entropiclbhelpers.h

open lattice boltzmann project www.openlb.org

/*  This file is part of the OpenLB library
 *
 *  Copyright (C) 2006, 2007 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.
*/

/** \file
 * A collection of dynamics classes (e.g. BGK) with which a Cell object
 * can be instantiated -- header file.
 */
#ifndef ENTROPIC_LB_HELPERS_H
#define ENTROPIC_LB_HELPERS_H

#include <cmath>

namespace olb {

template<typename T, template<typename U> class Lattice>
struct entropicLbHelpers 
{
    /// Computation of equilibrium distribution
    static T equilibrium( int iPop, T rho, const T u[Lattice<T>::d])
    {
        typedef Lattice<T> L;
        const T invCs = sqrt(L::invCs2);
        const T sqt3 = sqrt(3.0);
        T prod = (T)1;
        for (int iD=0; iD < Lattice<T>::d; ++iD)
        {
            T uc = u[iD] * invCs; // u[iD] / c_s

            prod *= ((T)2 - sqrt(1.0+uc*uc)) * 
                    pow((2.0 / sqt3 * uc + 
                    sqrt(1.0+uc*uc))/(1.0-uc/sqt3),
                        L::c[iPop][iD]/sqt3*invCs);
        }
        return rho*L::t[iPop]*prod-L::t[iPop];
    }
    
    /// Computation of equilibrium distribution
    static T equilibriumApprox( int iPop, T rho, const T u[Lattice<T>::d])
    {
        typedef Lattice<T> L;

        T uSqr = util::normSqr<T,L::d>(u);
        T cu = T();
        for (int iD=0; iD < Lattice<T>::d; ++iD)
        {
            cu += L::c[iPop][iD]*u[iD];
        }
        
        return rho * L::t[iPop] * (1.0 +
                cu*L::invCs2 - 0.5 * uSqr*L::invCs2 + 0.5*pow(L::invCs2,2)*cu*cu
                - 0.5*pow(L::invCs2,2)*cu*uSqr + pow(cu,3)*pow(L::invCs2,3)/6.0
                + 0.125*uSqr*uSqr*pow(L::invCs2,2) - 0.25*cu*cu*uSqr*pow(L::invCs2,3)
                + pow(cu,4)*pow(L::invCs2,4)/24.0)-L::t[iPop];
    }
};

}

#include "entropicLbHelpers2D.h"
#include "entropicLbHelpers3D.h"

#endif