turbulent_viscosity_fvcr_impl.h

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/*
 * Copyright (c) 2013:  G-CSC, Goethe University Frankfurt
 * Author: Christian Wehner
 * 
 * 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 __H__UG__NAVIER_STOKES_TURBULENT_VISCOSITY_DATA_IMPL_H_
#define __H__UG__NAVIER_STOKES_TURBULENT_VISCOSITY_DATA_IMPL_H_
 
namespace ug{
namespace NavierStokes{
 
template <typename TData, int dim, typename TImpl,typename TGridFunction>
void StdTurbulentViscosityData<TData,dim,TImpl,TGridFunction>::transferToLowerLevels(aSideNumber& aaData,ApproximationSpace<domain_type>& approximationSpace){
  for(int si = 0; si < approximationSpace.domain()->subset_handler()->num_subsets(); ++si){
    // transfer to lower levels, averaging over child edges (2d) / child faces (3d)
    for (size_t lev=approximationSpace.num_levels()-2;(int)lev>=0;lev--){
      const DoFDistribution& lDD = *approximationSpace.dof_distribution(GridLevel(lev, GridLevel::LEVEL));
      const MultiGrid& grid = *lDD.multi_grid();
      typedef typename DoFDistribution::traits<side_type>::const_iterator coarseLevelSideIter;
      coarseLevelSideIter clsIter, clsIterEnd;
      clsIter = lDD.template begin<side_type>(si);
      clsIterEnd = lDD.template end<side_type>(si);
      for (;clsIter != clsIterEnd;clsIter++){
        side_type* elem = *clsIter;
        size_t numChildren = grid.num_children<side_type>(elem);
        number avgValue=0;
        for (size_t i=0;i<numChildren;i++){
          avgValue += aaData[grid.get_child<side_type>(elem, i)];
        }
        avgValue/=numChildren;
        aaData[elem] = avgValue;
      }
      if (lev==0) break;
    }
  }
}
void StdTurbulentViscosityData<TData,dim,TImpl,TGridFunction>::transferToLowerLevels(aSideNumber& aaData,ApproximationSpace<domain_type>& approximationSpace) {…}
 
template <typename TData, int dim, typename TImpl,typename TGridFunction>
void StdTurbulentViscosityData<TData,dim,TImpl,TGridFunction>::fillAttachment(aSideDimVector& aaU,SmartPtr<TGridFunction> u){
  //  get domain
  domain_type& domain = *u->domain().get();
  //  create Multiindex
  std::vector<DoFIndex> multInd;
  for(int si = 0; si < domain.subset_handler()->num_subsets(); ++si){
    ElemIterator iter = u->template begin<side_type>(si);
    ElemIterator iterEnd = u->template end<side_type>(si);
    for(  ;iter !=iterEnd; ++iter)
    {
      side_type* side = iter;
      for (int d=0;d<dim;d++){
        u->dof_indices(side, d, multInd);
        aaU[side][d]=DoFRef(*u,multInd[0]);
      }
    }
  }
}
void StdTurbulentViscosityData<TData,dim,TImpl,TGridFunction>::fillAttachment(aSideDimVector& aaU,SmartPtr<TGridFunction> u) {…}
 
void assignValue(number& v,size_t ind,number value){
  v=value;  
}
void assignValue(number& v,size_t ind,number value) {…}
  
void assignValue(MathVector<2>& v,size_t ind,number value){
  v[ind]=value;
}
void assignValue(MathVector<2>& v,size_t ind,number value) {…}
  
void assignValue(MathVector<3>& v,size_t ind,number value){
  v[ind]=value;
}
void assignValue(MathVector<3>& v,size_t ind,number value) {…}
  
void assignValue(MathSymmetricMatrix<2>& v,size_t ind,number value){
  v[ind]=value;
}
void assignValue(MathSymmetricMatrix<2>& v,size_t ind,number value) {…}
  
void assignValue(MathSymmetricMatrix<3>& v,size_t ind,number value){
  v[ind]=value;
}
void assignValue(MathSymmetricMatrix<3>& v,size_t ind,number value) {…}
 
// go over all elements, interpolate data to barycenter, average by multiplying with corresponding element volume and deviding by complete adjacent element volume
// parameters: filtered values, filter volume (computed in function), original values
template <typename TData, int dim, typename TImpl,typename TGridFunction>
template <typename VType>
void StdTurbulentViscosityData<TData,dim,TImpl,TGridFunction>::elementFilter(PeriodicAttachmentAccessor<side_type,Attachment<VType> >& aaUHat,aSideNumber& aaVol,
                                       SmartPtr<TGridFunction> u,PeriodicAttachmentAccessor<side_type,Attachment<VType> >* aaU){
  bool useGridFunction = true;
  if (u==SPNULL) useGridFunction = false;
  
  std::vector<DoFIndex> multInd;
  
  //  get domain of grid function
  domain_type& domain = *m_uInfo->domain().get();
  DimCRFVGeometry<dim> geo;
 
  // set attachment values to zero
  SetAttachmentValues(aaUHat , m_uInfo->template begin<side_type>(), m_uInfo->template end<side_type>(), 0);
  SetAttachmentValues(aaVol , m_uInfo->template begin<side_type>(), m_uInfo->template end<side_type>(), 0);
 
  //  coord and vertex array
  MathVector<dim> coCoord[domain_traits<dim>::MaxNumVerticesOfElem];
  Vertex* vVrt[domain_traits<dim>::MaxNumVerticesOfElem];
 
  //  get position accessor
  typedef typename domain_type::position_accessor_type position_accessor_type;
  const position_accessor_type& posAcc = domain.position_accessor();
 
  // assemble deformation tensor fluxes
  for(int si = 0; si < domain.subset_handler()->num_subsets(); ++si)
  {
    //  get iterators
    ElemIterator iter = m_uInfo->template begin<elem_type>(si);
    ElemIterator iterEnd = m_uInfo->template end<elem_type>(si);
 
    //  loop elements of dimension
    for(  ;iter !=iterEnd; ++iter)
    {
      //  get Elem
      elem_type* elem = *iter;
      //  get vertices and extract corner coordinates
      const size_t numVertices = elem->num_vertices();
      MathVector<dim> bary,localBary;
      bary = 0;
 
      for(size_t i = 0; i < numVertices; ++i){
        vVrt[i] = elem->vertex(i);
        coCoord[i] = posAcc[vVrt[i]];
        bary += coCoord[i];
      };
      bary /= numVertices;
 
      //  reference object id
      ReferenceObjectID roid = elem->reference_object_id();
 
      //  get trial space
      const LocalShapeFunctionSet<dim>& rTrialSpace =
      LocalFiniteElementProvider::get<dim>(roid, LFEID(LFEID::CROUZEIX_RAVIART, dim, 1));
 
      //  get Reference Mapping
      DimReferenceMapping<dim, dim>& map = ReferenceMappingProvider::get<dim, dim>(roid, coCoord);
 
      map.global_to_local(localBary,bary);
 
      typedef typename grid_type::template traits<side_type>::secure_container side_secure_container;
      side_secure_container sides;
 
      UG_ASSERT(dynamic_cast<elem_type*>(elem) != NULL, "Only elements of type elem_type are currently supported");
 
      domain.grid()->associated_elements_sorted(sides, static_cast<elem_type*>(elem) );
      if (m_bAdaptive){
        std::vector<DoFIndex> ind;
        m_uInfo->dof_indices(elem,0,ind,true,true);
        get_constrained_sides_cr<side_type,side_secure_container,TGridFunction>(sides,*m_uInfo,ind);
      }
 
      //  memory for shapes
      std::vector<number> vShape;
 
      //  evaluate finite volume geometry
      if (!m_bAdaptive)
        geo.update(elem, &(coCoord[0]), domain.subset_handler().get());
      else
        geo.update_hanging(elem, &(coCoord[0]), domain.subset_handler().get());
 
      rTrialSpace.shapes(vShape, localBary);
 
      size_t nofsides = geo.num_scv();
 
      VType value;
      value = 0;
      number elementVolume = 0;
      for (size_t i=0;i<nofsides;i++){
        const typename DimCRFVGeometry<dim>::SCV& scv = geo.scv(i);
        size_t s = scv.node_id();
        VType localValue;
        if (useGridFunction)
          for (int d=0;d<dim;d++){
            u->dof_indices(sides[s], d, multInd);
            assignValue(localValue,d,DoFRef(*u,multInd[0]));
          }
        else
          localValue = (*aaU)[sides[s]];
        localValue *= vShape[s];
        value += localValue;
        elementVolume += scv.volume();
      }
      value *= elementVolume;
      for (size_t s=0;s<nofsides;s++){
        aaUHat[sides[s]] += value;
        aaVol[sides[s]] += elementVolume;
      }
    }
  }
  PeriodicBoundaryManager* pbm = (domain.grid())->periodic_boundary_manager();
  // average
  for(int si = 0; si < domain.subset_handler()->num_subsets(); ++si)
  {
    SideIterator sideIter = m_uInfo->template begin<side_type>(si);
    SideIterator sideIterEnd = m_uInfo->template end<side_type>(si);
    // no filtering in boundary nodes
    if ((m_turbZeroSg.size()!=0) && (m_turbZeroSg.contains(si)==true)){
      for(  ;sideIter !=sideIterEnd; sideIter++)
      {
        side_type* side = *sideIter;
        if (pbm && pbm->is_slave(side)) continue;
        if (useGridFunction){
          for (int d=0;d<dim;d++){
            u->dof_indices(side, d, multInd);
            assignValue(aaUHat[side],d,DoFRef(*u,multInd[0]));
          }
        }
        else
          aaUHat[side] = (*aaU)[side];
      }
    } else {
      for(  ;sideIter !=sideIterEnd; sideIter++)
      {
        side_type* side = *sideIter;
        if (pbm && pbm->is_slave(side)) continue;
        // constrained edges
        if (aaVol[side]==0) continue;
        aaUHat[side]/=(number)aaVol[side];
      }
    }
  } 
  if (m_bAdaptive){ 
    if (dim==2) constrainingSideAveraging<TGridFunction,side_type,ConstrainingEdge,VType>(aaUHat,m_uInfo);
    else {
      constrainingSideAveraging<TGridFunction,side_type,ConstrainingTriangle,VType>(aaUHat,m_uInfo);
      constrainingSideAveraging<TGridFunction,side_type,ConstrainingQuadrilateral,VType>(aaUHat,m_uInfo);
    }
  }
}
 
// go over all elements, interpolate data to scv barycenter, average by multiplying with corresponding scv volume and deviding by volume of complete control volume
template <typename TData, int dim, typename TImpl,typename TGridFunction>
template <typename VType>
void StdTurbulentViscosityData<TData,dim,TImpl,TGridFunction>::scvFilter(PeriodicAttachmentAccessor<side_type,Attachment<VType> >& aaUHat,aSideNumber& aaVol,
                                     SmartPtr<TGridFunction> u,PeriodicAttachmentAccessor<side_type,Attachment<VType> >* aaU){
  bool useGridFunction = true;
  if (u==NULL) useGridFunction = false;
 
  std::vector<DoFIndex> multInd;
  //  get domain of grid function
  domain_type& domain = *m_uInfo->domain().get();
  DimCRFVGeometry<dim> geo;
  
  // set attachment values to zero
  SetAttachmentValues(aaUHat , m_uInfo->template begin<side_type>(), m_uInfo->template end<side_type>(), 0);
  SetAttachmentValues(aaVol , m_uInfo->template begin<side_type>(), m_uInfo->template end<side_type>(), 0);
  
  //  coord and vertex array
  MathVector<dim> coCoord[domain_traits<dim>::MaxNumVerticesOfElem];
  Vertex* vVrt[domain_traits<dim>::MaxNumVerticesOfElem];
  
  //  get position accessor
  typedef typename domain_type::position_accessor_type position_accessor_type;
  const position_accessor_type& posAcc = domain.position_accessor();
  
  // assemble deformation tensor fluxes
  for(int si = 0; si < domain.subset_handler()->num_subsets(); ++si)
  {
    //  get iterators
    ElemIterator iter = m_uInfo->template begin<elem_type>(si);
    ElemIterator iterEnd = m_uInfo->template end<elem_type>(si);
    
    //  loop elements of dimension
    for(  ;iter !=iterEnd; ++iter)
    {
      //  get Elem
      elem_type* elem = *iter;
      //  get vertices and extract corner coordinates
      const size_t numVertices = elem->num_vertices();
      MathVector<dim> bary,localBary;
      bary = 0;
      
      for(size_t i = 0; i < numVertices; ++i){
        vVrt[i] = elem->vertex(i);
        coCoord[i] = posAcc[vVrt[i]];
        bary += coCoord[i];
      };
      bary /= numVertices;
      
      //  reference object id
      ReferenceObjectID roid = elem->reference_object_id();
      
      //  get trial space
      const LocalShapeFunctionSet<dim>& rTrialSpace =
      LocalFiniteElementProvider::get<dim>(roid, LFEID(LFEID::CROUZEIX_RAVIART, dim, 1));
      
      //  get Reference Mapping
      DimReferenceMapping<dim, dim>& map = ReferenceMappingProvider::get<dim, dim>(roid, coCoord);
      
      map.global_to_local(localBary,bary);
      
      typedef typename grid_type::template traits<side_type>::secure_container side_secure_container;
      side_secure_container sides;
      
      UG_ASSERT(dynamic_cast<elem_type*>(elem) != NULL, "Only elements of type elem_type are currently supported");
      
      domain.grid()->associated_elements_sorted(sides, static_cast<elem_type*>(elem) );
      
      //  evaluate finite volume geometry
      if (!m_bAdaptive){
        geo.update(elem, &(coCoord[0]), domain.subset_handler().get());
      } else {
        geo.update_hanging(elem, &(coCoord[0]), domain.subset_handler().get());
        if (geo.num_constrained_dofs()>0){
          m_uInfo->dof_indices(elem,0,multInd,true,true);
          get_constrained_sides_cr<side_type,side_secure_container,TGridFunction>(sides,*m_uInfo,multInd);
        }
      }
      
      size_t nNaturalSides = geo.num_sh();
      size_t nSides = geo.num_scv();
      
      MathVector<dim> scvBary,scvLocalBary;
      for (size_t i=0;i<nSides;i++){
        const typename DimCRFVGeometry<dim>::SCV& scv = geo.scv(i);
        size_t s = geo.node_id();
        scvBary = 0;
        // compute barycenter of scv (average of side corner nodes + element bary)
        for (size_t j=0;j<scv.num_corners();j++){
          scvBary += scv.global_corner(j);
        }
        scvBary/=(number)scv.num_corners();
        map.global_to_local(scvLocalBary,scvBary);
        //  memory for shapes
        std::vector<number> vShape;
        rTrialSpace.shapes(vShape, scvLocalBary);
        VType localValue = 0;
        for (size_t j=0;j<nNaturalSides;j++){
          if (useGridFunction){
            VType uValue;
            for (int d=0;d<dim;d++){
              u->dof_indices(sides[j], d, multInd);
              assignValue(uValue,d,DoFRef(*u,multInd[0]));
            }
            localValue += vShape[j]*uValue;
          } else
            localValue += vShape[j]*aaU[sides[j]];
        }
        localValue *= scv.volume();
        aaVol[sides[s]]  += scv.volume();
        aaUHat[sides[s]] += localValue;
      }
    }
  }
  PeriodicBoundaryManager* pbm = (domain.grid())->periodic_boundary_manager();
  // average
  for(int si = 0; si < domain.subset_handler()->num_subsets(); ++si)
  {
    SideIterator sideIter = m_uInfo->template begin<side_type>(si);
    SideIterator sideIterEnd = m_uInfo->template end<side_type>(si);
    // no filtering in boundary nodes
    if ((m_turbZeroSg.size()!=0) && (m_turbZeroSg.contains(si)==true)){
      for(  ;sideIter !=sideIterEnd; sideIter++)
      {
        side_type* side = *sideIter;
        if (pbm && pbm->is_slave(side)) continue;
        aaUHat[side] = aaU[side];
      }
    } else {
      for(  ;sideIter !=sideIterEnd; sideIter++)
      {
        side_type* side = *sideIter;
        if (pbm && pbm->is_slave(side)) continue;
        aaUHat[side]/=(number)aaVol[side];
      }
    }
  }
  if (m_bAdaptive){
    if (dim==2) constrainingSideAveraging<TGridFunction,side_type,ConstrainingEdge,VType>(aaUHat,m_uInfo);
    else {
      constrainingSideAveraging<TGridFunction,side_type,ConstrainingTriangle,VType>(aaUHat,m_uInfo);
      constrainingSideAveraging<TGridFunction,side_type,ConstrainingQuadrilateral,VType>(aaUHat,m_uInfo);
    }
  }
}
void StdTurbulentViscosityData<TData,dim,TImpl,TGridFunction>::scvFilter(PeriodicAttachmentAccessor<side_type,Attachment<VType> >& aaUHat,aSideNumber& aaVol, {…}
  
template <typename TData, int dim, typename TImpl,typename TGridFunction>
void StdTurbulentViscosityData<TData,dim,TImpl,TGridFunction>::assembleDeformationTensor(aSideTensor& aaDefTensor,aSideNumber& aaVol,SmartPtr<TGridFunction> u,aSideDimVector* aaU){
  bool useGridFunction = true;
  if (u==SPNULL) useGridFunction = false;
 
  //  get domain
  domain_type& domain = *m_uInfo->domain().get();
  // get periodic boundary manager
  PeriodicBoundaryManager* pbm = (domain.grid())->periodic_boundary_manager();
 
  //  create Multiindex
  std::vector<DoFIndex> multInd;
 
  DimCRFVGeometry<dim> geo;
 
  // add boundary subsets to enforce boundary subset computations in geo.update()
  for(size_t i = 0; i < m_turbZeroSg.size(); ++i){
    geo.add_boundary_subset(m_turbZeroSg[i]);
  }
 
  // set attachment values to zero
  SetAttachmentValues(aaDefTensor , m_uInfo->template begin<side_type>(), m_uInfo->template end<side_type>(), 0);
  SetAttachmentValues(aaVol , m_uInfo->template begin<side_type>(), m_uInfo->template end<side_type>(), 0);
 
  //  coord and vertex array
  MathVector<dim> coCoord[domain_traits<dim>::MaxNumVerticesOfElem];
  Vertex* vVrt[domain_traits<dim>::MaxNumVerticesOfElem];
 
  //  get position accessor
  typedef typename domain_type::position_accessor_type position_accessor_type;
  const position_accessor_type& posAcc = domain.position_accessor();
 
  for(int si = 0; si < domain.subset_handler()->num_subsets(); ++si){
    //  get iterators
    ElemIterator iter = m_uInfo->template begin<elem_type>(si);
    ElemIterator iterEnd = m_uInfo->template end<elem_type>(si);
 
    //  loop elements of dimension
    for(  ;iter !=iterEnd; ++iter)
    {
      //  get Elem
      elem_type* elem = *iter;
      //  get vertices and extract corner coordinates
      const size_t numVertices = elem->num_vertices();
      for(size_t i = 0; i < numVertices; ++i){
        vVrt[i] = elem->vertex(i);
        coCoord[i] = posAcc[vVrt[i]];
      };
 
      static const size_t MaxNumSidesOfElem = 10;
 
      typedef MathVector<dim> MVD;
      std::vector<MVD> uValue(MaxNumSidesOfElem);
      MVD ipVelocity;
 
      typedef typename grid_type::template traits<side_type>::secure_container side_secure_container;
      side_secure_container sides;
 
      UG_ASSERT(dynamic_cast<elem_type*>(elem) != NULL, "Only elements of type elem_type are currently supported");
 
      domain.grid()->associated_elements_sorted(sides, static_cast<elem_type*>(elem) );
 
      //  evaluate finite volume geometry
      if (!m_bAdaptive){
        geo.update(elem, &(coCoord[0]), domain.subset_handler().get());
      } else {
        geo.update_hanging(elem, &(coCoord[0]), domain.subset_handler().get());
        if (geo.num_constrained_dofs()>0){
          m_uInfo->dof_indices(elem,0,multInd,true,true);
          get_constrained_sides_cr<side_type,side_secure_container,TGridFunction>(sides,*m_uInfo,multInd);
        }
      }
 
      size_t nNaturalSides = geo.num_sh();
      size_t nSides = geo.num_scv();
      size_t nip = geo.num_scvf();
 
      if (useGridFunction){
        for (size_t s=0;s < nNaturalSides;s++){
          for (int d=0;d<dim;d++){
            m_uInfo->dof_indices(sides[s], d, multInd);
            uValue[s][d]=DoFRef(*u,multInd[0]);
          }
        }
      } else
      {
        for (size_t s=0;s < nNaturalSides;s++)
          uValue[s]=(*aaU)[sides[s]];
      }
 
      for (size_t i=0;i < nSides;i++)
      {
        const typename DimCRFVGeometry<dim>::SCV& scv = geo.scv(i);
        size_t s = scv.node_id();
        aaVol[sides[s]] += scv.volume();
      }
 
      for (size_t ip=0;ip<nip;ip++){
        //  get current SCVF
        ipVelocity = 0;
        const typename DimCRFVGeometry<dim>::SCVF& scvf = geo.scvf(ip);
        for (size_t s=0;s < nNaturalSides;s++){
          for (int d=0;d<dim;d++){
              ipVelocity[d] += scvf.shape(s)*uValue[s][d];
          };
        };
        dimMat ipDefTensorFlux;
        ipDefTensorFlux = 0;
        size_t ind = 0;
        for (int i=0;i<dim;i++){
          for (int j=i;j<dim;j++){
            ipDefTensorFlux[ind]= 0.5 * (ipVelocity[i] * scvf.normal()[j] + ipVelocity[j] * scvf.normal()[i]);
            ind++;
          }
        }
        aaDefTensor[sides[scvf.from()]]+=ipDefTensorFlux;
        aaDefTensor[sides[scvf.to()]]-=ipDefTensorFlux;
      }
      for(size_t sgi = 0; sgi < m_turbZeroSg.size(); ++sgi){
        const size_t sgsi=m_turbZeroSg[sgi];
        if (geo.num_bf(sgsi) == 0) continue;
        for(size_t bfi = 0; bfi < geo.num_bf(sgsi); ++bfi){
          const typename DimCRFVGeometry<dim>::BF& bf = geo.bf(sgsi, bfi);
          const size_t sideID = bf.node_id();
          size_t ind = 0;
          for (int i=0;i<dim;i++){
            for (int j=i;j<dim;j++){
              // bf ip and u position are identical for CR-FV-Geometry
              //for debug UG_LOG("[" << i << "," << j << "]" <<  0.5 * (uValue[sideID][i] * bf.normal()[j] + uValue[sideID][j] * bf.normal()[i]) << "\n");
              aaDefTensor[sides[sideID]][ind] -= 0.5 * (uValue[sideID][i] * bf.normal()[j] + uValue[sideID][j] * bf.normal()[i]);
              ind++;
            }
          }
        }
      }
    }
  }
  // average
  for(int si = 0; si < domain.subset_handler()->num_subsets(); ++si){
    SideIterator sideIter = m_uInfo->template begin<side_type>(si);
    SideIterator sideIterEnd = m_uInfo->template end<side_type>(si);
    //for debug UG_LOG("|||||||||||||||||||||||||||||||||||\n");
    //for debug UG_LOG("si=" << si << "\n");
    for(  ;sideIter !=sideIterEnd; sideIter++)
    {
      side_type* side = *sideIter;
      if (pbm && pbm->is_slave(side)) continue;
      aaDefTensor[side]/=(number)aaVol[side];
      //for debug UG_LOG("$$$$$$$$$$$$$$$$$$$$$$$$$$$$\n");
    //  MathVector<dim> posCo;
    //        for (int d=0;d<dim;d++)
    //                posCo[d] = 0.5*posAcc[side->vertex(0)][d] + 0.5*posAcc[side->vertex(1)][d];
            //for debug UG_LOG(" c=" << posCo << "\n");
    //for debug       for (int d1=0;d1<dim;d1++)
    //for debug         for (int d2=0;d2<dim;d2++)
                  //for debug UG_LOG(" tensor(" << d1 << "," << d2 << ")=" << aaDefTensor[side][d1][d2] << "\n");
      //for debug UG_LOG(" norm=" << FNorm(aaDefTensor[side]) << "\n");
    }
  }
  // handle constrained sides
  if (m_bAdaptive){
    if (dim==2) constrainingSideAveraging<TGridFunction,side_type,ConstrainingEdge,dimMat>(aaDefTensor,m_uInfo);
    else {
      constrainingSideAveraging<TGridFunction,side_type,ConstrainingTriangle,dimMat>(aaDefTensor,m_uInfo);
      constrainingSideAveraging<TGridFunction,side_type,ConstrainingQuadrilateral,dimMat>(aaDefTensor,m_uInfo);
    }
  }
}
void StdTurbulentViscosityData<TData,dim,TImpl,TGridFunction>::assembleDeformationTensor(aSideTensor& aaDefTensor,aSideNumber& aaVol,SmartPtr<TGridFunction> u,aSideDimVector* aaU) {…}
 
template <typename TData, int dim, typename TImpl,typename TGridFunction>
void StdTurbulentViscosityData<TData,dim,TImpl,TGridFunction>::scaleTensorByNorm(aSideTensor& aaTensor){
  //  get domain of grid function
  domain_type& domain = *m_uInfo->domain().get();
  // get periodic boundary manager
  PeriodicBoundaryManager* pbm = (domain.grid())->periodic_boundary_manager();
  // average
  for(int si = 0; si < domain.subset_handler()->num_subsets(); ++si){
    SideIterator sideIter = m_uInfo->template begin<side_type>(si);
    SideIterator sideIterEnd = m_uInfo->template end<side_type>(si);
    for(  ;sideIter !=sideIterEnd; sideIter++)
    {
      side_type* side = *sideIter;
      if (pbm && pbm->is_slave(side)) continue;
      //UG_LOG(aaTensor[side] << "\n");
      //UG_LOG(FNorm(aaTensor[side]) << "\n");
      //UG_LOG("--------------------\n");
      //for debug UG_LOG("&&&&&&&& norm = " << FNorm(aaTensor[side]) << "\n");
      aaTensor[side].scale_by_fnorm();
    }
  }
}
void StdTurbulentViscosityData<TData,dim,TImpl,TGridFunction>::scaleTensorByNorm(aSideTensor& aaTensor) {…}
        } {…}
 
template <typename TData, int dim, typename TImpl,typename TGridFunction>
void StdTurbulentViscosityData<TData,dim,TImpl,TGridFunction>::addUiUjTerm(aSideTensor& aaResult,const number factor,
                                       SmartPtr<TGridFunction> u,aSideDimVector* aaU){
  bool useGridFunction = true;
  if (u==SPNULL) useGridFunction = false;
  
  //  get domain of grid function
  domain_type& domain = *m_uInfo->domain().get();
  // get periodic boundary manager
  PeriodicBoundaryManager* pbm = (domain.grid())->periodic_boundary_manager();
  //  create Multiindex
  std::vector<DoFIndex> multInd;
    
  for(int si = 0; si < domain.subset_handler()->num_subsets(); ++si){
    SideIterator sideIter = m_uInfo->template begin<side_type>(si);
    SideIterator sideIterEnd = m_uInfo->template end<side_type>(si);
    for(  ;sideIter !=sideIterEnd; sideIter++)
    {
      side_type* side = *sideIter;
      if (pbm && pbm->is_slave(side)) continue;
      dimMat Tij;
      MathVector<dim> uValue;
      if (useGridFunction)
        for (int d=0;d<dim;d++){
          u->dof_indices(side, d, multInd);
          uValue[d]=DoFRef(*u,multInd[0]);
        }
      else 
        for (int d=0;d<dim;d++) uValue[d] = (*aaU)[side][d];
      size_t ind=0;
      for (int d1=0;d1 < dim;d1++)
        for (int d2=d1;d2 < dim;d2++){
          Tij[ind] = uValue[d1]*uValue[d2];
          ind++;
        }
      Tij*=factor;
      aaResult[side]+=Tij;
    }
  }
}
void StdTurbulentViscosityData<TData,dim,TImpl,TGridFunction>::addUiUjTerm(aSideTensor& aaResult,const number factor, {…}
 
template<typename TGridFunction>
void CRSmagorinskyTurbViscData<TGridFunction>::update(){
  //  get domain of grid function
  domain_type& domain = *m_u->domain().get();
  SetAttachmentValues(m_acTurbulentViscosity, m_grid->template begin<side_type>(), m_grid->template end<side_type>(), 0);
 
  //  coord and vertex array
  //  MathVector<dim> coCoord[domain_traits<dim>::MaxNumVerticesOfElem];
  //  Vertex* vVrt[domain_traits<dim>::MaxNumVerticesOfElem];
 
  // assemble deformation tensor fluxes
  this->assembleDeformationTensor(m_acDeformation,m_acVolume,m_u,NULL);
  // compute turbulent viscosity , loop over sides
  for(int si = 0; si < domain.subset_handler()->num_subsets(); ++si)
  {
    if ((m_turbZeroSg.size()!=0) && (m_turbZeroSg.contains(si)==true)) continue;
    SideIterator sideIter = m_u->template begin<side_type>(si);
    SideIterator sideIterEnd = m_u->template end<side_type>(si);
    for(  ;sideIter !=sideIterEnd; sideIter++)
    {
      //  get Elem
      side_type* side = *sideIter;
      if (m_pbm && m_pbm->is_slave(side)) continue;
      number delta = m_acVolume[side];
      // for possible other choices of delta see Fr�hlich p 160
      delta = pow(delta,(number)1.0/(number)dim);
      m_acTurbulentViscosity[side] = m_c*m_c * delta*delta * m_acDeformation[side].fnorm();
    }
  }
  if (m_bAdaptive){
    if (dim==2) constrainingSideAveraging<TGridFunction,side_type,ConstrainingEdge,number>(m_acTurbulentViscosity,m_u);
    else {
      constrainingSideAveraging<TGridFunction,side_type,ConstrainingTriangle,number>(m_acTurbulentViscosity,m_u);
      constrainingSideAveraging<TGridFunction,side_type,ConstrainingQuadrilateral,number>(m_acTurbulentViscosity,m_u);
    }
  }
  // transfer attachment data to lower levels
  this->transferToLowerLevels(m_acTurbulentViscosity,*m_spApproxSpace);
}
void CRSmagorinskyTurbViscData<TGridFunction>::update() {…}
 
template<typename TGridFunction>
void CRDynamicTurbViscData<TGridFunction>::update(){
  //  get domain of grid function
  domain_type& domain = *m_u->domain().get();
 
  //  get position accessor
  // for debug 
  typedef typename domain_type::position_accessor_type position_accessor_type;
  // for debug 
  const position_accessor_type& posAcc = domain.position_accessor();
 
  // initialize attachment values with 0
//  SetAttachmentValues(m_acDeformation , m_grid->template begin<side_type>(), m_grid->template end<side_type>(), 0);
  SetAttachmentValues(m_acTurbulentViscosity, m_grid->template begin<side_type>(), m_grid->template end<side_type>(), 0);
//  SetAttachmentValues(m_acVolume,m_grid->template begin<side_type>(), m_grid->template end<side_type>(), 0);
  SetAttachmentValues(m_acTurbulentCNew,m_grid->template begin<side_type>(), m_grid->template end<side_type>(), 0);
//  SetAttachmentValues(m_acVolumeHat,m_grid->template begin<side_type>(), m_grid->template end<side_type>(), 0);
//  SetAttachmentValues(m_acUHat,m_grid->template begin<side_type>(), m_grid->template end<side_type>(), 0);
//  SetAttachmentValues(m_acDeformationHat,m_grid->template begin<side_type>(), m_grid->template end<side_type>(), 0);
//  SetAttachmentValues(m_acLij,m_grid->template begin<side_type>(), m_grid->template end<side_type>(), 0);
  SetAttachmentValues(m_acMij,m_grid->template begin<side_type>(), m_grid->template end<side_type>(), 0);
 
  // compute Lij term \hat{u_i u_j} - \hat{u_i} \hat{u_j}
  // \hat{u}
  this->elementFilter(m_acUHat,m_acVolumeHat,m_u,&m_acUHat);
  // use Mij attachment to store first Lij part
  // u_i u_j
  this->addUiUjTerm(m_acMij,1.0,m_u,NULL);
  // \hat{u_i u_j}
  this->elementFilter(m_acLij,m_acVolumeHat,SPNULL,&m_acMij);
  // \hat{u_i u_j} - \hat{u_i} \hat{u_j}
  this->addUiUjTerm(m_acLij,-1.0,SPNULL,&m_acUHat);
 
  // Mij term
  // first term |\hat{S}| \hat{S}
  // assemble \hat{S} using \hat{u}
  this->assembleDeformationTensor(m_acDeformationHat,m_acVolume,SPNULL,&m_acUHat);
  // normalize \hat{S}
  this->scaleTensorByNorm(m_acDeformationHat);
  // Mij second term \hat{|S|S}
  // compute S
  this->assembleDeformationTensor(m_acDeformation,m_acVolume,m_u,NULL);
  // compute |S| S
  this->scaleTensorByNorm(m_acDeformation);
  // filter |S| S
  //for debug UG_LOG("------------------------------------------------------\n");
  this->elementFilter(m_acMij,m_acVolumeHat,SPNULL,&m_acDeformation);
 
  // complete Mij term computation by scaling and adding the two terms,
  // solve the local least squares problem and compute local c and local turbulent viscosity
  for(int si = 0; si < domain.subset_handler()->num_subsets(); ++si)
  {
    if ((m_turbZeroSg.size()!=0) && (m_turbZeroSg.contains(si)==true)) continue;
    SideIterator sideIter = m_u->template begin<side_type>(si);
    SideIterator sideIterEnd = m_u->template end<side_type>(si);
    for(  ;sideIter !=sideIterEnd; sideIter++){
      side_type* side = *sideIter;
      if (m_pbm && m_pbm->is_slave(side)) continue;
      // use fixed ratio \hat{delta} / delta or compute it from filter width
      number kappa;
      if (m_fixedRatio) kappa = m_kappa;
      else {
        number delta = m_acVolume[side];
        delta = pow(delta,(number)1.0/(number)dim);
        number deltaHat = m_acVolumeHat[side];
        deltaHat = pow(deltaHat,(number)1.0/(number)dim);
        kappa = deltaHat /(number) delta;
      }
      m_acDeformationHat[side] *= -kappa*kappa;
      m_acMij[side] += m_acDeformationHat[side];
      // compute local c
      // solve least squares problem
      number c = 0;
      for (int d1=0;d1<dim;d1++)
        for (int d2=0;d2<dim;d2++)
          c += m_acLij[side](d1,d2)*m_acMij[side](d1,d2);
      number denom=0;
      //for debug UG_LOG("c=" << c << "\n");
      for (int d1=0;d1<dim;d1++)
        for (int d2=0;d2<dim;d2++)
          denom += m_acMij[side](d1,d2)*m_acMij[side](d1,d2);
      if (denom>1e-15)
        c/=(number)(2.0*denom);
      else c=0;
 
//      UG_LOG("c=" << c << "\n");
 
      if (m_spaceFilter==false){
        if (m_timeFilter==false){
          m_acTurbulentViscosity[side] = c * m_acDeformation[side].fnorm();
          UG_LOG("nu_t = " << m_acTurbulentViscosity[side]  << " c = " << c << " kappa = " << kappa << " co=[" << 0.5*(posAcc[side->vertex(0)][0] + posAcc[side->vertex(1)][0]) << "," << 0.5*(posAcc[side->vertex(0)][1] + posAcc[side->vertex(1)][1]) << "]\n");
        } else {
          m_acTurbulentC[side]= (m_timeFilterEps * c + (1-m_timeFilterEps)*m_acTurbulentC[side]);
          m_acTurbulentViscosity[side] = m_acTurbulentC[side] * m_acDeformation[side].fnorm();
        }
        if (m_acTurbulentViscosity[side]+m_viscosityNumber<m_small) m_acTurbulentViscosity[side] = m_viscosityNumber + m_small;     }
      else{
        // store c in viscosity attachment
        m_acTurbulentViscosity[side] = c;
      }
    }
  }
  if (m_spaceFilter==true){
    // filter c
    if (m_timeFilter==false)
      // c has been stored in viscosity attachment
      this->elementFilter(m_acTurbulentC,m_acVolumeHat,SPNULL,&m_acTurbulentViscosity);
    else
      this->elementFilter(m_acTurbulentCNew,m_acVolumeHat,SPNULL,&m_acTurbulentViscosity);
    // compute turbulent viscosity
    for(int si = 0; si < domain.subset_handler()->num_subsets(); ++si)
    {
      //for debug UG_LOG("si = " << si << "\n");
      if ((m_turbZeroSg.size()!=0) && (m_turbZeroSg.contains(si)==true)) continue;
      SideIterator sideIter = m_u->template begin<side_type>(si);
      SideIterator sideIterEnd = m_u->template end<side_type>(si);
      for(  ;sideIter !=sideIterEnd; sideIter++){
        side_type* side = *sideIter;
        if (m_pbm && m_pbm->is_slave(side)) continue;
        if (m_timeFilter==true)
          // time averaging, note that c has been stored in m_acVolumeHat
          m_acTurbulentC[side]= (m_timeFilterEps * m_acTurbulentCNew[side] + (1-m_timeFilterEps)*m_acTurbulentC[side]);
        m_acTurbulentViscosity[side] = m_acTurbulentC[side] * m_acDeformation[side].fnorm();
        UG_LOG("nu_t = " << m_acTurbulentViscosity[side]  << " c = " << m_acTurbulentC[side] << " co=[" << 0.5*(posAcc[side->vertex(0)][0] + posAcc[side->vertex(1)][0]) << "," << 0.5*(posAcc[side->vertex(0)][1] + posAcc[side->vertex(1)][1]) << "]\n");
        if (m_acTurbulentViscosity[side]+m_viscosityNumber<m_small) m_acTurbulentViscosity[side] = m_viscosityNumber+m_small;
        // for debug 
        // UG_LOG("nu_t = " << m_acTurbulentViscosity[side]  << " c = " << m_acTurbulentC[side] << " co=[" << 0.5*(posAcc[side->vertex(0)][0] + posAcc[side->vertex(1)][0]) << "," << 0.5*(posAcc[side->vertex(0)][1] + posAcc[side->vertex(1)][1]) << "]\n");
      }
    }
  }
  if (m_bAdaptive){
    if (dim==2) constrainingSideAveraging<TGridFunction,side_type,ConstrainingEdge,number>(m_acTurbulentViscosity,m_u);
    else {
      constrainingSideAveraging<TGridFunction,side_type,ConstrainingTriangle,number>(m_acTurbulentViscosity,m_u);
      constrainingSideAveraging<TGridFunction,side_type,ConstrainingQuadrilateral,number>(m_acTurbulentViscosity,m_u);
    }
  }
  // transfer attachment data to lower levels
  this->transferToLowerLevels(m_acTurbulentViscosity,*m_spApproxSpace);
}
void CRDynamicTurbViscData<TGridFunction>::update() {…}
 
} // namespace NavierStokes
} // end namespace ug
 
#endif /* __H__UG__NAVIER_STOKES_TURBULENT_VISCOSITY_DATA_IMPL_H_ */
            assignValue(aaUHat[side],d,DoFRef(*u,multInd[0])); {…}
          for (int d=0;d<dim;d++) {…}
        if (pbm && pbm->is_slave(side)) continue; {…}
      for(  ;sideIter !=sideIterEnd; sideIter++) {…}
    SideIterator sideIterEnd = m_uInfo->template end<side_type>(si); {…}
 {…}
void StdTurbulentViscosityData<TData,dim,TImpl,TGridFunction>::elementFilter(PeriodicAttachmentAccessor<side_type,Attachment<VType> >& aaUHat,aSideNumber& aaVol, {…}