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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.
*/
/** \file
* A collection of dynamics classes (e.g. BGK) with which a Cell object
* can be instantiated -- header file.
*/
#ifndef ENTROPIC_LB_HELPERS_3D_H
#define ENTROPIC_LB_HELPERS_3D_H
#include <cmath>
namespace olb {
template<typename T>
struct entropicLbHelpers<T, descriptors::D3Q19<>> {
/// Computation of equilibrium distribution with an expansion
/// with respect to a small velocity u
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
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