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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
* Specialized helper functions for advanced techniques around LB
* implementations. They implement the physics of the first-order terms
* of the Chapman-Enskog expansion and are useful whenever a transition
* from hydrodynamical variables (rho, u) to kinetic variables (f) si to
* be implemented. Additionally, they are used for the implementation of
* the stable RLB dynamics.
*
* This file is all about efficiency. The generic
* template code is specialized for commonly used Lattices, so that a
* maximum performance can be taken out of each case.
*/
#ifndef FIRST_ORDER_LB_HELPERS_H
#define FIRST_ORDER_LB_HELPERS_H
#include "latticeDescriptors.h"
#include "core/cell.h"
#include "core/util.h"
#include "lbHelpers.h"
namespace olb {
/// General first-order functions
template<typename T, typename DESCRIPTOR>
struct firstOrderLbHelpers {
/// Compute off-equilibrium part of the f's from the stress tensor Pi.
/** Implements the following formula (with Einstein index contraction):
* \f[ f_i^{neq} = t_i / (2 c_s^4) *
* (c_{ia} c_{ib} - c_s^2 \delta_{ab}) \Pi_{ab} \f]
* By Pi we mean the tensor computed from the off-equilibrium functions:
* \f[ \Pi = \sum c_i c_i f_i^{neq}
* = \sum c_i c_i f_i - \rho u u - c_s^2 \rho\ Id \f]
*/
static T fromPiToFneq (
int iPop, const T pi[util::TensorVal<DESCRIPTOR >::n] )
{
typedef DESCRIPTOR L;
T fNeq = T();
int iPi = 0;
// Iterate only over superior triangle + diagonal, and add
// the elements under the diagonal by symmetry
for (int iAlpha=0; iAlpha<L::d; ++iAlpha) {
for (int iBeta=iAlpha; iBeta<L::d; ++iBeta) {
T toAdd = descriptors::c<L>(iPop,iAlpha)*descriptors::c<L>(iPop,iBeta);
if (iAlpha==iBeta) {
toAdd -= 1./descriptors::invCs2<T,L>();
} else {
toAdd *= (T)2; // multiply off-diagonal elements by 2
} // because the Q tensor is symmetric
toAdd *= pi[iPi++];
fNeq += toAdd;
}
}
fNeq *= descriptors::t<T,L>(iPop) * descriptors::invCs2<T,L>() * descriptors::invCs2<T,L>() / (T)2;
return fNeq;
}
static T fromJneqToFneq ( int iPop, const T jNeq[DESCRIPTOR::d] )
{
T fNeq = T();
for ( int iD = 0; iD < DESCRIPTOR::d; ++iD ) {
fNeq += descriptors::c<DESCRIPTOR>(iPop,iD) * jNeq[iD];
}
fNeq *= descriptors::t<T,DESCRIPTOR>(iPop) * descriptors::invCs2<T,DESCRIPTOR>();
return fNeq;
}
}; // struct firstOrderLbHelpers
/// Specific helper functions for RLB dynamics
template<typename T, typename DESCRIPTOR>
struct rlbHelpers {
/// Renormalized DESCRIPTOR Boltzmann collision operator, fIn --> fOut
static T rlbCollision (
Cell<T,DESCRIPTOR>& cell, T rho, const T u[DESCRIPTOR::d],
const T pi[util::TensorVal<DESCRIPTOR >::n], T omega )
{
typedef DESCRIPTOR L;
const T uSqr = util::normSqr<T,L::d>(u);
cell[0] = lbHelpers<T,DESCRIPTOR>::equilibrium(0, rho, u, uSqr)
+ ((T)1-omega) *
firstOrderLbHelpers<T,DESCRIPTOR>::fromPiToFneq(0, pi);
for (int iPop=1; iPop<=L::q/2; ++iPop) {
cell[iPop] =
lbHelpers<T,DESCRIPTOR>::equilibrium(iPop, rho, u, uSqr);
cell[iPop+L::q/2] =
lbHelpers<T,DESCRIPTOR>::equilibrium(iPop+L::q/2, rho, u, uSqr);
T fNeq = ((T)1-omega) *
firstOrderLbHelpers<T,DESCRIPTOR>::fromPiToFneq(iPop, pi);
cell[iPop] += fNeq;
cell[iPop+L::q/2] += fNeq;
}
return uSqr;
}
}; // struct rlbHelpers
} // namespace olb
// The specialized code is directly included. That is because we never want
// it to be precompiled so that in both the precompiled and the
// "include-everything" version, the compiler can apply all the
// optimizations it wants.
#include "firstOrderLbHelpers2D.h"
#include "firstOrderLbHelpers3D.h"
#endif
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