//--------------------------------------------------------------------------
//-------- 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
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__);

    }
  }
}