inamuroAnalyticalDynamics.hh

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/* This file is part of the Palabos library.
 *
 * Copyright (C) 2011 FlowKit Sarl
 * Avenue de Chailly 23
 * 1012 Lausanne, Switzerland
 * E-mail contact: contact@flowkit.com
 *
 * The most recent release of Palabos can be downloaded at 
 * <http://www.palabos.org/>
 *
 * The library Palabos is free software: you can redistribute it and/or
 * modify it under the terms of the GNU Affero General Public License as
 * published by the Free Software Foundation, either version 3 of the
 * License, or (at your option) any later version.
 *
 * The library 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 Affero General Public License for more details.
 *
 * You should have received a copy of the GNU Affero General Public License
 * along with this program.  If not, see <http://www.gnu.org/licenses/>.
*/

/* Orestis Malaspinas contributed this code.
 */

#ifndef INAMURO_ANALYTICAL_DYNAMICS_HH
#define INAMURO_ANALYTICAL_DYNAMICS_HH

#include "boundaryCondition/inamuroAnalyticalDynamics.h"
#include "latticeBoltzmann/indexTemplates.h"
#include "core/util.h"
#include "core/latticeStatistics.h"
#include "core/dynamicsIdentifiers.h"
#include <cmath>

namespace plb {

template<typename T, template<typename U> class Descriptor, int direction, int orientation>
void InamuroAnalyticalClosure ( Cell<T,Descriptor>& cell, Dynamics<T,Descriptor> const& dynamics )
{
    typedef Descriptor<T> L;

    // Along all the commented parts of this code there will be an example based
    // on the situation where the wall's normal vector if (0,1) and the
    // numerotation of the velocites are done according to the D2Q9 
    // lattice of the OpenLB library.

    // Find all the missing populations
    // (directions 3,4,5)
    std::vector<plint> missInd = 
            indexTemplates::subIndexOutgoing<L,direction,orientation>();

    // Will contain the missing poputations that are not normal to the wall.
    // (directions 3,5)
    std::vector<plint> missDiagInd = missInd;

    for (pluint iPop = 0; iPop < missInd.size(); ++iPop)
    {
        plint numOfNonNullComp = 0;
        for (int iDim = 0; iDim < L:: d; ++iDim)
            numOfNonNullComp += abs(L::c[missInd[iPop]][iDim]);

        if (numOfNonNullComp == 1)
        {
            missDiagInd.erase(missDiagInd.begin()+iPop);
            break;
        }
    }

    // Will contain the populations normal to the wall's normal vector.
    // (directions 2,6)
    std::vector<plint> perpInd = indexTemplates::subIndex<L,direction,0>();
    for (pluint iPop = 0; iPop < perpInd.size(); ++iPop)
    {
        if (L::c[perpInd[iPop]][0] == 0 && L::c[perpInd[iPop]][1] == 0)
        {
            perpInd.erase(perpInd.begin() + iPop);
            break;
        }
    }

    T rho = dynamics.computeDensity(cell);
    Array<T,L::d> u;
    dynamics.computeVelocity(cell, u);

    T rhoCs = T();
    Array<T,L::d> jCs;
    for (int iDim = 0; iDim < L::d; ++iDim)
        jCs[iDim] = T();

    T fSum = T();
    for (pluint iPop = 0; iPop < missInd.size(); ++iPop)
    {
        fSum += cell[indexTemplates::opposite<L>(missInd[iPop])];
    }
    // do not forget the "+1" in the rhoCs equation in the numerator (it's
    // here because fEq = usualfEq - t[i])
    rhoCs = ((T)6 * (-orientation * rho * u[direction] + fSum) + (T)1) /
        ((T)3 * u[direction] * u[direction] - orientation * (T)3 * u[direction] + (T)1);

    T fDiffPerp = T();
    for (pluint iPop = 0; iPop < perpInd.size(); ++iPop)
       fDiffPerp += L::c[perpInd[iPop]][(direction + 1)%2] * cell[perpInd[iPop]];
    fDiffPerp *= orientation;

    T fDiffDiag = T();
    for (pluint iPop = 0; iPop < missDiagInd.size(); ++iPop)
        fDiffDiag += L::c[indexTemplates::opposite<L>(missDiagInd[iPop])][(direction + 1)%2]
                    * cell[indexTemplates::opposite<L>(missDiagInd[iPop])];
    fDiffDiag *= orientation;

    jCs[(direction + 1)%L::d] = (
            - orientation * (T)6 * rho * u[(direction+1)%L::d]
            + orientation * rhoCs * u[(direction+1)%L::d]
            - (T)3 * rhoCs * u[direction]*u[(direction+1)%L::d]
            + (T)6*(fDiffPerp + fDiffDiag))
            / ( -orientation + (T)3 * u[direction] );

    for (int iDim = 0; iDim < L::d; ++iDim)
        jCs[iDim] += rhoCs*u[iDim];

    T jSqr = VectorTemplate<T,Descriptor>::normSqr(jCs);

    for (pluint iPop = 0; iPop < missInd.size(); ++iPop) {
        cell[missInd[iPop]] = dynamics.computeEquilibrium (
                missInd[iPop], Descriptor<T>::rhoBar(rhoCs), jCs, jSqr );
    }
}

template<typename T, template<typename U> class Descriptor,
         int direction, int orientation>
int InamuroAnalyticalVelocityDynamics<T,Descriptor,direction,orientation>::id =
    meta::registerCompositeDynamics<T,Descriptor, InamuroAnalyticalVelocityDynamics<T,Descriptor,direction,orientation> >
            ( std::string("Boundary_InamuroAnalytical_")+util::val2str(direction) +
              std::string("_")+util::val2str(orientation) );

template<typename T, template<typename U> class Descriptor, int direction, int orientation>
InamuroAnalyticalVelocityDynamics<T,Descriptor,direction,orientation>::InamuroAnalyticalVelocityDynamics (
        Dynamics<T,Descriptor>* baseDynamics, bool automaticPrepareCollision )
    : VelocityDirichletBoundaryDynamics<T,Descriptor,direction,orientation>(baseDynamics,automaticPrepareCollision)
{ }

template<typename T, template<typename U> class Descriptor, int direction, int orientation>
InamuroAnalyticalVelocityDynamics<T,Descriptor,direction,orientation>*
    InamuroAnalyticalVelocityDynamics<T,Descriptor, direction, orientation>::clone() const
{
    return new InamuroAnalyticalVelocityDynamics<T,Descriptor,direction,orientation>(*this);
}
 
template<typename T, template<typename U> class Descriptor,
         int direction, int orientation>
int InamuroAnalyticalVelocityDynamics<T,Descriptor,direction,orientation>::getId() const {
    return id;
}

template<typename T, template<typename U> class Descriptor, int direction, int orientation>
void InamuroAnalyticalVelocityDynamics<T,Descriptor,direction,orientation>::completePopulations (
        Cell<T,Descriptor>& cell ) const
{
    InamuroAnalyticalClosure<T,Descriptor,direction,orientation>(cell, *this);
}


template<typename T, template<typename U> class Descriptor,
         int direction, int orientation>
int InamuroAnalyticalPressureDynamics<T,Descriptor,direction,orientation>::id =
    meta::registerCompositeDynamics<T,Descriptor, InamuroAnalyticalPressureDynamics<T,Descriptor,direction,orientation> >
            ( std::string("Boundary_InamuroAnalyticalPressure_")+util::val2str(direction) +
              std::string("_")+util::val2str(orientation) );

template<typename T, template<typename U> class Descriptor, int direction, int orientation>
InamuroAnalyticalPressureDynamics<T,Descriptor,direction,orientation>::InamuroAnalyticalPressureDynamics (
        Dynamics<T,Descriptor>* baseDynamics, bool automaticPrepareCollision )
    : DensityDirichletBoundaryDynamics<T,Descriptor,direction,orientation>(baseDynamics,automaticPrepareCollision)
{ }

template<typename T, template<typename U> class Descriptor, int direction, int orientation>
InamuroAnalyticalPressureDynamics<T,Descriptor,direction,orientation>*
    InamuroAnalyticalPressureDynamics<T,Descriptor, direction, orientation>::clone() const
{
    return new InamuroAnalyticalPressureDynamics<T,Descriptor,direction,orientation>(*this);
}
 
template<typename T, template<typename U> class Descriptor,
         int direction, int orientation>
int InamuroAnalyticalPressureDynamics<T,Descriptor,direction,orientation>::getId() const {
    return id;
}

template<typename T, template<typename U> class Descriptor, int direction, int orientation>
void InamuroAnalyticalPressureDynamics<T,Descriptor,direction,orientation>::completePopulations (
        Cell<T,Descriptor>& cell ) const
{
    InamuroAnalyticalClosure<T,Descriptor,direction,orientation>(cell, *this);
}

}  // namespace plb


#endif  // INAMURO_ANALYTICAL_DYNAMICS_HH