 // Solid Bound startx, starty, x length and y length
  UpdateBound[0]->SetParams(Xi[0], Yi[0], Xi[1]-Xi[0],Yi[1]-Yi[0]);
  UpdateBound[1]->SetParams(Xi[1], Yi[1], Xi[2]-Xi[1],Yi[2]-Yi[1]);
  UpdateBound[2]->SetParams(Xi[2], Yi[2], Xi[3]-Xi[2],Yi[3]-Yi[2]);
  UpdateBound[3]->SetParams(Xi[3], Yi[3], Xi[0]-Xi[3],Yi[0]-Yi[3]);
  

// Free boundary xmid, ymid, radius_a, radius_b, start angle, end angle
  UpdateIntface->SetParams(C_x, C_y, T_a, T_b, phi1, phi2);   
   
   
  N_RootCells = Out.numberoftriangles; 

  // allocate auxillary fields
  Coordinates = Out.pointlist;
  Triangles = Out.trianglelist;
  PartMarker = new int[Out.numberofpoints];

  // generate new vertices
  N_G = Out.numberofpoints;
  NewVertices = new TVertex*[N_G];

  for (i=0;i<N_G;i++)
     NewVertices[i] = new TVertex(Coordinates[2*i], Coordinates[2*i+1]);

//       // set bounding box
//   left = bottom = 1e8;
//   right = top = -1e8;
// 
//    for(i=0;i<In.numberofpoints;i++)
//     {
//       if(left>In.pointlist[2*i]) left = In.pointlist[2*i];
//       if(right<In.pointlist[2*i]) right = In.pointlist[2*i];
//       if(top<In.pointlist[2*i+1]) top = In.pointlist[2*i+1];
//       if(bottom>In.pointlist[2*i+1]) bottom = In.pointlist[2*i+1];
//     }  
 
/* // Solid Bound startx, starty, x length and y length
  UpdateSlipBound[0]->SetParams(Xi[0], Yi[0], Xi[1]-Xi[0],Yi[1]-Yi[0]);
  UpdateSlipBound[1]->SetParams(Xi[1], Yi[1], Xi[2]-Xi[1],Yi[2]-Yi[1]);
  UpdateSlipBound[2]->SetParams(Xi[2], Yi[2], Xi[3]-Xi[2],Yi[3]-Yi[2]);
  UpdateSlipBound[3]->SetParams(Xi[3], Yi[3], Xi[0]-Xi[3],Yi[0]-Yi[3]);

// Free boundary xmid, ymid, radius_a, radius_b, start angle, end angle
  UpdateIntface->SetParams(C_x, C_y, T_a, T_b, phi1, phi2);*/  
  
 // generate cells
  CellTree = new TBaseCell*[N_RootCells];

  for (i=0;i<N_RootCells;i++)
  {
    CellTree[i] = new TMacroCell(TDatabase::RefDescDB[Triangle], 0);

    CellTree[i]->SetVertex(0, NewVertices[Out.trianglelist[3*i    ]]);
    CellTree[i]->SetVertex(1, NewVertices[Out.trianglelist[3*i + 1]]);
    CellTree[i]->SetVertex(2, NewVertices[Out.trianglelist[3*i + 2]]);

      ((TMacroCell *) CellTree[i])->SetSubGridID(0);
  }

  Domain->SetTreeInfo(CellTree, N_RootCells);

  // initialize iterators
  TDatabase::IteratorDB[It_EQ]->SetParam(Domain);
  TDatabase::IteratorDB[It_LE]->SetParam(Domain);
  TDatabase::IteratorDB[It_Finest]->SetParam(Domain);
  TDatabase::IteratorDB[It_Between]->SetParam(Domain);
  TDatabase::IteratorDB[It_OCAF]->SetParam(Domain);   
  
  // search neighbours
  N_G = Out.numberofpoints;
  PointNeighb = new int[N_G];

  memset(PointNeighb, 0, N_G *SizeOfInt);

  for (i=0;i<3*N_RootCells;i++)
    PointNeighb[Triangles[i]]++;

  maxEpV=0;

  for (i=0;i<N_G;i++)
    if (PointNeighb[i] > maxEpV) maxEpV = PointNeighb[i];
  delete [] PointNeighb;

  PointNeighb = new int[++maxEpV * N_G];

  memset(PointNeighb, 0, maxEpV * N_G *SizeOfInt);
      
   // first colomn contains the number of following elements
   // for every point at first column we set the number of neighbour points
   // at further columns we set the index of corresponding cells
  for(i=0;i<3*N_RootCells;i++)
  {
    j = Triangles[i]*maxEpV;
    PointNeighb[j]++;
    PointNeighb[j + PointNeighb[j]] = i / 3;
  }
 
  // generate new edges
  N_G = Out.numberofedges;
  for (i=0;i<N_G;i++)
  {
    a = Out.edgelist[2*i];
    b = Out.edgelist[2*i+1];
    Neib[0] = -1;
    Neib[1] = -1;
    CurrNeib = 0;

    len1 = PointNeighb[a*maxEpV];
    len2 = PointNeighb[b*maxEpV];

  // find indexes of cells containing the current edge
   for (j=1;j<=len1;j++)
    {
      Neighb_tmp = PointNeighb[a*maxEpV + j];
       for (k=1;k<=len2;k++)
        if (Neighb_tmp == PointNeighb[b*maxEpV + k])
        {
          Neib[CurrNeib++] = Neighb_tmp;
          break;
        }
      if (CurrNeib == 2) break;
    }

//          cout<<BDpart << " BDpart CurrComp "<< CurrComp <<endl;
 
     
    
    if (Out.edgemarkerlist[i]) // 0 for inner edges and Boundcomp+1 for Boundedge respect
    {
      CurrComp = Out.edgemarkerlist[i] - 1;
      if (CurrComp >= 100000) CurrComp -= 100000;
      
      BDpart=Domain->GetBdPartID(CurrComp);
      CurrComp= Domain->GetLocalBdCompID(CurrComp);

//      cout<<BDpart << " BDpart CurrComp "<< CurrComp <<endl;
 
      if(Domain->GetBdPart(BDpart)->GetBdComp(CurrComp)->GetTofXY(
            NewVertices[a]->GetX(), NewVertices[a]->GetY(), T_a) ||
          Domain->GetBdPart(BDpart)->GetBdComp(CurrComp)->GetTofXY(
            NewVertices[b]->GetX(), NewVertices[b]->GetY(), T_b))
       {
          cerr<<"Error: could not set parameter values"<<endl;
          OutPut(NewVertices[a]<<endl);
          OutPut(NewVertices[b]<<endl);
        //  exit(0);
       }
       
// ===============================================================================       
 //  due to the hole the orientation of the circle is colck-wise  from out side
// the parameter of the starting edge (in 0, 2pi) is for e.g (0, 0.9) (colck-wise) 
// while refining to get the mid point we should get  the mid point parameter as 0.95 
// but we will get only (0+0.9)/2 =0.45 (wrong mid point). So we change.
//  Note only if the orientation is colck-wise  !!!!!!!
// ===============================================================================  

     if(BDpart==1 && CurrComp==0  && fabs(T_a)==0 ) T_a=1;      
       
       
//       cout<<BDpart << " BDpart CurrComp "<< CurrComp <<endl;
     
     
      if (CurrNeib == 2)    // 2 cells contain the current edge
       {
        if(Domain->GetBdPart(BDpart)->GetBdComp(CurrComp)->IsFreeBoundary())
     {
          Joint = new TIsoInterfaceJoint(Domain->GetBdPart(BDpart)->GetBdComp(CurrComp),
                  T_a, T_b, CellTree[Neib[0]], CellTree[Neib[1]]);
     }
        else
     {
          Joint = new TInterfaceJoint(Domain->GetBdPart(BDpart)->GetBdComp(CurrComp),
                  T_a, T_b, CellTree[Neib[0]], CellTree[Neib[1]]);
     }
       }
      else
       {
        if(Domain->GetBdPart(BDpart)->GetBdComp(CurrComp)->IsFreeBoundary())
     {
          Joint = new TIsoBoundEdge(Domain->GetBdPart(BDpart)->GetBdComp(CurrComp), T_a, T_b);
//     cout<<" FreeBoundary"<<endl;
     }
        else
         { 
          Joint = new TBoundEdge(Domain->GetBdPart(BDpart)->GetBdComp(CurrComp), T_a, T_b);
         }
       }
    }
    else // inner edge
    {
    if (CurrNeib != 2)
        cerr << "Error!!!!!!!! not enough neighbours!" << endl;

    Joint = new TJointEqN(CellTree[Neib[0]], CellTree[Neib[1]]);
    }

    // find the local index for the point 'a' on the cell
    for (j=0;j<3;j++)
      if (Triangles[3*Neib[0]+j] == a) break;

    // find the local index for the point 'b' on the cell
    for (k=0;k<3;k++)
      if (Triangles[3*Neib[0]+k] == b) break;

   k = k*10 + j;

    switch (k)
    {
      case  1:
      case 10:
        j = 0;
        break;
      case 12:
      case 21:
        j = 1;
        break;
      case  2:
      case 20:
        j = 2;
        break;
    }

  CellTree[Neib[0]]->SetJoint(j, Joint);

   if (Neib[1] != -1)
    {
      // find the local index for the point 'a' on the cell
      for (j=0;j<3;j++)
        if (Triangles[3*Neib[1]+j] == a) break;

      // find the local index for the point 'b' on the cell
      for (k=0;k<3;k++)
        if (Triangles[3*Neib[1]+k] == b) break;

      k = k*10 + j;

      switch (k) // j will contain the local index for the current
      {
        case  1:
        case 10:
          j = 0;
          break;
        case 12:
        case 21:
          j = 1;
          break;
        case  2:
        case 20:
          j = 2;
          break;
      }

      CellTree[Neib[1]]->SetJoint(j, Joint);
    }

  if (Joint->GetType() == InterfaceJoint ||
        Joint->GetType() == IsoInterfaceJoint)
      ((TInterfaceJoint *) Joint)->CheckOrientation();
  }
 

  delete [] NewVertices;
  delete [] PointNeighb;
  delete [] In.pointlist;
  delete [] In.pointmarkerlist;
  delete [] In.segmentlist;
  delete [] In.segmentmarkerlist;
  
  if(Out.pointlist!=NULL) {
    free(Out.pointlist); Out.pointlist = NULL;}
  if(Out.pointattributelist!=NULL) { 
    free(Out.pointattributelist); Out.pointattributelist = NULL;}
  if(Out.pointmarkerlist!=NULL) {
    free(Out.pointmarkerlist); Out.pointmarkerlist = NULL;}
  if(Out.trianglelist!=NULL) {
    free(Out.trianglelist); Out.trianglelist = NULL;}
  if(Out.triangleattributelist!=NULL) {
    free(Out.triangleattributelist); Out.triangleattributelist = NULL;}
  if(Out.trianglearealist!=NULL) {
    free(Out.trianglearealist); Out.trianglearealist = NULL;}
  if(Out.neighborlist!=NULL) {
    free(Out.neighborlist); Out.neighborlist = NULL;}
  if(Out.segmentlist!=NULL) {
    free(Out.segmentlist); Out.segmentlist = NULL;}
  if(Out.segmentmarkerlist!=NULL) {
    free(Out.segmentmarkerlist); Out.segmentmarkerlist = NULL;}
  if(Out.holelist!=NULL) {
    free(Out.holelist); Out.holelist = NULL;}
  if(Out.regionlist!=NULL) {
    free(Out.regionlist); Out.regionlist = NULL;}
  if(Out.edgelist!=NULL) {
    free(Out.edgelist); Out.edgelist = NULL;}
  if(Out.edgemarkerlist!=NULL) {
    free(Out.edgemarkerlist); Out.edgemarkerlist = NULL;}
  if(Out.normlist!=NULL) {
    free(Out.normlist); Out.normlist = NULL;} 
  
//======================================================================
// Triangular for grid generation --end
//======================================================================


//   cout<< "tetgen" <<endl;
//   exit(0);
  
 
} // TriaReMeshGen