entropicLbHelpers3D.h

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/*  This file is part of the OpenLB library
 *
 *  Copyright (C) 2006, 2007 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 ENTROPIC_LB_HELPERS_3D_H
#define ENTROPIC_LB_HELPERS_3D_H
 
#include "utilities/omath.h"
 
namespace olb {
 
template<typename T>
struct entropicLbHelpers<T, descriptors::D3Q19<>> {
  static T equilibrium( int iPop, T rho, const T u[3])
  {
    typedef descriptors::D3Q19<> L;
 
    T c_u = descriptors::c<L>(iPop,0)*u[0] + descriptors::c<L>(iPop,1)*u[1] + descriptors::c<L>(iPop,2)*u[2];;
    T c_u2 = c_u*c_u;
    T c_u3 = c_u2*c_u;
    T c_u4 = c_u3*c_u;
    T c_u5 = c_u4*c_u;
    T c_u6 = c_u5*c_u;
    T c_u7 = c_u6*c_u;
 
    T uSqr = u[0]*u[0] + u[1]*u[1] + u[2]*u[2];
    T uSqr2 = uSqr*uSqr;
    T uSqr3 = uSqr2*uSqr;
 
    T powUx = u[0]*u[0]*u[0]*u[0]*u[0]; // u_x^5
    T powUy = u[1]*u[1]*u[1]*u[1]*u[1]; // u_y^5
    T powUz = u[2]*u[2]*u[2]*u[2]*u[2]; // u_z^5
 
    T C = descriptors::c<L>(iPop,0) * powUx + descriptors::c<L>(iPop,1) * powUy
          + descriptors::c<L>(iPop,2) * powUz;
 
    powUx *= u[0]; // u_x^6
    powUy *= u[1]; // u_y^6
    powUz *= u[2]; // u_z^6
 
    T E = powUx + powUy + powUz;
 
    powUx *= u[0]; // u_x^7
    powUy *= u[1]; // u_y^7
    powUz *= u[2]; // u_z^7
 
    T F = descriptors::c<L>(iPop,0) * powUx + descriptors::c<L>(iPop,1) * powUy + descriptors::c<L>(iPop,2) * powUz;
 
    return descriptors::t<T,L>(iPop) * rho *
           ((T)1
            + c_u*(C*(T)81/(T)20 + uSqr2*(T)27/(T)8 - uSqr*(T)9/(T)2
                   - E*(T)81/(T)24 - uSqr3*(T)81/(T)48 + (T)3)
 
            + c_u2*(uSqr2*(T)81/(T)16 - uSqr*(T)27/(T)4
                    + C*(T)243/(T)40 + (T)9/(T)2)
 
            + c_u3*(uSqr2*(T)243/(T)48 - uSqr*(T)81/(T)12 + (T)27/(T)6)
 
            - c_u4*uSqr*(T)243/(T)48
            + c_u4*(T)81/(T)24
 
            - c_u5*uSqr*(T)729/(T)240
            + c_u5*(T)243/(T)120
 
            + c_u6*(T)729/(T)720
 
            + c_u7*(T)2187/(T)5040
 
            - C*uSqr*(T)81/(T)40
 
            + C*(T)27/(T)20 - uSqr3*(T)27/(T)48 - E*(T)27/(T)24
            - F*(T)81/(T)56 - uSqr*(T)3/(T)2 + uSqr2*(T)9/(T)8
           )
           - descriptors::t<T,L>(iPop);
  }
 
};
 
}
 
#endif