extendedFiniteDifferenceBoundary3D.hh

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/*  This file is part of the OpenLB library
 *
 *  Copyright (C) 2007 Orestis Malaspinas, Jonas Latt
 *  E-mail contact: info@openlb.net
 *  The most recent release of OpenLB can be downloaded at
 *  <http://www.openlb.net/>
 *
 *  This program is free software; you can redistribute it and/or
 *  modify it under the terms of the GNU General Public License
 *  as published by the Free Software Foundation; either version 2
 *  of the License, or (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public
 *  License along with this program; if not, write to the Free
 *  Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
 *  Boston, MA  02110-1301, USA.
*/
 
#ifndef EXTENDED_FINITE_DIFFERENCE_BOUNDARY_3D_HH
#define EXTENDED_FINITE_DIFFERENCE_BOUNDARY_3D_HH
 
#include "extendedFiniteDifferenceBoundary3D.h"
#include "utilities/finiteDifference3D.h"
#include "core/util.h"
#include "dynamics/lbm.h"
 
 
namespace olb {
 
 
template<typename T, typename DESCRIPTOR, int direction, int orientation>
ExtendedFdPlaneBoundaryPostProcessor3D <T,DESCRIPTOR,direction,orientation>::
ExtendedFdPlaneBoundaryPostProcessor3D(int x0_, int x1_, int y0_, int y1_, int z0_, int z1_)
  : x0(x0_), x1(x1_), y0(y0_), y1(y1_), z0(z0_), z1(z1_)
{
  OLB_PRECONDITION(x0==x1 || y0==y1 || z0==z1);
  this->getName() = "ExtendedFdPlaneBoundaryPostProcessor3D";
}
 
template<typename T, typename DESCRIPTOR, int direction, int orientation>
void ExtendedFdPlaneBoundaryPostProcessor3D<T,DESCRIPTOR,direction,orientation>::
processSubDomain(BlockLattice<T,DESCRIPTOR>& blockLattice,
                 int x0_, int x1_, int y0_, int y1_, int z0_, int z1_)
{
  typedef DESCRIPTOR L;
  using namespace olb::util::tensorIndices3D;
  typedef lbm<DESCRIPTOR> lbH;
  enum {x,y,z};
 
 
  for (int iX=x0; iX<=x1; ++iX) {
    for (int iY=y0; iY<=y1; ++iY) {
      for (int iZ=z0; iZ<=z1; ++iZ) {
        Cell<T,DESCRIPTOR> cell = blockLattice.get(iX,iY,iZ);
        T rho, u[L::d];
        cell.computeRhoU(rho,u);
        T dx_U[DESCRIPTOR::d], dy_U[DESCRIPTOR::d], dz_U[DESCRIPTOR::d];
        interpolateGradients<0>(blockLattice, dx_U, iX, iY, iZ);
        interpolateGradients<1>(blockLattice, dy_U, iX, iY, iZ);
        interpolateGradients<2>(blockLattice, dz_U, iX, iY, iZ);
 
        T rhoGradU[L::d][L::d];
        rhoGradU[x][x] = rho *dx_U[x];
        rhoGradU[x][y] = rho *dx_U[y];
        rhoGradU[x][z] = rho *dx_U[z];
        rhoGradU[y][x] = rho *dy_U[x];
        rhoGradU[y][y] = rho *dy_U[y];
        rhoGradU[y][z] = rho *dy_U[z];
        rhoGradU[z][x] = rho *dz_U[x];
        rhoGradU[z][y] = rho *dz_U[y];
        rhoGradU[z][z] = rho *dz_U[z];
 
        T omega = blockLattice.getDynamics(iX, iY, iZ) -> getOmega();
        T sToPi = - (T)1 / descriptors::invCs2<T,DESCRIPTOR>() / omega;
        T pi[util::TensorVal<DESCRIPTOR >::n];
 
        pi[xx] = (T)2 * rhoGradU[x][x] * sToPi;
        pi[yy] = (T)2 * rhoGradU[y][y] * sToPi;
        pi[zz] = (T)2 * rhoGradU[z][z] * sToPi;
        pi[xy] = (rhoGradU[x][y] + rhoGradU[y][x]) * sToPi;
        pi[xz] = (rhoGradU[x][z] + rhoGradU[z][x]) * sToPi;
        pi[yz] = (rhoGradU[y][z] + rhoGradU[z][y]) * sToPi;
 
        // here ends the "regular" fdBoudaryCondition
        // implemented in OpenLB
 
        T uSqr = util::normSqr<T,DESCRIPTOR::d>(u);
 
        // first we compute the term
        // (c_{i\alpha} \nabla_\beta)(rho*u_\alpha*u_\beta)
        T dx_rho, dy_rho, dz_rho;
        interpolateGradients<0>(blockLattice, dx_rho, iX, iY, iZ);
        interpolateGradients<1>(blockLattice, dy_rho, iX, iY, iZ);
        interpolateGradients<2>(blockLattice, dz_rho, iX, iY, iZ);
        for (int iPop = 0; iPop < L::q; ++iPop) {
          T cGradRhoUU = T();
          for (int iAlpha=0; iAlpha < L::d; ++iAlpha) {
            cGradRhoUU += descriptors::c<L>(iPop,iAlpha) * (
                            dx_rho*u[iAlpha]*u[x] +
                            dx_U[iAlpha]*rho*u[x] +
                            dx_U[x]*rho*u[iAlpha] + //end of dx derivative
                            dy_rho*u[iAlpha]*u[y] +
                            dy_U[iAlpha]*rho*u[y] +
                            dy_U[y]*rho*u[iAlpha] +//end of dy derivative
                            dz_rho*u[iAlpha]*u[z] +
                            dz_U[iAlpha]*rho*u[z] +
                            dz_U[z]*rho*u[iAlpha]);
          }
 
          // then we compute the term
          // c_{i\gamma}\nabla_{\gamma}(\rho*u_\alpha * u_\beta)
          T cDivRhoUU[L::d][L::d]; //first step towards QcdivRhoUU
          for (int iAlpha = 0; iAlpha < L::d; ++iAlpha) {
            for (int iBeta = 0; iBeta < L::d; ++iBeta) {
              cDivRhoUU[iAlpha][iBeta] = descriptors::c<L>(iPop,x)*
                                         (dx_rho*u[iAlpha]*u[iBeta] +
                                          dx_U[iAlpha]*rho*u[iBeta] +
                                          dx_U[iBeta]*rho*u[iAlpha])
                                         +descriptors::c<L>(iPop,y)*
                                         (dy_rho*u[iAlpha]*u[iBeta] +
                                          dy_U[iAlpha]*rho*u[iBeta] +
                                          dy_U[iBeta]*rho*u[iAlpha])
                                         +descriptors::c<L>(iPop,z)*
                                         (dz_rho*u[iAlpha]*u[iBeta] +
                                          dz_U[iAlpha]*rho*u[iBeta] +
                                          dz_U[iBeta]*rho*u[iAlpha]);
            }
          }
 
          //Finally we can compute
          // Q_{i\alpha\beta}c_{i\gamma}\nabla_{\gamma}(\rho*u_\alpha * u_\beta)
          // and Q_{i\alpha\beta}\rho\nabla_{\alpha}u_\beta
          T qCdivRhoUU = T();
          T qRhoGradU = T();
          for (int iAlpha = 0; iAlpha < L::d; ++iAlpha) {
            for (int iBeta = 0; iBeta < L::d; ++iBeta) {
              int ci_ci = descriptors::c<L>(iPop,iAlpha)*descriptors::c<L>(iPop,iBeta);
              qCdivRhoUU  += ci_ci * cDivRhoUU[iAlpha][iBeta];
              qRhoGradU += ci_ci * rhoGradU[iAlpha][iBeta];
              if (iAlpha == iBeta) {
                qCdivRhoUU -= cDivRhoUU[iAlpha][iBeta]/descriptors::invCs2<T,L>();
                qRhoGradU  -= rhoGradU[iAlpha][iBeta]/descriptors::invCs2<T,L>();
              }
            }
          }
 
          // we then can reconstruct the value of the populations
          // according to the complete C-E expansion term
          cell[iPop] = lbH::equilibrium(iPop,rho,u,uSqr)
                       - descriptors::t<T,L>(iPop) * descriptors::invCs2<T,L>() / omega
                       * (qRhoGradU - cGradRhoUU + 0.5*descriptors::invCs2<T,L>()*qCdivRhoUU);
        }
      }
    }
  }
}
 
template<typename T, typename DESCRIPTOR, int direction, int orientation>
void ExtendedFdPlaneBoundaryPostProcessor3D<T,DESCRIPTOR,direction,orientation>::
process(BlockLattice<T,DESCRIPTOR>& blockLattice)
{
  processSubDomain(blockLattice, x0, x1, y0, y1, z0, z1);
}
 
template<typename T, typename DESCRIPTOR, int direction, int orientation>
template<int deriveDirection>
void ExtendedFdPlaneBoundaryPostProcessor3D<T,DESCRIPTOR,direction,orientation>::
interpolateGradients(BlockLattice<T,DESCRIPTOR> const& blockLattice,
                     T velDeriv[DESCRIPTOR::d],
                     int iX, int iY, int iZ) const
{
  fd::DirectedGradients3D<T, DESCRIPTOR, direction, orientation, deriveDirection, direction==deriveDirection>::
  interpolateVector(velDeriv, blockLattice, iX, iY, iZ);
}
 
template<typename T, typename DESCRIPTOR, int direction, int orientation>
template<int deriveDirection>
void ExtendedFdPlaneBoundaryPostProcessor3D<T,DESCRIPTOR,direction,orientation>::
interpolateGradients(BlockLattice<T,DESCRIPTOR> const& blockLattice,
                     T& rhoDeriv, int iX, int iY, int iZ) const
{
  fd::DirectedGradients3D<T, DESCRIPTOR, direction, orientation, deriveDirection, direction==deriveDirection>::
  interpolateScalar(rhoDeriv, blockLattice, iX, iY, iZ);
}
 
 
 
template<typename T, typename DESCRIPTOR, int direction, int orientation>
ExtendedFdPlaneBoundaryProcessorGenerator3D<T,DESCRIPTOR,direction,orientation>::
ExtendedFdPlaneBoundaryProcessorGenerator3D(int x0_, int x1_, int y0_, int y1_, int z0_, int z1_)
  : PostProcessorGenerator3D<T,DESCRIPTOR>(x0_, x1_, y0_, y1_, z0_, z1_)
{ }
 
template<typename T, typename DESCRIPTOR, int direction, int orientation>
PostProcessor3D<T,DESCRIPTOR>*
ExtendedFdPlaneBoundaryProcessorGenerator3D<T,DESCRIPTOR,direction,orientation>::generate() const
{
  return new ExtendedFdPlaneBoundaryPostProcessor3D<T,DESCRIPTOR,direction,orientation>
         (this->x0, this->x1, this->y0, this->y1, this->z0, this->z1);
}
 
template<typename T, typename DESCRIPTOR, int direction, int orientation>
PostProcessorGenerator3D<T,DESCRIPTOR>*
ExtendedFdPlaneBoundaryProcessorGenerator3D<T,DESCRIPTOR,direction,orientation>::clone() const
{
  return new ExtendedFdPlaneBoundaryProcessorGenerator3D<T,DESCRIPTOR,direction,orientation>
         (this->x0, this->x1, this->y0, this->y1, this->z0, this->z1);
}
 
 
}  // namespace olb
 
#endif