extendedfinitedifferenceboundary2d.hh

open lattice boltzmann project www.openlb.org

/*  This file is part of the OpenLB library
 *
 *  Copyright (C) 2007 Orestis Malaspinas, Jonas Latt
 *  Address: Rue General Dufour 24,  1211 Geneva 4, Switzerland 
 *  E-mail: [e-mail]
 *
 *  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_2D_HH
#define EXTENDED_FINITE_DIFFERENCE_BOUNDARY_2D_HH

#include "extendedFiniteDifferenceBoundary2D.h"
#include "core/finiteDifference2D.h"
#include "core/blockLattice2D.h"
#include "core/util.h"
#include "core/lbHelpers.h"
#include "core/firstOrderLbHelpers.h"
#include "core/boundaryInstantiator2D.h"


namespace olb {


///////////  ExtendedStraightFdBoundaryPostProcessor2D ///////////////////////////////////

template<typename T, template<typename U> class Lattice, int direction, int orientation>
ExtendedStraightFdBoundaryPostProcessor2D<T,Lattice,direction,orientation>::
    ExtendedStraightFdBoundaryPostProcessor2D(int x0_, int x1_, int y0_, int y1_)
    : x0(x0_), x1(x1_), y0(y0_), y1(y1_) 
{
    OLB_PRECONDITION(x0==x1 || y0==y1);
}

template<typename T, template<typename U> class Lattice, int direction, int orientation>
void ExtendedStraightFdBoundaryPostProcessor2D<T,Lattice,direction,orientation>::
    processSubDomain(BlockLattice2D<T,Lattice>& blockLattice, int x0_, int x1_, int y0_, int y1_)
{
    using namespace olb::util::tensorIndices2D;
    typedef lbHelpers<T,Lattice> lbH;
    typedef Lattice<T> L;
    enum {x,y};

    int newX0, newX1, newY0, newY1;
    if ( util::intersect (
                x0, x1, y0, y1,
                x0_, x1_, y0_, y1_,
                newX0, newX1, newY0, newY1 ) )
    {
        for (int iX=newX0; iX<=newX1; ++iX) {
            for (int iY=newY0; iY<=newY1; ++iY) {
                Cell<T,Lattice>& cell = blockLattice.get(iX,iY);
                T rho, u[L::d];
                cell.computeRhoU(rho,u);

                T uSqr = util::normSqr<T,Lattice<T>::d>(u);

                T dx_U[L::d], dy_U[L::d];
                interpolateGradients<0>(blockLattice, dx_U, iX, iY);
                interpolateGradients<1>(blockLattice, dy_U, iX, iY);

                T rhoGradU[L::d][L::d];
                rhoGradU[x][x] = rho * dx_U[x];
                rhoGradU[x][y] = rho * dx_U[y];
                rhoGradU[y][x] = rho * dy_U[x];
                rhoGradU[y][y] = rho * dy_U[y];

                T omega = cell.getDynamics() -> getOmega();
                T sToPi = - (T)1 / Lattice<T>::invCs2 / omega;
                
                T pi[util::TensorVal<Lattice<T> >::n];
                pi[xx] = (T)2 * rhoGradU[x][x] * sToPi;
                pi[yy] = (T)2 * rhoGradU[y][y] * sToPi;
                pi[xy] = (rhoGradU[x][y] + rhoGradU[y][x]) * sToPi; 
                // here ends the "regular" fdBoudaryCondition 
                // implemented in OpenLB

                // first we compute the term 
                // (c_{i\alpha} \nabla_\beta)(rho*u_\alpha*u_\beta)
                T dx_rho, dy_rho;
                interpolateGradients<0>(blockLattice, dx_rho, iX, iY);
                interpolateGradients<1>(blockLattice, dy_rho, iX, iY);
                for (int iPop = 0; iPop < L::q; ++iPop) {
                    T cGradRhoUU = T();
                    for (int iAlpha=0; iAlpha < L::d; ++iAlpha)
                    {
                        cGradRhoUU += L::c[iPop][iAlpha] * (
                            dx_rho*u[iAlpha]*u[x] +
                            dx_U[iAlpha]*rho*u[x] +
                            dx_U[x]*rho*u[iAlpha] + //end of dx derivatice
                            dy_rho*u[iAlpha]*u[y] +
                            dy_U[iAlpha]*rho*u[y] +
                            dy_U[y]*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] = L::c[iPop][x] *
                                            (dx_rho*u[iAlpha]*u[iBeta] +
                                             dx_U[iAlpha]*rho*u[iBeta] +
                                             dx_U[iBeta]*rho*u[iAlpha])
                                                       + L::c[iPop][y] *
                                            (dy_rho*u[iAlpha]*u[iBeta] +
                                             dy_U[iAlpha]*rho*u[iBeta] +
                                             dy_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 = L::c[iPop][iAlpha]*L::c[iPop][iBeta];
                            qCdivRhoUU  += ci_ci * cDivRhoUU[iAlpha][iBeta];
                            qRhoGradU   += ci_ci * rhoGradU[iAlpha][iBeta];
                            if (iAlpha == iBeta) {
                                qCdivRhoUU -= cDivRhoUU[iAlpha][iBeta]/L::invCs2;
                                qRhoGradU  -= rhoGradU[iAlpha][iBeta]/L::invCs2;
                            }
                        }
                    }

                    // 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)
                                 - L::t[iPop] * L::invCs2 / omega
                                     * (qRhoGradU - cGradRhoUU + 0.5*L::invCs2*qCdivRhoUU);
                }
            }
        }
    }
}

template<typename T, template<typename U> class Lattice, int direction, int orientation>
void ExtendedStraightFdBoundaryPostProcessor2D<T,Lattice,direction,orientation>::
    process(BlockLattice2D<T,Lattice>& blockLattice)
{
    processSubDomain(blockLattice, x0, x1, y0, y1);
}

template<typename T, template<typename U> class Lattice, int direction, int orientation>
template<int deriveDirection>
void ExtendedStraightFdBoundaryPostProcessor2D<T,Lattice,direction,orientation>::
    interpolateGradients(BlockLattice2D<T,Lattice> const& blockLattice,
                         T velDeriv[Lattice<T>::d], int iX, int iY) const
{
    fd::DirectedGradients2D<T, Lattice, direction, orientation, direction==deriveDirection>::
        interpolateVector(velDeriv, blockLattice, iX, iY);
}

template<typename T, template<typename U> class Lattice, int direction, int orientation>
template<int deriveDirection>
void ExtendedStraightFdBoundaryPostProcessor2D<T,Lattice,direction,orientation>::
    interpolateGradients(BlockLattice2D<T,Lattice> const& blockLattice, T& rhoDeriv, int iX, int iY) const
{
    fd::DirectedGradients2D<T, Lattice, direction, orientation, direction==deriveDirection>::
        interpolateScalar(rhoDeriv, blockLattice, iX, iY);