ContinuityMassElemSuppAlg<AlgTraits>::ContinuityMassElemSuppAlg(
   Realm &realm,
   ElemDataRequests& dataPreReqs,
   const bool lumpedMass)
  : SupplementalAlgorithm(realm),
    densityNm1_(NULL),
    densityN_(NULL),
    densityNp1_(NULL),
    coordinates_(NULL),
    dt_(0.0),
    gamma1_(0.0),
    gamma2_(0.0),
    gamma3_(0.0),
    lumpedMass_(lumpedMass),
    ipNodeMap_(realm.get_volume_master_element(AlgTraits::topo_)->ipNodeMap())
{
  // save off fields; shove state N into Nm1 if this is BE
  stk::mesh::MetaData & meta_data = realm_.meta_data();
  ScalarFieldType *density = meta_data.get_field<ScalarFieldType>(stk::topology::NODE_RANK, "density");
  densityNm1_ = realm_.number_of_states() == 2 ? &(density->field_of_state(stk::mesh::StateN)) : &(density->field_of_state(stk::mesh::StateNM1));
  densityN_ = &(density->field_of_state(stk::mesh::StateN));
  densityNp1_ = &(density->field_of_state(stk::mesh::StateNP1));
  coordinates_ = meta_data.get_field<VectorFieldType>(stk::topology::NODE_RANK, realm_.get_coordinates_name());

  MasterElement *meSCV = realm.get_volume_master_element(AlgTraits::topo_);

  // compute shape function
  if ( lumpedMass_ )
    meSCV->shifted_shape_fcn(&v_shape_function_(0,0));
  else
    meSCV->shape_fcn(&v_shape_function_(0,0));

  // add master elements
  dataPreReqs.add_cvfem_volume_me(meSCV);

  // fields and data
  dataPreReqs.add_gathered_nodal_field(*coordinates_, AlgTraits::nDim_);
  dataPreReqs.add_gathered_nodal_field(*densityNm1_, 1);
  dataPreReqs.add_gathered_nodal_field(*densityN_, 1);
  dataPreReqs.add_gathered_nodal_field(*densityNp1_, 1);
  dataPreReqs.add_master_element_call(SCV_VOLUME);
}
Beispiel #2
0
ScalarAdvDiffElemKernel<AlgTraits>::ScalarAdvDiffElemKernel(
  const stk::mesh::BulkData& bulkData,
  const SolutionOptions& solnOpts,
  ScalarFieldType* scalarQ,
  ScalarFieldType* diffFluxCoeff,
  ElemDataRequests& dataPreReqs)
  : Kernel(),
    scalarQ_(scalarQ),
    diffFluxCoeff_(diffFluxCoeff),
    lrscv_(sierra::nalu::MasterElementRepo::get_surface_master_element(AlgTraits::topo_)->adjacentNodes()),
    shiftedGradOp_(solnOpts.get_shifted_grad_op(scalarQ->name()))
{
  // Save of required fields
  const stk::mesh::MetaData& metaData = bulkData.mesh_meta_data();
  coordinates_ = metaData.get_field<VectorFieldType>(
    stk::topology::NODE_RANK, solnOpts.get_coordinates_name());
  massFlowRate_ = metaData.get_field<GenericFieldType>(
    stk::topology::ELEMENT_RANK, "mass_flow_rate_scs");

  MasterElement *meSCS = sierra::nalu::MasterElementRepo::get_surface_master_element(AlgTraits::topo_);

  get_scs_shape_fn_data<AlgTraits>([&](double* ptr){meSCS->shape_fcn(ptr);}, v_shape_function_);
  const bool skewSymmetric = solnOpts.get_skew_symmetric(scalarQ->name());
  get_scs_shape_fn_data<AlgTraits>([&](double* ptr){skewSymmetric ? meSCS->shifted_shape_fcn(ptr) : meSCS->shape_fcn(ptr);}, 
                                   v_adv_shape_function_);

  dataPreReqs.add_cvfem_surface_me(meSCS);

  // fields and data
  dataPreReqs.add_coordinates_field(*coordinates_, AlgTraits::nDim_, CURRENT_COORDINATES);
  dataPreReqs.add_gathered_nodal_field(*scalarQ_, 1);
  dataPreReqs.add_gathered_nodal_field(*diffFluxCoeff_, 1);
  dataPreReqs.add_element_field(*massFlowRate_, AlgTraits::numScsIp_);
  dataPreReqs.add_master_element_call(SCS_AREAV, CURRENT_COORDINATES);
  if ( shiftedGradOp_ )
    dataPreReqs.add_master_element_call(SCS_SHIFTED_GRAD_OP, CURRENT_COORDINATES);
  else
    dataPreReqs.add_master_element_call(SCS_GRAD_OP, CURRENT_COORDINATES);
}
//--------------------------------------------------------------------------
//-------- execute ---------------------------------------------------------
//--------------------------------------------------------------------------
void
AssembleContinuityElemSolverAlgorithm::execute()
{

  stk::mesh::MetaData & meta_data = realm_.meta_data();

  const int nDim = meta_data.spatial_dimension();

  // time step
  const double dt = realm_.get_time_step();
  const double gamma1 = realm_.get_gamma1();
  const double projTimeScale = dt/gamma1;

  // deal with interpolation procedure
  const double interpTogether = realm_.get_mdot_interp();
  const double om_interpTogether = 1.0-interpTogether;

  // space for LHS/RHS; nodesPerElem*nodesPerElem and nodesPerElem
  std::vector<double> lhs;
  std::vector<double> rhs;
  std::vector<stk::mesh::Entity> connected_nodes;

  // supplemental algorithm setup
  const size_t supplementalAlgSize = supplementalAlg_.size();
  for ( size_t i = 0; i < supplementalAlgSize; ++i )
    supplementalAlg_[i]->setup();

  // nodal fields to gather
  std::vector<double> ws_vrtm;
  std::vector<double> ws_Gpdx;
  std::vector<double> ws_coordinates;
  std::vector<double> ws_pressure;
  std::vector<double> ws_density;

  // geometry related to populate
  std::vector<double> ws_scs_areav;
  std::vector<double> ws_dndx;
  std::vector<double> ws_dndx_lhs;
  std::vector<double> ws_deriv;
  std::vector<double> ws_det_j;
  std::vector<double> ws_shape_function;

  // integration point data that depends on size
  std::vector<double> uIp(nDim);
  std::vector<double> rho_uIp(nDim);
  std::vector<double> GpdxIp(nDim);
  std::vector<double> dpdxIp(nDim);

  // pointers to everyone...
  double *p_uIp = &uIp[0];
  double *p_rho_uIp = &rho_uIp[0];
  double *p_GpdxIp = &GpdxIp[0];
  double *p_dpdxIp = &dpdxIp[0];

  // deal with state
  ScalarFieldType &densityNp1 = density_->field_of_state(stk::mesh::StateNP1);

  // define some common selectors
  stk::mesh::Selector s_locally_owned_union = meta_data.locally_owned_part()
    & stk::mesh::selectUnion(partVec_) 
    & !(realm_.get_inactive_selector());

  stk::mesh::BucketVector const& elem_buckets =
    realm_.get_buckets( stk::topology::ELEMENT_RANK, s_locally_owned_union );
  for ( stk::mesh::BucketVector::const_iterator ib = elem_buckets.begin();
        ib != elem_buckets.end() ; ++ib ) {
    stk::mesh::Bucket & b = **ib ;
    const stk::mesh::Bucket::size_type length   = b.size();

    // extract master element
    MasterElement *meSCS = realm_.get_surface_master_element(b.topology());
    MasterElement *meSCV = realm_.get_volume_master_element(b.topology());

    // extract master element specifics
    const int nodesPerElement = meSCS->nodesPerElement_;
    const int numScsIp = meSCS->numIntPoints_;
    const int *lrscv = meSCS->adjacentNodes();

    // resize some things; matrix related
    const int lhsSize = nodesPerElement*nodesPerElement;
    const int rhsSize = nodesPerElement;
    lhs.resize(lhsSize);
    rhs.resize(rhsSize);
    connected_nodes.resize(nodesPerElement);

    // algorithm related
    ws_vrtm.resize(nodesPerElement*nDim);
    ws_Gpdx.resize(nodesPerElement*nDim);
    ws_coordinates.resize(nodesPerElement*nDim);
    ws_pressure.resize(nodesPerElement);
    ws_density.resize(nodesPerElement);
    ws_scs_areav.resize(numScsIp*nDim);
    ws_dndx.resize(nDim*numScsIp*nodesPerElement);
    ws_dndx_lhs.resize(nDim*numScsIp*nodesPerElement);
    ws_deriv.resize(nDim*numScsIp*nodesPerElement);
    ws_det_j.resize(numScsIp);
    ws_shape_function.resize(numScsIp*nodesPerElement);

    // pointers
    double *p_lhs = &lhs[0];
    double *p_rhs = &rhs[0];
    double *p_vrtm = &ws_vrtm[0];
    double *p_Gpdx = &ws_Gpdx[0];
    double *p_coordinates = &ws_coordinates[0];
    double *p_pressure = &ws_pressure[0];
    double *p_density = &ws_density[0];
    double *p_scs_areav = &ws_scs_areav[0];
    double *p_dndx = &ws_dndx[0];
    double *p_dndx_lhs = reducedSensitivities_ ? &ws_dndx_lhs[0] : &ws_dndx[0];
    double *p_shape_function = &ws_shape_function[0];

    if ( shiftMdot_)
      meSCS->shifted_shape_fcn(&p_shape_function[0]);
    else
      meSCS->shape_fcn(&p_shape_function[0]);

    // resize possible supplemental element alg
    for ( size_t i = 0; i < supplementalAlgSize; ++i )
      supplementalAlg_[i]->elem_resize(meSCS, meSCV);

    for ( stk::mesh::Bucket::size_type k = 0 ; k < length ; ++k ) {

      // get elem
      stk::mesh::Entity elem = b[k];

      // zero lhs/rhs
      for ( int p = 0; p < lhsSize; ++p )
        p_lhs[p] = 0.0;
      for ( int p = 0; p < rhsSize; ++p )
        p_rhs[p] = 0.0;

      //===============================================
      // gather nodal data; this is how we do it now..
      //===============================================
      stk::mesh::Entity const *  node_rels = b.begin_nodes(k);
      int num_nodes = b.num_nodes(k);

      // sanity check on num nodes
      ThrowAssert( num_nodes == nodesPerElement );

      for ( int ni = 0; ni < num_nodes; ++ni ) {
        stk::mesh::Entity node = node_rels[ni];

        // set connected nodes
        connected_nodes[ni] = node;

        // pointers to real data
        const double * Gjp    = stk::mesh::field_data(*Gpdx_, node );
        const double * coords = stk::mesh::field_data(*coordinates_, node );
        const double * vrtm   = stk::mesh::field_data(*velocityRTM_, node );

        // gather scalars
        p_pressure[ni] = *stk::mesh::field_data(*pressure_, node );
        p_density[ni]  = *stk::mesh::field_data(densityNp1, node );

        // gather vectors
        const int niNdim = ni*nDim;
        for ( int j=0; j < nDim; ++j ) {
          p_vrtm[niNdim+j] = vrtm[j];
          p_Gpdx[niNdim+j] = Gjp[j];
          p_coordinates[niNdim+j] = coords[j];
        }
      }

      // compute geometry
      double scs_error = 0.0;
      meSCS->determinant(1, &p_coordinates[0], &p_scs_areav[0], &scs_error);

      // compute dndx for residual
      if ( shiftPoisson_ )
        meSCS->shifted_grad_op(1, &p_coordinates[0], &ws_dndx[0], &ws_deriv[0], &ws_det_j[0], &scs_error);
      else
        meSCS->grad_op(1, &p_coordinates[0], &ws_dndx[0], &ws_deriv[0], &ws_det_j[0], &scs_error);
      
      // compute dndx for LHS
      if ( reducedSensitivities_ )
        meSCS->shifted_grad_op(1, &p_coordinates[0], &ws_dndx_lhs[0], &ws_deriv[0], &ws_det_j[0], &scs_error);

      for ( int ip = 0; ip < numScsIp; ++ip ) {

        // left and right nodes for this ip
        const int il = lrscv[2*ip];
        const int ir = lrscv[2*ip+1];

        // corresponding matrix rows
        int rowL = il*nodesPerElement;
        int rowR = ir*nodesPerElement;

        // setup for ip values; sneak in geometry for possible reduced sens
        for ( int j = 0; j < nDim; ++j ) {
          p_uIp[j] = 0.0;
          p_rho_uIp[j] = 0.0;
          p_GpdxIp[j] = 0.0;
          p_dpdxIp[j] = 0.0;
        }
        double rhoIp = 0.0;

        const int offSet = ip*nodesPerElement;
        for ( int ic = 0; ic < nodesPerElement; ++ic ) {

          const double r = p_shape_function[offSet+ic];
          const double nodalPressure = p_pressure[ic];
          const double nodalRho = p_density[ic];

          rhoIp += r*nodalRho;

          double lhsfac = 0.0;
          const int offSetDnDx = nDim*nodesPerElement*ip + ic*nDim;
          for ( int j = 0; j < nDim; ++j ) {
            p_GpdxIp[j] += r*p_Gpdx[nDim*ic+j];
            p_uIp[j] += r*p_vrtm[nDim*ic+j];
            p_rho_uIp[j] += r*nodalRho*p_vrtm[nDim*ic+j];
            p_dpdxIp[j] += p_dndx[offSetDnDx+j]*nodalPressure;
            lhsfac += -p_dndx_lhs[offSetDnDx+j]*p_scs_areav[ip*nDim+j];
          }

          // assemble to lhs; left
          p_lhs[rowL+ic] += lhsfac;

          // assemble to lhs; right
          p_lhs[rowR+ic] -= lhsfac;

        }

        // assemble mdot
        double mdot = 0.0;
        for ( int j = 0; j < nDim; ++j ) {
          mdot += (interpTogether*p_rho_uIp[j] + om_interpTogether*rhoIp*p_uIp[j] 
                   - projTimeScale*(p_dpdxIp[j] - p_GpdxIp[j]))*p_scs_areav[ip*nDim+j];
        }

        // residual; left and right
        p_rhs[il] -= mdot/projTimeScale;
        p_rhs[ir] += mdot/projTimeScale;
      }

      // call supplemental
      for ( size_t i = 0; i < supplementalAlgSize; ++i )
        supplementalAlg_[i]->elem_execute( &lhs[0], &rhs[0], elem, meSCS, meSCV);

      apply_coeff(connected_nodes, rhs, lhs, __FILE__);

    }
  }
}
//--------------------------------------------------------------------------
//-------- execute ---------------------------------------------------------
//--------------------------------------------------------------------------
void
AssembleHeatCondIrradWallSolverAlgorithm::execute()
{

  stk::mesh::MetaData & meta_data = realm_.meta_data();

  const int nDim = meta_data.spatial_dimension();

  const double sigma = realm_.get_stefan_boltzmann();

  // space for LHS/RHS; nodesPerFace*nodesPerFace and nodesPerFace
  std::vector<double> lhs;
  std::vector<double> rhs;
  std::vector<stk::mesh::Entity> connected_nodes;

  // nodal fields to gather
  std::vector<double> ws_irradiation;
  std::vector<double> ws_emissivity;
  std::vector<double> ws_temperature;

  // geometry related to populate
  std::vector<double> ws_shape_function;

  // setup for buckets; union parts and ask for locally owned
  stk::mesh::Selector s_locally_owned_union = meta_data.locally_owned_part()
    &stk::mesh::selectUnion(partVec_);
  stk::mesh::BucketVector const& face_buckets =
    realm_.get_buckets( meta_data.side_rank(), s_locally_owned_union );

  for ( stk::mesh::BucketVector::const_iterator ib = face_buckets.begin();
        ib != face_buckets.end() ; ++ib ) {
    stk::mesh::Bucket & b = **ib ;

    // extract master element specifics
    MasterElement *meFC = realm_.get_surface_master_element(b.topology());
    const int nodesPerFace = meFC->nodesPerElement_;
    const int numScsIp = meFC->numIntPoints_;

    // resize some things; matrix related
    const int lhsSize = nodesPerFace*nodesPerFace;
    const int rhsSize = nodesPerFace;
    lhs.resize(lhsSize);
    rhs.resize(rhsSize);
    connected_nodes.resize(nodesPerFace);

    // algorithm related
    ws_irradiation.resize(nodesPerFace);
    ws_emissivity.resize(nodesPerFace);
    ws_temperature.resize(nodesPerFace);
    ws_shape_function.resize(numScsIp*nodesPerFace);

    // pointers
    double *p_lhs = &lhs[0];
    double *p_rhs = &rhs[0];
    double *p_irradiation = &ws_irradiation[0];
    double *p_emissivity = &ws_emissivity[0];
    double *p_temperature = &ws_temperature[0];
    double *p_shape_function = &ws_shape_function[0];

    if ( useShifted_ )
      meFC->shifted_shape_fcn(&p_shape_function[0]);
    else
      meFC->shape_fcn(&p_shape_function[0]);

    const stk::mesh::Bucket::size_type length   = b.size();
    for ( stk::mesh::Bucket::size_type k = 0 ; k < length ; ++k ) {

      // zero lhs/rhs
      for ( int p = 0; p < lhsSize; ++p )
        p_lhs[p] = 0.0;
      for ( int p = 0; p < rhsSize; ++p )
        p_rhs[p] = 0.0;

      // face data
      double * areaVec = stk::mesh::field_data(*exposedAreaVec_, b, k);

      // face node relations for nodal gather
      stk::mesh::Entity const * face_node_rels = b.begin_nodes(k);
      
      int num_nodes = b.num_nodes(k);
      for ( int ni = 0; ni < num_nodes; ++ni ) {

        // get the node and form connected_node
        stk::mesh::Entity node = face_node_rels[ni];
        connected_nodes[ni] = node;

        // gather scalar
        p_irradiation[ni] = *stk::mesh::field_data(*irradiation_, node);
        p_emissivity[ni] = *stk::mesh::field_data(*emissivity_, node);
        p_temperature[ni] = *stk::mesh::field_data(*temperature_, node);
      }

      // start the assembly
      for ( int ip = 0; ip < numScsIp; ++ip ) {
	
        double magA = 0.0;
        for ( int j=0; j < nDim; ++j ) {
          magA += areaVec[ip*nDim+j]*areaVec[ip*nDim+j];
        }
        magA = std::sqrt(magA);
	
        const int nn = ip;
        const int offSet = ip*nodesPerFace;
	
        // form boundary ip values
        double irradiationBip = 0.0;
        double emissivityBip = 0.0;
        double tBip = 0.0;
        for ( int ic = 0; ic < nodesPerFace; ++ic ) {
          const double r = p_shape_function[offSet+ic];
          irradiationBip += r*p_irradiation[ic];
          emissivityBip += r*p_emissivity[ic];
          tBip += r*p_temperature[ic];
        }

        // form rhs contribution
        const double radiation = emissivityBip*(irradiationBip - sigma*std::pow(tBip,4))*magA;
        p_rhs[nn] += radiation;
	
        // sensitivities
        const int rowR = nn*nodesPerFace;
        const double lhsFac = 4.0*sigma*emissivityBip*magA*std::pow(tBip,3);
        for ( int ic = 0; ic < nodesPerFace; ++ic ) {
          const double r = p_shape_function[offSet+ic];
          p_lhs[rowR+ic] += r*lhsFac;
        }
      }
      
      apply_coeff(connected_nodes, rhs, lhs, __FILE__);

    }
  }
}
//--------------------------------------------------------------------------
//-------- execute ---------------------------------------------------------
//--------------------------------------------------------------------------
void
AssemblePressureForceBCSolverAlgorithm::execute()
{

  stk::mesh::BulkData & bulk_data = realm_.bulk_data();
  stk::mesh::MetaData & meta_data = realm_.meta_data();

  const int nDim = meta_data.spatial_dimension();

   // space for LHS/RHS; nodesPerElem*nDim*nodesPerElem*nDim and nodesPerElem*nDim
  std::vector<double> lhs;
  std::vector<double> rhs;
  std::vector<stk::mesh::Entity> connected_nodes;

  // nodal fields to gather
  std::vector<double> ws_face_coordinates;
  std::vector<double> ws_bcScalarQ;

  // master element
  std::vector<double> ws_face_shape_function;

  // define vector of parent topos; should always be UNITY in size
  std::vector<stk::topology> parentTopo;

  // define some common selectors
  stk::mesh::Selector s_locally_owned_union = meta_data.locally_owned_part()
    &stk::mesh::selectUnion(partVec_);

  stk::mesh::BucketVector const& face_buckets =
    realm_.get_buckets( meta_data.side_rank(), s_locally_owned_union );
  for ( stk::mesh::BucketVector::const_iterator ib = face_buckets.begin();
        ib != face_buckets.end() ; ++ib ) {
    stk::mesh::Bucket & b = **ib ;

    // extract connected element topology
    b.parent_topology(stk::topology::ELEMENT_RANK, parentTopo);
    ThrowAssert ( parentTopo.size() == 1 );
    stk::topology theElemTopo = parentTopo[0];

    // volume master element
    MasterElement *meSCS = realm_.get_surface_master_element(theElemTopo);
    const int nodesPerElement = meSCS->nodesPerElement_;

    // face master element
    MasterElement *meFC = realm_.get_surface_master_element(b.topology());
    const int nodesPerFace = meFC->nodesPerElement_;
    std::vector<int> face_node_ordinal_vec(nodesPerFace);

    // resize some things; matrix related
    const int lhsSize = nodesPerElement*nDim*nodesPerElement*nDim;
    const int rhsSize = nodesPerElement*nDim;
    lhs.resize(lhsSize);
    rhs.resize(rhsSize);
    connected_nodes.resize(nodesPerElement);

    // algorithm related; element
    ws_face_coordinates.resize(nodesPerFace*nDim);
    ws_bcScalarQ.resize(nodesPerFace);
    ws_face_shape_function.resize(nodesPerFace*nodesPerFace);

    // pointers
    double *p_lhs = &lhs[0];
    double *p_rhs = &rhs[0];
    double *p_face_coordinates = &ws_face_coordinates[0];
    double *p_bcScalarQ = &ws_bcScalarQ[0];
    double *p_face_shape_function = &ws_face_shape_function[0];

    // shape functions
    if (use_shifted_integration_)
    {
      meFC->shifted_shape_fcn(&p_face_shape_function[0]);
    }
    else{
      meFC->shape_fcn(&p_face_shape_function[0]);
    }

    const size_t length   = b.size();

    for ( size_t k = 0 ; k < length ; ++k ) {

      // zero lhs/rhs
      for ( int p = 0; p < lhsSize; ++p )
        p_lhs[p] = 0.0;
      for ( int p = 0; p < rhsSize; ++p )
        p_rhs[p] = 0.0;

      // get face
      stk::mesh::Entity face = b[k];

      //======================================
      // gather nodal data off of face
      //======================================
      stk::mesh::Entity const * face_node_rels = bulk_data .begin_nodes(face);
      int num_face_nodes = bulk_data.num_nodes(face);
      // sanity check on num nodes
      ThrowAssert( num_face_nodes == nodesPerFace );
      for ( int ni = 0; ni < num_face_nodes; ++ni ) {
        stk::mesh::Entity node = face_node_rels[ni];

        p_bcScalarQ[ni] = *stk::mesh::field_data(*bcScalarQ_, node);

        // gather vectors
        double * coords = stk::mesh::field_data(*coordinates_, node);
        const int offSet = ni*nDim;
        for ( int i=0; i < nDim; ++i ) {
          p_face_coordinates[offSet+i] = coords[i];
        }
      }

      // extract the connected element to this exposed face; should be single in size!
      const stk::mesh::Entity* face_elem_rels = bulk_data.begin_elements(face);
      ThrowAssert( bulk_data.num_elements(face) == 1 );

      // get element; its face ordinal number and populate face_node_ordinal_vec
      stk::mesh::Entity element = face_elem_rels[0];
      const int face_ordinal = bulk_data.begin_element_ordinals(face)[0];
      theElemTopo.side_node_ordinals(face_ordinal, face_node_ordinal_vec.begin());

      //==========================================
      // gather nodal data off of element; n/a
      //==========================================
      stk::mesh::Entity const * elem_node_rels = bulk_data.begin_nodes(element);
      int num_nodes = bulk_data.num_nodes(element);
      // sanity check on num nodes
      ThrowAssert( num_nodes == nodesPerElement );
      for ( int ni = 0; ni < num_nodes; ++ni ) {
        stk::mesh::Entity node = elem_node_rels[ni];
        // set connected nodes
        connected_nodes[ni] = node;
      }

      // pointer to face data
      double * areaVec = stk::mesh::field_data(*exposedAreaVec_, face);

      // loop over face nodes
      for ( int ip = 0; ip < num_face_nodes; ++ip ) {

        const int nearestNode = face_node_ordinal_vec[ip];

        const int offSetSF_face = ip*nodesPerFace;

        // interpolate to bip
        double fluxBip = 0.0;
        for ( int ic = 0; ic < nodesPerFace; ++ic ) {
          const double r = p_face_shape_function[offSetSF_face+ic];
          fluxBip += r*p_bcScalarQ[ic];
        }

        // assemble for each of the ith component
        for ( int i = 0; i < nDim; ++i ) {
          const int indexR = nearestNode*nDim + i;
          p_rhs[indexR] -= fluxBip*areaVec[ip*nDim+i];
          // RHS only, no need to populate LHS (is zeroed out)
        }
      }

      apply_coeff(connected_nodes, rhs, lhs, __FILE__);
    }
  }
}
//--------------------------------------------------------------------------
//-------- execute ---------------------------------------------------------
//--------------------------------------------------------------------------
void
SurfaceForceAndMomentWallFunctionAlgorithm::execute()
{

  // check to see if this is a valid step to process output file
  const int timeStepCount = realm_.get_time_step_count();
  const bool processMe = (timeStepCount % frequency_) == 0 ? true : false;

  // do not waste time here
  if ( !processMe )
    return;

  stk::mesh::BulkData & bulk_data = realm_.bulk_data();
  stk::mesh::MetaData & meta_data = realm_.meta_data();

  const int nDim = meta_data.spatial_dimension();

  // set min and max values
  double yplusMin = 1.0e8;
  double yplusMax = -1.0e8;

  // bip values
  std::vector<double> uBip(nDim);
  std::vector<double> uBcBip(nDim);
  std::vector<double> unitNormal(nDim);

  // tangential work array
  std::vector<double> uiTangential(nDim);
  std::vector<double> uiBcTangential(nDim);

  // pointers to fixed values
  double *p_uBip = &uBip[0];
  double *p_uBcBip = &uBcBip[0];
  double *p_unitNormal= &unitNormal[0];
  double *p_uiTangential = &uiTangential[0];
  double *p_uiBcTangential = &uiBcTangential[0];

  // nodal fields to gather
  std::vector<double> ws_velocityNp1;
  std::vector<double> ws_bcVelocity;
  std::vector<double> ws_pressure;
  std::vector<double> ws_density;
  std::vector<double> ws_viscosity;

  // master element
  std::vector<double> ws_face_shape_function;

  // deal with state
  VectorFieldType &velocityNp1 = velocity_->field_of_state(stk::mesh::StateNP1);
  ScalarFieldType &densityNp1 = density_->field_of_state(stk::mesh::StateNP1);
  const double currentTime = realm_.get_current_time();

  // local force and MomentWallFunction; i.e., to be assembled
  double l_force_moment[9] = {};

  // work force, MomentWallFunction and radius; i.e., to be pused to cross_product()
  double ws_p_force[3] = {};
  double ws_v_force[3] = {};
  double ws_t_force[3] = {};
  double ws_moment[3] = {};
  double ws_radius[3] = {};

  // centroid
  double centroid[3] = {};
  for ( size_t k = 0; k < parameters_.size(); ++k)
    centroid[k] = parameters_[k];

  // define some common selectors
  stk::mesh::Selector s_locally_owned_union = meta_data.locally_owned_part()
    &stk::mesh::selectUnion(partVec_);

  stk::mesh::BucketVector const& face_buckets =
    realm_.get_buckets( meta_data.side_rank(), s_locally_owned_union );
  for ( stk::mesh::BucketVector::const_iterator ib = face_buckets.begin();
        ib != face_buckets.end() ; ++ib ) {
    stk::mesh::Bucket & b = **ib ;

    // face master element
    MasterElement *meFC = realm_.get_surface_master_element(b.topology());
    const int nodesPerFace = meFC->nodesPerElement_;

    // algorithm related; element
    ws_velocityNp1.resize(nodesPerFace*nDim);
    ws_bcVelocity.resize(nodesPerFace*nDim);
    ws_pressure.resize(nodesPerFace);
    ws_density.resize(nodesPerFace);
    ws_viscosity.resize(nodesPerFace);
    ws_face_shape_function.resize(nodesPerFace*nodesPerFace);

    // pointers
    double *p_velocityNp1 = &ws_velocityNp1[0];
    double *p_bcVelocity = &ws_bcVelocity[0];
    double *p_pressure = &ws_pressure[0];
    double *p_density = &ws_density[0];
    double *p_viscosity = &ws_viscosity[0];
    double *p_face_shape_function = &ws_face_shape_function[0];

    // shape functions
    if ( useShifted_ )
      meFC->shifted_shape_fcn(&p_face_shape_function[0]);
    else
      meFC->shape_fcn(&p_face_shape_function[0]);

    const stk::mesh::Bucket::size_type length   = b.size();

    for ( stk::mesh::Bucket::size_type k = 0 ; k < length ; ++k ) {

      // get face
      stk::mesh::Entity face = b[k];

      // face node relations
      stk::mesh::Entity const * face_node_rels = bulk_data.begin_nodes(face);

      //======================================
      // gather nodal data off of face
      //======================================
      for ( int ni = 0; ni < nodesPerFace; ++ni ) {
        stk::mesh::Entity node = face_node_rels[ni];

        // gather scalars
        p_pressure[ni]    = *stk::mesh::field_data(*pressure_, node);
        p_density[ni]    = *stk::mesh::field_data(densityNp1, node);
        p_viscosity[ni] = *stk::mesh::field_data(*viscosity_, node);

        // gather vectors
        double * uNp1 = stk::mesh::field_data(velocityNp1, node);
        double * uBc = stk::mesh::field_data(*bcVelocity_, node);
        const int offSet = ni*nDim;
        for ( int j=0; j < nDim; ++j ) {
          p_velocityNp1[offSet+j] = uNp1[j];
          p_bcVelocity[offSet+j] = uBc[j];
        }
      }

      // pointer to face data
      const double * areaVec = stk::mesh::field_data(*exposedAreaVec_, face);
      const double *wallNormalDistanceBip = stk::mesh::field_data(*wallNormalDistanceBip_, face);
      const double *wallFrictionVelocityBip = stk::mesh::field_data(*wallFrictionVelocityBip_, face);

      for ( int ip = 0; ip < nodesPerFace; ++ip ) {

        // offsets
        const int offSetAveraVec = ip*nDim;
        const int offSetSF_face = ip*nodesPerFace;

        // zero out vector quantities; squeeze in aMag
        double aMag = 0.0;
        for ( int j = 0; j < nDim; ++j ) {
          p_uBip[j] = 0.0;
          p_uBcBip[j] = 0.0;
          const double axj = areaVec[offSetAveraVec+j];
          aMag += axj*axj;
        }
        aMag = std::sqrt(aMag);

        // interpolate to bip
        double pBip = 0.0;
        double rhoBip = 0.0;
        double muBip = 0.0;
        for ( int ic = 0; ic < nodesPerFace; ++ic ) {
          const double r = p_face_shape_function[offSetSF_face+ic];
          pBip += r*p_pressure[ic];
          rhoBip += r*p_density[ic];
          muBip += r*p_viscosity[ic];
          const int offSetFN = ic*nDim;
          for ( int j = 0; j < nDim; ++j ) {
            p_uBip[j] += r*p_velocityNp1[offSetFN+j];
            p_uBcBip[j] += r*p_bcVelocity[offSetFN+j];
          }
        }

        // form unit normal
        for ( int j = 0; j < nDim; ++j ) {
          p_unitNormal[j] = areaVec[offSetAveraVec+j]/aMag;
        }

        // determine tangential velocity
        double uTangential = 0.0;
        for ( int i = 0; i < nDim; ++i ) {
          double uiTan = 0.0;
          double uiBcTan = 0.0;
          for ( int j = 0; j < nDim; ++j ) {
            const double ninj = p_unitNormal[i]*p_unitNormal[j];
            if ( i==j ) {
              const double om_nini = 1.0 - ninj;
              uiTan += om_nini*p_uBip[j];
              uiBcTan += om_nini*p_uBcBip[j];
            }
            else {
              uiTan -= ninj*p_uBip[j];
              uiBcTan -= ninj*p_uBcBip[j];
            }
          }
          // save off tangential components and augment magnitude
          p_uiTangential[i] = uiTan;
          p_uiBcTangential[i] = uiBcTan;
          uTangential += (uiTan-uiBcTan)*(uiTan-uiBcTan);
        }
        uTangential = std::sqrt(uTangential);

        // extract bip data
        const double yp = wallNormalDistanceBip[ip];
        const double utau= wallFrictionVelocityBip[ip];

        // determine yplus
        const double yplusBip = rhoBip*yp*utau/muBip;

        // min and max
        yplusMin = std::min(yplusMin, yplusBip);
        yplusMax = std::max(yplusMax, yplusBip);

        double lambda = muBip/yp*aMag;
        if ( yplusBip > yplusCrit_)
          lambda = rhoBip*kappa_*utau/std::log(elog_*yplusBip)*aMag;

        // extract nodal fields
        stk::mesh::Entity node = face_node_rels[ip];
        const double * coord = stk::mesh::field_data(*coordinates_, node );
        double *pressureForce = stk::mesh::field_data(*pressureForce_, node );
        double *tauWall = stk::mesh::field_data(*tauWall_, node );
        double *yplus = stk::mesh::field_data(*yplus_, node );
        const double assembledArea = *stk::mesh::field_data(*assembledArea_, node );

        // load radius; assemble force -sigma_ij*njdS
        double uParallel = 0.0;
        for ( int i = 0; i < nDim; ++i ) {
          const double ai = areaVec[offSetAveraVec+i];
          ws_radius[i] = coord[i] - centroid[i];
          const double uDiff = p_uiTangential[i] - p_uiBcTangential[i];
          ws_p_force[i] = pBip*ai;
          ws_v_force[i] = lambda*uDiff;
          ws_t_force[i] = ws_p_force[i] + ws_v_force[i];
          pressureForce[i] += ws_p_force[i];;
          uParallel += uDiff*uDiff;
        }

        cross_product(&ws_t_force[0], &ws_moment[0], &ws_radius[0]);

        // assemble for and moment
        for ( int j = 0; j < 3; ++j ) {
          l_force_moment[j] += ws_p_force[j];
          l_force_moment[j+3] += ws_v_force[j];
          l_force_moment[j+6] += ws_moment[j];
        }

        // assemble tauWall; area weighting is hiding in lambda/assembledArea
        *tauWall += lambda*std::sqrt(uParallel)/assembledArea;

        // deal with yplus
        *yplus += yplusBip*aMag/assembledArea;

      }
    }
  }

  if ( processMe ) {
    // parallel assemble and output
    double g_force_moment[9] = {};
    stk::ParallelMachine comm = NaluEnv::self().parallel_comm();

    // Parallel assembly of L2
    stk::all_reduce_sum(comm, &l_force_moment[0], &g_force_moment[0], 9);

    // min/max
    double g_yplusMin = 0.0, g_yplusMax = 0.0;
    stk::all_reduce_min(comm, &yplusMin, &g_yplusMin, 1);
    stk::all_reduce_max(comm, &yplusMax, &g_yplusMax, 1);

    // deal with file name and banner
    if ( NaluEnv::self().parallel_rank() == 0 ) {
      std::ofstream myfile;
      myfile.open(outputFileName_.c_str(), std::ios_base::app);
      myfile << std::setprecision(6) 
             << std::setw(w_) 
             << currentTime << std::setw(w_) 
             << g_force_moment[0] << std::setw(w_) << g_force_moment[1] << std::setw(w_) << g_force_moment[2] << std::setw(w_)
             << g_force_moment[3] << std::setw(w_) << g_force_moment[4] << std::setw(w_) << g_force_moment[5] <<  std::setw(w_)
             << g_force_moment[6] << std::setw(w_) << g_force_moment[7] << std::setw(w_) << g_force_moment[8] <<  std::setw(w_)
             << g_yplusMin << std::setw(w_) << g_yplusMax << std::endl;
      myfile.close();
    }
  }

}
//--------------------------------------------------------------------------
//-------- execute ---------------------------------------------------------
//--------------------------------------------------------------------------
void
SurfaceForceAndMomentAlgorithm::execute()
{
  // check to see if this is a valid step to process output file
  const int timeStepCount = realm_.get_time_step_count();
  const bool processMe = (timeStepCount % frequency_) == 0 ? true : false;

  // do not waste time here
  if ( !processMe )
    return;

  // common
  stk::mesh::BulkData & bulk_data = realm_.bulk_data();
  stk::mesh::MetaData & meta_data = realm_.meta_data();
  const int nDim = meta_data.spatial_dimension();

  // set min and max values
  double yplusMin = 1.0e8;
  double yplusMax = -1.0e8;

  // nodal fields to gather
  std::vector<double> ws_pressure;
  std::vector<double> ws_density;
  std::vector<double> ws_viscosity;

  // master element
  std::vector<double> ws_face_shape_function;

  // deal with state
  ScalarFieldType &densityNp1 = density_->field_of_state(stk::mesh::StateNP1);

  // define vector of parent topos; should always be UNITY in size
  std::vector<stk::topology> parentTopo;

  const double currentTime = realm_.get_current_time();

  // local force and moment; i.e., to be assembled
  double l_force_moment[9] = {};

  // work force, moment and radius; i.e., to be pushed to cross_product()
  double ws_p_force[3] = {};
  double ws_v_force[3] = {};
  double ws_t_force[3] = {};
  double ws_tau[3] = {};
  double ws_moment[3] = {};
  double ws_radius[3] = {};

  // will need surface normal
  double ws_normal[3] = {};

  // centroid
  double centroid[3] = {};
  for ( size_t k = 0; k < parameters_.size(); ++k)
    centroid[k] = parameters_[k];

  // define some common selectors
  stk::mesh::Selector s_locally_owned_union = meta_data.locally_owned_part()
    &stk::mesh::selectUnion(partVec_);

  stk::mesh::BucketVector const& face_buckets =
    realm_.get_buckets( meta_data.side_rank(), s_locally_owned_union );
  for ( stk::mesh::BucketVector::const_iterator ib = face_buckets.begin();
        ib != face_buckets.end() ; ++ib ) {
    stk::mesh::Bucket & b = **ib ;

    // face master element
    MasterElement *meFC = realm_.get_surface_master_element(b.topology());
    const int nodesPerFace = meFC->nodesPerElement_;
    std::vector<int> face_node_ordinal_vec(nodesPerFace);

    // extract connected element topology
    b.parent_topology(stk::topology::ELEMENT_RANK, parentTopo);
    ThrowAssert ( parentTopo.size() == 1 );
    stk::topology theElemTopo = parentTopo[0];

    // extract master element for this element topo
    MasterElement *meSCS = realm_.get_surface_master_element(theElemTopo);

    // algorithm related; element
    ws_pressure.resize(nodesPerFace);
    ws_density.resize(nodesPerFace);
    ws_viscosity.resize(nodesPerFace);
    ws_face_shape_function.resize(nodesPerFace*nodesPerFace);
    
    // pointers
    double *p_pressure = &ws_pressure[0];
    double *p_density = &ws_density[0];
    double *p_viscosity = &ws_viscosity[0];
    double *p_face_shape_function = &ws_face_shape_function[0];

    // shape functions
    if ( useShifted_ )
      meFC->shifted_shape_fcn(&p_face_shape_function[0]);
    else
      meFC->shape_fcn(&p_face_shape_function[0]);

    const stk::mesh::Bucket::size_type length   = b.size();

    for ( stk::mesh::Bucket::size_type k = 0 ; k < length ; ++k ) {

      // get face
      stk::mesh::Entity face = b[k];

      // face node relations
      stk::mesh::Entity const * face_node_rels = bulk_data.begin_nodes(face);

      //======================================
      // gather nodal data off of face
      //======================================
      for ( int ni = 0; ni < nodesPerFace; ++ni ) {
        stk::mesh::Entity node = face_node_rels[ni];
        // gather scalars
        p_pressure[ni]    = *stk::mesh::field_data(*pressure_, node);
        p_density[ni] = *stk::mesh::field_data(densityNp1, node);
        p_viscosity[ni] = *stk::mesh::field_data(*viscosity_, node);
      }

      // pointer to face data
      const double * areaVec = stk::mesh::field_data(*exposedAreaVec_, face);

      // extract the connected element to this exposed face; should be single in size!
      const stk::mesh::Entity* face_elem_rels = bulk_data.begin_elements(face);
      ThrowAssert( bulk_data.num_elements(face) == 1 );

      // get element; its face ordinal number and populate face_node_ordinal_vec
      stk::mesh::Entity element = face_elem_rels[0];
      const int face_ordinal = bulk_data.begin_element_ordinals(face)[0];
      theElemTopo.side_node_ordinals(face_ordinal, face_node_ordinal_vec.begin());

      // get the relations off of element
      stk::mesh::Entity const * elem_node_rels = bulk_data.begin_nodes(element);

      for ( int ip = 0; ip < nodesPerFace; ++ip ) {

        // offsets
        const int offSetAveraVec = ip*nDim;
        const int offSetSF_face = ip*nodesPerFace;

        // interpolate to bip
        double pBip = 0.0;
        double rhoBip = 0.0;
        double muBip = 0.0;
        for ( int ic = 0; ic < nodesPerFace; ++ic ) {
          const double r = p_face_shape_function[offSetSF_face+ic];
          pBip += r*p_pressure[ic];
          rhoBip += r*p_density[ic];
          muBip += r*p_viscosity[ic];
        }

        // extract nodal fields
        stk::mesh::Entity node = face_node_rels[ip];
        const double * coord = stk::mesh::field_data(*coordinates_, node );
        const double *duidxj = stk::mesh::field_data(*dudx_, node );
        double *pressureForce = stk::mesh::field_data(*pressureForce_, node );
        double *tauWall = stk::mesh::field_data(*tauWall_, node );
        double *yplus = stk::mesh::field_data(*yplus_, node );
        const double assembledArea = *stk::mesh::field_data(*assembledArea_, node );

        // divU and aMag
        double divU = 0.0;
        double aMag = 0.0;
        for ( int j = 0; j < nDim; ++j) {
          divU += duidxj[j*nDim+j];
          aMag += areaVec[offSetAveraVec+j]*areaVec[offSetAveraVec+j];
        }
        aMag = std::sqrt(aMag);

        // normal
        for ( int i = 0; i < nDim; ++i ) {
          const double ai = areaVec[offSetAveraVec+i];
          ws_normal[i] = ai/aMag;
        }

        // load radius; assemble force -sigma_ij*njdS and compute tau_ij njDs
        for ( int i = 0; i < nDim; ++i ) {
          const double ai = areaVec[offSetAveraVec+i];
          ws_radius[i] = coord[i] - centroid[i];
          // set forces
          ws_v_force[i] = 2.0/3.0*muBip*divU*includeDivU_*ai;
          ws_p_force[i] = pBip*ai;
          pressureForce[i] += pBip*ai;
          double dflux = 0.0;
          double tauijNj = 0.0;
          const int offSetI = nDim*i;
          for ( int j = 0; j < nDim; ++j ) {
            const int offSetTrans = nDim*j+i;
            dflux += -muBip*(duidxj[offSetI+j] + duidxj[offSetTrans])*areaVec[offSetAveraVec+j];
            tauijNj += -muBip*(duidxj[offSetI+j] + duidxj[offSetTrans])*ws_normal[j];
          }
          // accumulate viscous force and set tau for component i
          ws_v_force[i] += dflux;
          ws_tau[i] = tauijNj;
        }

        // compute total force and tangential tau
        double tauTangential = 0.0;
        for ( int i = 0; i < nDim; ++i ) {
          ws_t_force[i] = ws_p_force[i] + ws_v_force[i];
          double tauiTangential = (1.0-ws_normal[i]*ws_normal[i])*ws_tau[i];
          for ( int j = 0; j < nDim; ++j ) {
            if ( i != j )
              tauiTangential -= ws_normal[i]*ws_normal[j]*ws_tau[j];
          }
          tauTangential += tauiTangential*tauiTangential;
        }

        // assemble nodal quantities; scaled by area for L2 lumped nodal projection
        const double areaFac = aMag/assembledArea;
        *tauWall += std::sqrt(tauTangential)*areaFac;

        cross_product(&ws_t_force[0], &ws_moment[0], &ws_radius[0]);

        // assemble force and moment
        for ( int j = 0; j < 3; ++j ) {
          l_force_moment[j] += ws_p_force[j];
          l_force_moment[j+3] += ws_v_force[j];
          l_force_moment[j+6] += ws_moment[j];
        }

        // deal with yplus
        const int opposingNode = meSCS->opposingNodes(face_ordinal,ip);
        const int nearestNode = face_node_ordinal_vec[ip];

        // left and right nodes; right is on the face; left is the opposing node
        stk::mesh::Entity nodeL = elem_node_rels[opposingNode];
        stk::mesh::Entity nodeR = elem_node_rels[nearestNode];

        // extract nodal fields
        const double * coordL = stk::mesh::field_data(*coordinates_, nodeL );
        const double * coordR = stk::mesh::field_data(*coordinates_, nodeR );

        // determine yp (approximated by 1/4 distance along edge)
        double ypBip = 0.0;
        for ( int j = 0; j < nDim; ++j ) {
          const double nj = ws_normal[j];
          const double ej = 0.25*(coordR[j] - coordL[j]);
          ypBip += nj*ej*nj*ej;
        }
        ypBip = std::sqrt(ypBip);

        const double tauW = std::sqrt(tauTangential);
        const double uTau = std::sqrt(tauW/rhoBip);
        const double yplusBip = rhoBip*ypBip/muBip*uTau;

        // nodal field
        *yplus += yplusBip*areaFac;

        // min and max
        yplusMin = std::min(yplusMin, yplusBip);
        yplusMax = std::max(yplusMax, yplusBip);

      }
    }
  }

  if ( processMe ) {
    // parallel assemble and output
    double g_force_moment[9] = {};
    stk::ParallelMachine comm = NaluEnv::self().parallel_comm();

    // Parallel assembly of L2
    stk::all_reduce_sum(comm, &l_force_moment[0], &g_force_moment[0], 9);

    // min/max
    double g_yplusMin = 0.0, g_yplusMax = 0.0;
    stk::all_reduce_min(comm, &yplusMin, &g_yplusMin, 1);
    stk::all_reduce_max(comm, &yplusMax, &g_yplusMax, 1);

    // deal with file name and banner
    if ( NaluEnv::self().parallel_rank() == 0 ) {
      std::ofstream myfile;
      myfile.open(outputFileName_.c_str(), std::ios_base::app);
      myfile << std::setprecision(6) 
             << std::setw(w_) 
             << currentTime << std::setw(w_) 
             << g_force_moment[0] << std::setw(w_) << g_force_moment[1] << std::setw(w_) << g_force_moment[2] << std::setw(w_)
             << g_force_moment[3] << std::setw(w_) << g_force_moment[4] << std::setw(w_) << g_force_moment[5] <<  std::setw(w_)
             << g_force_moment[6] << std::setw(w_) << g_force_moment[7] << std::setw(w_) << g_force_moment[8] <<  std::setw(w_)
             << g_yplusMin << std::setw(w_) << g_yplusMax << std::endl;
      myfile.close();
    }
  }

}
//--------------------------------------------------------------------------
//-------- execute ---------------------------------------------------------
//--------------------------------------------------------------------------
void
AssembleNodalGradUBoundaryAlgorithm::execute()
{

  stk::mesh::MetaData & meta_data = realm_.meta_data();

  const int nDim = meta_data.spatial_dimension();

  // extract fields
  GenericFieldType *exposedAreaVec = meta_data.get_field<GenericFieldType>(meta_data.side_rank(), "exposed_area_vector");
  ScalarFieldType *dualNodalVolume = meta_data.get_field<ScalarFieldType>(stk::topology::NODE_RANK, "dual_nodal_volume");

  // nodal fields to gather; gather everything other than what we are assembling
  std::vector<double> ws_vectorQ;

  // geometry related to populate
  std::vector<double> ws_shape_function;

  // ip data
  std::vector<double>qIp(nDim);

  // define some common selectors
  stk::mesh::Selector s_locally_owned_union = meta_data.locally_owned_part()
    &stk::mesh::selectUnion(partVec_);

  stk::mesh::BucketVector const& face_buckets =
    realm_.get_buckets( meta_data.side_rank(), s_locally_owned_union );
  for ( stk::mesh::BucketVector::const_iterator ib = face_buckets.begin();
        ib != face_buckets.end() ; ++ib ) {
    stk::mesh::Bucket & b = **ib ;
    const stk::mesh::Bucket::size_type length   = b.size();

    // extract master element
    MasterElement *meFC = realm_.get_surface_master_element(b.topology());

    // extract master element specifics
    const int nodesPerFace = meFC->nodesPerElement_;
    const int numScsIp = meFC->numIntPoints_;

    // algorithm related
    ws_vectorQ.resize(nodesPerFace*nDim);
    ws_shape_function.resize(numScsIp*nodesPerFace);

    // pointers
    double *p_vectorQ = &ws_vectorQ[0];
    double *p_shape_function = &ws_shape_function[0];

    if ( useShifted_ )
      meFC->shifted_shape_fcn(&p_shape_function[0]);
    else
      meFC->shape_fcn(&p_shape_function[0]);

    for ( stk::mesh::Bucket::size_type k = 0 ; k < length ; ++k ) {

      // face data
      double * areaVec = stk::mesh::field_data(*exposedAreaVec, b, k);

      //===============================================
      // gather nodal data; this is how we do it now..
      //===============================================
      stk::mesh::Entity const * face_node_rels = b.begin_nodes(k);
      int num_nodes = b.num_nodes(k);

      // sanity check on num nodes
      ThrowAssert( num_nodes == nodesPerFace );

      for ( int ni = 0; ni < num_nodes; ++ni ) {
        stk::mesh::Entity node = face_node_rels[ni];

        // pointers to real data
        double * vectorQ = stk::mesh::field_data(*vectorQ_, node );

        // gather vectors
        const int offSet = ni*nDim;
        for ( int j=0; j < nDim; ++j ) {
          p_vectorQ[offSet+j] = vectorQ[j];
        }
      }

      // start assembly
      for ( int ip = 0; ip < numScsIp; ++ip ) {

        // nearest node
        const int nn = ip;

        stk::mesh::Entity nodeNN = face_node_rels[nn];

        // pointer to fields to assemble
        double *gradQNN = stk::mesh::field_data(*dqdx_, nodeNN );

        // suplemental
        double volNN = *stk::mesh::field_data(*dualNodalVolume, nodeNN);

        // interpolate to scs point; operate on saved off ws_field
        for (int j =0; j < nDim; ++j )
          qIp[j] = 0.0;

        const int offSet = ip*nodesPerFace;
        for ( int ic = 0; ic < nodesPerFace; ++ic ) {
          const double r = p_shape_function[offSet+ic];
          for ( int j = 0; j < nDim; ++j ) {
            qIp[j] += r*p_vectorQ[ic*nDim+j];
          }
        }

        // nearest node volume
        double inv_volNN = 1.0/volNN;

        // assemble to nearest node
        for ( int i = 0; i < nDim; ++i ) {
          const int row_gradQ = i*nDim;
          double qip = qIp[i];
          for ( int j = 0; j < nDim; ++j ) {
            double fac = qip*areaVec[ip*nDim+j];
            gradQNN[row_gradQ+j] += fac*inv_volNN;
          }
        }
      }
    }
  }
}
//--------------------------------------------------------------------------
//-------- execute ---------------------------------------------------------
//--------------------------------------------------------------------------
void
AssembleNodalGradUElemAlgorithm::execute()
{

  stk::mesh::MetaData & meta_data = realm_.meta_data();

  const int nDim = meta_data.spatial_dimension();

  // extract fields
  ScalarFieldType *dualNodalVolume = meta_data.get_field<ScalarFieldType>(stk::topology::NODE_RANK, "dual_nodal_volume");
  VectorFieldType *coordinates = meta_data.get_field<VectorFieldType>(stk::topology::NODE_RANK, realm_.get_coordinates_name());

  // nodal fields to gather; gather everything other than what we are assembling
  std::vector<double> ws_vectorQ;
  std::vector<double> ws_dualVolume;
  std::vector<double> ws_coordinates;

  // geometry related to populate
  std::vector<double> ws_scs_areav;
  std::vector<double> ws_shape_function;

  // ip data
  std::vector<double>qIp(nDim);

  // define some common selectors
  stk::mesh::Selector s_locally_owned_union = meta_data.locally_owned_part()
    &stk::mesh::selectUnion(partVec_);

  stk::mesh::BucketVector const& elem_buckets =
    realm_.get_buckets( stk::topology::ELEMENT_RANK, s_locally_owned_union );
  for ( stk::mesh::BucketVector::const_iterator ib = elem_buckets.begin();
        ib != elem_buckets.end() ; ++ib ) {
    stk::mesh::Bucket & b = **ib ;
    const stk::mesh::Bucket::size_type length   = b.size();

    // extract master element
    MasterElement *meSCS = realm_.get_surface_master_element(b.topology());

    // extract master element specifics
    const int nodesPerElement = meSCS->nodesPerElement_;
    const int numScsIp = meSCS->numIntPoints_;
    const int *lrscv = meSCS->adjacentNodes();

    // algorithm related
    ws_vectorQ.resize(nodesPerElement*nDim);
    ws_dualVolume.resize(nodesPerElement);
    ws_coordinates.resize(nodesPerElement*nDim);
    ws_scs_areav.resize(numScsIp*nDim);
    ws_shape_function.resize(numScsIp*nodesPerElement);

    // pointers.
    double *p_vectorQ = &ws_vectorQ[0];
    double *p_dualVolume = &ws_dualVolume[0];
    double *p_coordinates = &ws_coordinates[0];
    double *p_scs_areav = &ws_scs_areav[0];
    double *p_shape_function = &ws_shape_function[0];

    if ( useShifted_ )
      meSCS->shifted_shape_fcn(&p_shape_function[0]);
    else
      meSCS->shape_fcn(&p_shape_function[0]);

    for ( stk::mesh::Bucket::size_type k = 0 ; k < length ; ++k ) {

      //===============================================
      // gather nodal data; this is how we do it now..
      //===============================================
      stk::mesh::Entity const * node_rels = b.begin_nodes(k);
      int num_nodes = b.num_nodes(k);

      // sanity check on num nodes
      ThrowAssert( num_nodes == nodesPerElement );

      // note: we absolutely need to gather coords since it
      // is required to compute the area vector. however,
      // ws_scalarQ and ws_dualVolume are choices to avoid
      // field data call for interpolation

      for ( int ni = 0; ni < num_nodes; ++ni ) {
        stk::mesh::Entity node = node_rels[ni];

        // pointers to real data
        double * coords = stk::mesh::field_data(*coordinates, node);
        double * vectorQ = stk::mesh::field_data(*vectorQ_, node);

        // gather scalars
        p_dualVolume[ni] = *stk::mesh::field_data(*dualNodalVolume, node);

        // gather vectors
        const int offSet = ni*nDim;
        for ( int j=0; j < nDim; ++j ) {
          p_coordinates[offSet+j] = coords[j];
          p_vectorQ[offSet+j] = vectorQ[j];
        }
      }

      // compute geometry
      double scs_error = 0.0;
      meSCS->determinant(1, &p_coordinates[0], &p_scs_areav[0], &scs_error);

      // start assembly
      for ( int ip = 0; ip < numScsIp; ++ip ) {

        // left and right nodes for this ip
        const int il = lrscv[2*ip];
        const int ir = lrscv[2*ip+1];

        stk::mesh::Entity nodeL = node_rels[il];
        stk::mesh::Entity nodeR = node_rels[ir];

        // pointer to fields to assemble
        double *gradQL = stk::mesh::field_data(*dqdx_, nodeL);
        double *gradQR = stk::mesh::field_data(*dqdx_, nodeR);

        // interpolate to scs point; operate on saved off ws_field
        for (int j=0; j < nDim; ++j )
          qIp[j] = 0.0;

        const int offSet = ip*nodesPerElement;
        for ( int ic = 0; ic < nodesPerElement; ++ic ) {
          const double r = p_shape_function[offSet+ic];
          for ( int j = 0; j < nDim; ++j ) {
            qIp[j] += r*p_vectorQ[ic*nDim+j];
          }
        }

        // left and right volume
        double inv_volL = 1.0/p_dualVolume[il];
        double inv_volR = 1.0/p_dualVolume[ir];

        // assemble to il/ir
        for ( int i = 0; i < nDim; ++i ) {
          const int row_gradQ = i*nDim;
          const double qip = qIp[i];
          for ( int j = 0; j < nDim; ++j ) {
            double fac = qip*p_scs_areav[ip*nDim+j];
            gradQL[row_gradQ+j] += fac*inv_volL;
            gradQR[row_gradQ+j] -= fac*inv_volR;
          }
        }
      }
    }
  }
}
//--------------------------------------------------------------------------
//-------- execute ---------------------------------------------------------
//--------------------------------------------------------------------------
void
AssembleContinuityElemOpenSolverAlgorithm::execute()
{

  stk::mesh::BulkData & bulk_data = realm_.bulk_data();
  stk::mesh::MetaData & meta_data = realm_.meta_data();

  const int nDim = meta_data.spatial_dimension();
  
  // extract noc
  const std::string dofName = "pressure";
  const double includeNOC 
    = (realm_.get_noc_usage(dofName) == true) ? 1.0 : 0.0;

  // space for LHS/RHS; nodesPerElem*nodesPerElem and nodesPerElem
  std::vector<double> lhs;
  std::vector<double> rhs;
  std::vector<stk::mesh::Entity> connected_nodes;

  // ip values; both boundary and opposing surface
  std::vector<double> uBip(nDim);
  std::vector<double> rho_uBip(nDim);
  std::vector<double> GpdxBip(nDim);
  std::vector<double> coordBip(nDim);
  std::vector<double> coordScs(nDim);

  // pointers to fixed values
  double *p_uBip = &uBip[0];
  double *p_rho_uBip = &rho_uBip[0];
  double *p_GpdxBip = &GpdxBip[0];
  double *p_coordBip = &coordBip[0];
  double *p_coordScs = &coordScs[0];

  // nodal fields to gather
  std::vector<double> ws_coordinates;
  std::vector<double> ws_pressure;
  std::vector<double> ws_vrtm;
  std::vector<double> ws_Gpdx;
  std::vector<double> ws_density;
  std::vector<double> ws_bcPressure;
  // master element
  std::vector<double> ws_shape_function;
  std::vector<double> ws_shape_function_lhs;
  std::vector<double> ws_face_shape_function;

  // time step
  const double dt = realm_.get_time_step();
  const double gamma1 = realm_.get_gamma1();
  const double projTimeScale = dt/gamma1;

  // deal with interpolation procedure
  const double interpTogether = realm_.get_mdot_interp();
  const double om_interpTogether = 1.0-interpTogether;

  // deal with state
  ScalarFieldType &densityNp1 = density_->field_of_state(stk::mesh::StateNP1);

  // define vector of parent topos; should always be UNITY in size
  std::vector<stk::topology> parentTopo;

  // define some common selectors
  stk::mesh::Selector s_locally_owned_union = meta_data.locally_owned_part()
    &stk::mesh::selectUnion(partVec_);

  stk::mesh::BucketVector const& face_buckets =
    realm_.get_buckets( meta_data.side_rank(), s_locally_owned_union );
  for ( stk::mesh::BucketVector::const_iterator ib = face_buckets.begin();
        ib != face_buckets.end() ; ++ib ) {
    stk::mesh::Bucket & b = **ib ;

    // extract connected element topology
    b.parent_topology(stk::topology::ELEMENT_RANK, parentTopo);
    ThrowAssert ( parentTopo.size() == 1 );
    stk::topology theElemTopo = parentTopo[0];

    // volume master element
    MasterElement *meSCS = realm_.get_surface_master_element(theElemTopo);
    const int nodesPerElement = meSCS->nodesPerElement_;
    const int numScsIp = meSCS->numIntPoints_;

    // face master element
    MasterElement *meFC = realm_.get_surface_master_element(b.topology());
    const int nodesPerFace = b.topology().num_nodes();
    const int numScsBip = meFC->numIntPoints_;
    std::vector<int> face_node_ordinal_vec(nodesPerFace);

    // resize some things; matrix related
    const int lhsSize = nodesPerElement*nodesPerElement;
    const int rhsSize = nodesPerElement;
    lhs.resize(lhsSize);
    rhs.resize(rhsSize);
    connected_nodes.resize(nodesPerElement);

    // algorithm related; element
    ws_coordinates.resize(nodesPerElement*nDim);
    ws_pressure.resize(nodesPerElement);
    ws_vrtm.resize(nodesPerFace*nDim);
    ws_Gpdx.resize(nodesPerFace*nDim);
    ws_density.resize(nodesPerFace);
    ws_bcPressure.resize(nodesPerFace);
    ws_shape_function.resize(numScsIp*nodesPerElement);
    ws_shape_function_lhs.resize(numScsIp*nodesPerElement);
    ws_face_shape_function.resize(numScsBip*nodesPerFace);

    // pointers
    double *p_lhs = &lhs[0];
    double *p_rhs = &rhs[0];
    double *p_coordinates = &ws_coordinates[0];
    double *p_pressure = &ws_pressure[0];
    double *p_vrtm = &ws_vrtm[0];
    double *p_Gpdx = &ws_Gpdx[0];
    double *p_density = &ws_density[0];
    double *p_bcPressure = &ws_bcPressure[0];
    double *p_shape_function = &ws_shape_function[0];
    double *p_shape_function_lhs = shiftPoisson_ ? &ws_shape_function[0] : reducedSensitivities_ ? &ws_shape_function_lhs[0] : &ws_shape_function[0];
    double *p_face_shape_function = &ws_face_shape_function[0];

    // shape functions; interior
    if ( shiftPoisson_ )
      meSCS->shifted_shape_fcn(&p_shape_function[0]);
    else
      meSCS->shape_fcn(&p_shape_function[0]);

    if ( !shiftPoisson_ && reducedSensitivities_ )
      meSCS->shifted_shape_fcn(&p_shape_function_lhs[0]);

    // shape functions; boundary
    if ( shiftMdot_ )
      meFC->shifted_shape_fcn(&p_face_shape_function[0]);
    else
      meFC->shape_fcn(&p_face_shape_function[0]);

    const stk::mesh::Bucket::size_type length   = b.size();

    for ( stk::mesh::Bucket::size_type k = 0 ; k < length ; ++k ) {

      // zero lhs/rhs
      for ( int p = 0; p < lhsSize; ++p )
        p_lhs[p] = 0.0;
      for ( int p = 0; p < rhsSize; ++p )
        p_rhs[p] = 0.0;

      // get face
      stk::mesh::Entity face = b[k];

      //======================================
      // gather nodal data off of face
      //======================================
      stk::mesh::Entity const * face_node_rels = bulk_data.begin_nodes(face);
      int num_face_nodes = bulk_data.num_nodes(face);
      // sanity check on num nodes
      ThrowAssert( num_face_nodes == nodesPerFace );
      for ( int ni = 0; ni < num_face_nodes; ++ni ) {
        stk::mesh::Entity node = face_node_rels[ni];

        // gather scalars
        p_density[ni] = *stk::mesh::field_data(densityNp1, node);
        p_bcPressure[ni] = *stk::mesh::field_data(*pressureBc_, node);

        // gather vectors
        const double * vrtm = stk::mesh::field_data(*velocityRTM_, node);
        const double * Gjp = stk::mesh::field_data(*Gpdx_, node);
        const int offSet = ni*nDim;
        for ( int j=0; j < nDim; ++j ) {
          p_vrtm[offSet+j] = vrtm[j];
          p_Gpdx[offSet+j] = Gjp[j];
        }
      }

      // pointer to face data
      const double * areaVec = stk::mesh::field_data(*exposedAreaVec_, face);

      // extract the connected element to this exposed face; should be single in size!
      const stk::mesh::Entity* face_elem_rels = bulk_data.begin_elements(face);
      ThrowAssert( bulk_data.num_elements(face) == 1 );

      // get element; its face ordinal number and populate face_node_ordinal_vec
      stk::mesh::Entity element = face_elem_rels[0];
      const stk::mesh::ConnectivityOrdinal* face_elem_ords = bulk_data.begin_element_ordinals(face);
      const int face_ordinal = face_elem_ords[0];
      theElemTopo.side_node_ordinals(face_ordinal, face_node_ordinal_vec.begin());

      // mapping from ip to nodes for this ordinal
      const int *ipNodeMap = meSCS->ipNodeMap(face_ordinal);

      //======================================
      // gather nodal data off of element
      //======================================
      stk::mesh::Entity const * elem_node_rels = bulk_data.begin_nodes(element);
      int num_nodes = bulk_data.num_nodes(element);
      // sanity check on num nodes
      ThrowAssert( num_nodes == nodesPerElement );
      for ( int ni = 0; ni < num_nodes; ++ni ) {
        stk::mesh::Entity node = elem_node_rels[ni];

        // set connected nodes
        connected_nodes[ni] = node;

        // gather scalars
        p_pressure[ni] = *stk::mesh::field_data(*pressure_, node);

        // gather vectors
        const double * coords = stk::mesh::field_data(*coordinates_, node);
        const int offSet = ni*nDim;
        for ( int j=0; j < nDim; ++j ) {
          p_coordinates[offSet+j] = coords[j];
        }
      }

      // loop over boundary ips
      for ( int ip = 0; ip < numScsBip; ++ip ) {

        const int nearestNode = ipNodeMap[ip];
        const int opposingScsIp = meSCS->opposingFace(face_ordinal,ip);

        // zero out vector quantities
        for ( int j = 0; j < nDim; ++j ) {
          p_uBip[j] = 0.0;
          p_rho_uBip[j] = 0.0;
          p_GpdxBip[j] = 0.0;
          p_coordBip[j] = 0.0;
          p_coordScs[j] = 0.0;
        }
        double rhoBip = 0.0;

        // interpolate to bip
        double pBip = 0.0;
        const int offSetSF_face = ip*nodesPerFace;
        for ( int ic = 0; ic < nodesPerFace; ++ic ) {
          const int fn = face_node_ordinal_vec[ic];
          const double r = p_face_shape_function[offSetSF_face+ic];
          const double rhoIC = p_density[ic];
          rhoBip += r*rhoIC;
          pBip += r*p_bcPressure[ic];
          const int offSetFN = ic*nDim;
          const int offSetEN = fn*nDim;
          for ( int j = 0; j < nDim; ++j ) {
            p_uBip[j] += r*p_vrtm[offSetFN+j];
            p_rho_uBip[j] += r*rhoIC*p_vrtm[offSetFN+j];
            p_GpdxBip[j] += r*p_Gpdx[offSetFN+j];
            p_coordBip[j] += r*p_coordinates[offSetEN+j];
          }
        }

        // data at interior opposing face
        double pScs = 0.0;
        const int offSetSF_elem = opposingScsIp*nodesPerElement;
        for ( int ic = 0; ic < nodesPerElement; ++ic ) {
          const double r = p_shape_function[offSetSF_elem+ic];
          pScs += r*p_pressure[ic];
          const int offSet = ic*nDim;
          for ( int j = 0; j < nDim; ++j ) {
            p_coordScs[j] += r*p_coordinates[offSet+j];
          }
        }

        // form axdx, asq and mdot (without dp/dn or noc)
        double asq = 0.0;
        double axdx = 0.0;
        double mdot = 0.0;
        for ( int j = 0; j < nDim; ++j ) {
          const double dxj = p_coordBip[j] - p_coordScs[j];
          const double axj = areaVec[ip*nDim+j];
          asq += axj*axj;
          axdx += axj*dxj;
          mdot += (interpTogether*p_rho_uBip[j] + om_interpTogether*rhoBip*p_uBip[j] 
                   + projTimeScale*p_GpdxBip[j])*axj;
        }
	
        const double inv_axdx = 1.0/axdx;
	
        // deal with noc
        double noc = 0.0;
        for ( int j = 0; j < nDim; ++j ) {
          const double dxj = p_coordBip[j] - p_coordScs[j];
          const double axj = areaVec[ip*nDim+j];
          const double kxj = axj - asq*inv_axdx*dxj; // NOC
          noc += kxj*p_GpdxBip[j];
        }

        // lhs for pressure system
        int rowR = nearestNode*nodesPerElement;

        for ( int ic = 0; ic < nodesPerElement; ++ic ) {
          const double r = p_shape_function_lhs[offSetSF_elem+ic];
          p_lhs[rowR+ic] += r*asq*inv_axdx;
        }

        // final mdot
        mdot += -projTimeScale*((pBip-pScs)*asq*inv_axdx + noc*includeNOC);

        // residual
        p_rhs[nearestNode] -= mdot/projTimeScale;
      }

      apply_coeff(connected_nodes, rhs, lhs, __FILE__);

    }
  }
}
//--------------------------------------------------------------------------
//-------- execute ---------------------------------------------------------
//--------------------------------------------------------------------------
void
ComputeMdotElemAlgorithm::execute()
{

  stk::mesh::MetaData & meta_data = realm_.meta_data();

  const int nDim = meta_data.spatial_dimension();

  // time step
  const double dt = realm_.get_time_step();
  const double gamma1 = realm_.get_gamma1();
  const double projTimeScale = dt/gamma1;

  // deal with interpolation procedure
  const double interpTogether = realm_.get_mdot_interp();
  const double om_interpTogether = 1.0-interpTogether;

  // nodal fields to gather
  std::vector<double> ws_vrtm;
  std::vector<double> ws_Gpdx;
  std::vector<double> ws_coordinates;
  std::vector<double> ws_pressure;
  std::vector<double> ws_density;

  // geometry related to populate
  std::vector<double> ws_scs_areav;
  std::vector<double> ws_dndx;
  std::vector<double> ws_deriv;
  std::vector<double> ws_det_j;
  std::vector<double> ws_shape_function;

  // integration point data that depends on size
  std::vector<double> uIp(nDim);
  std::vector<double> rho_uIp(nDim);
  std::vector<double> GpdxIp(nDim);
  std::vector<double> dpdxIp(nDim);

  // pointers to everyone...
  double *p_uIp = &uIp[0];
  double *p_rho_uIp = &rho_uIp[0];
  double *p_GpdxIp = &GpdxIp[0];
  double *p_dpdxIp = &dpdxIp[0];

  // deal with state
  ScalarFieldType &densityNp1 = density_->field_of_state(stk::mesh::StateNP1);

  // define some common selectors
  stk::mesh::Selector s_locally_owned_union = meta_data.locally_owned_part()
    &stk::mesh::selectUnion(partVec_);

  stk::mesh::BucketVector const& elem_buckets =
    realm_.get_buckets( stk::topology::ELEMENT_RANK, s_locally_owned_union );
  for ( stk::mesh::BucketVector::const_iterator ib = elem_buckets.begin();
        ib != elem_buckets.end() ; ++ib ) {
    stk::mesh::Bucket & b = **ib ;
    const stk::mesh::Bucket::size_type length   = b.size();

    // extract master element
    MasterElement *meSCS = realm_.get_surface_master_element(b.topology());

    // extract master element specifics
    const int nodesPerElement = meSCS->nodesPerElement_;
    const int numScsIp = meSCS->numIntPoints_;

    // algorithm related
    ws_vrtm.resize(nodesPerElement*nDim);
    ws_Gpdx.resize(nodesPerElement*nDim);
    ws_coordinates.resize(nodesPerElement*nDim);
    ws_pressure.resize(nodesPerElement);
    ws_density.resize(nodesPerElement);
    ws_scs_areav.resize(numScsIp*nDim);
    ws_dndx.resize(nDim*numScsIp*nodesPerElement);
    ws_deriv.resize(nDim*numScsIp*nodesPerElement);
    ws_det_j.resize(numScsIp);
    ws_shape_function.resize(numScsIp*nodesPerElement);

    // pointers
    double *p_vrtm = &ws_vrtm[0];
    double *p_Gpdx = &ws_Gpdx[0];
    double *p_coordinates = &ws_coordinates[0];
    double *p_pressure = &ws_pressure[0];
    double *p_density = &ws_density[0];
    double *p_scs_areav = &ws_scs_areav[0];
    double *p_dndx = &ws_dndx[0];
    double *p_shape_function = &ws_shape_function[0];
    
    if ( shiftMdot_)
      meSCS->shifted_shape_fcn(&p_shape_function[0]);
    else
      meSCS->shape_fcn(&p_shape_function[0]);
    
    for ( stk::mesh::Bucket::size_type k = 0 ; k < length ; ++k ) {

      // pointers to elem data
      double * mdot = stk::mesh::field_data(*massFlowRate_, b, k );

      //===============================================
      // gather nodal data; this is how we do it now..
      //===============================================
      stk::mesh::Entity const * node_rels = b.begin_nodes(k);
      int num_nodes = b.num_nodes(k);

      // sanity check on num nodes
      ThrowAssert( num_nodes == nodesPerElement );

      for ( int ni = 0; ni < num_nodes; ++ni ) {
        stk::mesh::Entity node = node_rels[ni];

        // pointers to real data
        const double * vrtm   = stk::mesh::field_data(*velocityRTM_, node);
        const double * Gjp    = stk::mesh::field_data(*Gpdx_, node);
        const double * coords = stk::mesh::field_data(*coordinates_, node);

        // gather scalars
        p_pressure[ni] = *stk::mesh::field_data(*pressure_, node);
        p_density[ni]  = *stk::mesh::field_data(densityNp1, node);

        // gather vectors
        const int offSet = ni*nDim;
        for ( int j=0; j < nDim; ++j ) {
          p_vrtm[offSet+j] = vrtm[j];
          p_Gpdx[offSet+j] = Gjp[j];
          p_coordinates[offSet+j] = coords[j];
        }
      }

      // compute geometry
      double scs_error = 0.0;
      meSCS->determinant(1, &p_coordinates[0], &p_scs_areav[0], &scs_error);

      // compute dndx
      if (shiftPoisson_)
        meSCS->shifted_grad_op(1, &p_coordinates[0], &p_dndx[0], &ws_deriv[0], &ws_det_j[0], &scs_error);
      else
        meSCS->grad_op(1, &p_coordinates[0], &p_dndx[0], &ws_deriv[0], &ws_det_j[0], &scs_error);
      
      for ( int ip = 0; ip < numScsIp; ++ip ) {

        // setup for ip values
        for ( int j = 0; j < nDim; ++j ) {
          p_uIp[j] = 0.0;
          p_rho_uIp[j] = 0.0;
          p_GpdxIp[j] = 0.0;
          p_dpdxIp[j] = 0.0;
        }
        double rhoIp = 0.0;

        const int offSet = ip*nodesPerElement;
        for ( int ic = 0; ic < nodesPerElement; ++ic ) {

          const double r = p_shape_function[offSet+ic];
          const double nodalPressure = p_pressure[ic];
          const double nodalRho = p_density[ic];

          rhoIp += r*nodalRho;

          const int offSetDnDx = nDim*nodesPerElement*ip + ic*nDim;
          for ( int j = 0; j < nDim; ++j ) {
            p_GpdxIp[j] += r*p_Gpdx[nDim*ic+j];
            p_uIp[j] += r*p_vrtm[nDim*ic+j];
            p_rho_uIp[j] += r*nodalRho*p_vrtm[nDim*ic+j];
            p_dpdxIp[j] += p_dndx[offSetDnDx+j]*nodalPressure;
          }
        }

        // assemble mdot
        double tmdot = 0.0;
        for ( int j = 0; j < nDim; ++j ) {
          tmdot += (interpTogether*p_rho_uIp[j] + om_interpTogether*rhoIp*p_uIp[j] 
                    - projTimeScale*(p_dpdxIp[j] - p_GpdxIp[j]))*p_scs_areav[ip*nDim+j];
        }

        mdot[ip] = tmdot;

      }
    }
  }

  // check for edge-mdot assembly
  if ( assembleMdotToEdge_ )
    assemble_edge_mdot();
}
//--------------------------------------------------------------------------
//-------- execute ---------------------------------------------------------
//--------------------------------------------------------------------------
void
ComputeLowReynoldsSDRWallAlgorithm::execute()
{

  stk::mesh::BulkData & bulk_data = realm_.bulk_data();
  stk::mesh::MetaData & meta_data = realm_.meta_data();

  const int nDim = meta_data.spatial_dimension();

  // nodal fields to gather
  std::vector<double> ws_density;
  std::vector<double> ws_viscosity;

  // master element
  std::vector<double> ws_face_shape_function;

  // deal with state
  ScalarFieldType &densityNp1 = density_->field_of_state(stk::mesh::StateNP1);

  // define vector of parent topos; should always be UNITY in size
  std::vector<stk::topology> parentTopo;

  // define some common selectors
  stk::mesh::Selector s_locally_owned_union = meta_data.locally_owned_part()
    &stk::mesh::selectUnion(partVec_);

  stk::mesh::BucketVector const& face_buckets =
    realm_.get_buckets( meta_data.side_rank(), s_locally_owned_union );
  for ( stk::mesh::BucketVector::const_iterator ib = face_buckets.begin();
        ib != face_buckets.end() ; ++ib ) {
    stk::mesh::Bucket & b = **ib ;

    // extract connected element topology
    b.parent_topology(stk::topology::ELEMENT_RANK, parentTopo);
    ThrowAssert ( parentTopo.size() == 1 );
    stk::topology theElemTopo = parentTopo[0];

    // extract master element
    MasterElement *meSCS = realm_.get_surface_master_element(theElemTopo);

    // face master element
    MasterElement *meFC = realm_.get_surface_master_element(b.topology());
    const int nodesPerFace = b.topology().num_nodes();
    std::vector<int> face_node_ordinal_vec(nodesPerFace);

    // algorithm related; element
    ws_density.resize(nodesPerFace);
    ws_viscosity.resize(nodesPerFace);
    ws_face_shape_function.resize(nodesPerFace*nodesPerFace);

    // pointers
    double *p_density = &ws_density[0];
    double *p_viscosity = &ws_viscosity[0];
    double *p_face_shape_function = &ws_face_shape_function[0];

    // shape functions
    if ( useShifted_ )
      meFC->shifted_shape_fcn(&p_face_shape_function[0]);
    else
      meFC->shape_fcn(&p_face_shape_function[0]);

    const stk::mesh::Bucket::size_type length   = b.size();

    for ( stk::mesh::Bucket::size_type k = 0 ; k < length ; ++k ) {

      // get face
      stk::mesh::Entity face = b[k];

      //======================================
      // gather nodal data off of face
      //======================================
      stk::mesh::Entity const * face_node_rels = bulk_data.begin_nodes(face);
      int num_face_nodes = bulk_data.num_nodes(face);
      // sanity check on num nodes
      ThrowAssert( num_face_nodes == nodesPerFace );
      for ( int ni = 0; ni < num_face_nodes; ++ni ) {
        stk::mesh::Entity node = face_node_rels[ni];

        // gather scalars
        p_density[ni]    = *stk::mesh::field_data(densityNp1, node);
        p_viscosity[ni] = *stk::mesh::field_data(*viscosity_, node);
      }

      // pointer to face data
      const double * areaVec = stk::mesh::field_data(*exposedAreaVec_, face);

      // extract the connected element to this exposed face; should be single in size!
      const stk::mesh::Entity* face_elem_rels = bulk_data.begin_elements(face);
      ThrowAssert( bulk_data.num_elements(face) == 1 );

      // get element; its face ordinal number and populate face_node_ordinal_vec
      stk::mesh::Entity element = face_elem_rels[0];
      const int face_ordinal = bulk_data.begin_element_ordinals(face)[0];
      theElemTopo.side_node_ordinals(face_ordinal, face_node_ordinal_vec.begin());

      // get the relations off of element
      stk::mesh::Entity const * elem_node_rels = bulk_data.begin_nodes(element);

      // loop over face nodes
      for ( int ip = 0; ip < num_face_nodes; ++ip ) {

        const int offSetAveraVec = ip*nDim;

        const int opposingNode = meSCS->opposingNodes(face_ordinal,ip);
        const int nearestNode = face_node_ordinal_vec[ip];

        // left and right nodes; right is on the face; left is the opposing node
        stk::mesh::Entity nodeL = elem_node_rels[opposingNode];
        stk::mesh::Entity nodeR = elem_node_rels[nearestNode];

        // extract nodal fields
        const double * coordL = stk::mesh::field_data(*coordinates_, nodeL );
        const double * coordR = stk::mesh::field_data(*coordinates_, nodeR );

        // aMag
        double aMag = 0.0;
        for ( int j = 0; j < nDim; ++j ) {
          const double axj = areaVec[offSetAveraVec+j];
          aMag += axj*axj;
        }
        aMag = std::sqrt(aMag);

        // interpolate to bip
        double rhoBip = 0.0;
        double muBip = 0.0;
        const int offSetSF_face = ip*nodesPerFace;
        for ( int ic = 0; ic < nodesPerFace; ++ic ) {
          const double r = p_face_shape_function[offSetSF_face+ic];
          rhoBip += r*p_density[ic];
          muBip += r*p_viscosity[ic];
        }
        const double nuBip = muBip/rhoBip;

        // determine yp (approximated by 1/4 distance along edge)
        double ypbip = 0.0;
        for ( int j = 0; j < nDim; ++j ) {
          const double nj = areaVec[offSetAveraVec+j]/aMag;
          const double ej = 0.25*(coordR[j] - coordL[j]);
          ypbip += nj*ej*nj*ej;
        }
        ypbip = std::sqrt(ypbip);

        // compute low Re wall sdr
        const double lowReSdr = wallFactor_*6.0*nuBip/betaOne_/ypbip/ypbip;

        // assemble to nodal quantities; will normalize and assemble in driver
        double * assembledWallArea = stk::mesh::field_data(*assembledWallArea_, nodeR );
        double * sdrBc = stk::mesh::field_data(*sdrBc_, nodeR );

        *assembledWallArea += aMag;
        *sdrBc += lowReSdr*aMag;
      }
    }
  }
}