entropicdynamics.hh

open lattice boltzmann project www.openlb.org

/*  This file is part of the OpenLB library
 *
 *  Copyright (C) 2006, 2007 Orestis Malaspinas, Jonas Latt
 *  Address: EPFL-STI-LIN Station 9 1015 Lausanne
 *  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 -- generic implementation.
 */
#ifndef ENTROPIC_LB_DYNAMICS_HH
#define ENTROPIC_LB_DYNAMICS_HH

#include <algorithm>
#include <limits>
#include "core/lbHelpers.h"
#include "entropicDynamics.h"
#include "entropicLbHelpers.h"

namespace olb {

//==============================================================================//
/////////////////////////// Class EntropicDynamics ///////////////////////////////
//==============================================================================//
/** \param omega_ relaxation parameter, related to the dynamic viscosity
 *  \param momenta_ a Momenta object to know how to compute velocity momenta
 */
template<typename T, template<typename U> class Lattice>
EntropicDynamics<T,Lattice>::EntropicDynamics (
        T omega_, Momenta<T,Lattice>& momenta_ )
    : BasicDynamics<T,Lattice>(momenta_),
      omega(omega_)
{ }

template<typename T, template<typename U> class Lattice>
EntropicDynamics<T,Lattice>* EntropicDynamics<T,Lattice>::clone() const {
    return new EntropicDynamics<T,Lattice>(*this);
}

template<typename T, template<typename U> class Lattice>
T EntropicDynamics<T,Lattice>::computeEquilibrium(int iPop, T rho, const T u[Lattice<T>::d], T uSqr) const
{
    return entropicLbHelpers<T,Lattice>::equilibrium(iPop,rho,u);
}

template<typename T, template<typename U> class Lattice>
void EntropicDynamics<T,Lattice>::collide (
        Cell<T,Lattice>& cell,
        LatticeStatistics<T>& statistics )
{
    typedef Lattice<T> L;
    typedef entropicLbHelpers<T,Lattice> eLbH;
    
    T rho, u[Lattice<T>::d];
    this->momenta.computeRhoU(cell, rho, u);
    T uSqr = util::normSqr<T,L::d>(u);
    
    T f[L::q], fEq[L::q], fNeq[L::q];
    for (int iPop = 0; iPop < L::q; ++iPop)
    {
        fEq[iPop]  = eLbH::equilibrium(iPop,rho,u);
        fNeq[iPop] = cell[iPop] - fEq[iPop];
        f[iPop]    = cell[iPop] + L::t[iPop];
        fEq[iPop] += L::t[iPop];
    }
    //==============================================================================//
    //============= Evaluation of alpha using a Newton Raphson algorithm ===========//
    //==============================================================================//

    T alpha = 2.0;
    bool converged = getAlpha(alpha,f,fNeq);
    if (!converged)
    {
        std::cout << "Newton-Raphson failed to converge.\n";
        exit(1);
    }
    
    OLB_ASSERT(converged,"Entropy growth failed to converge!");
    
    T omegaTot = omega / 2.0 * alpha;
    for (int iPop=0; iPop < Lattice<T>::q; ++iPop) 
    {
        cell[iPop] *= (T)1-omegaTot;
        cell[iPop] += omegaTot * (fEq[iPop]-L::t[iPop]);
    }
    
    if (cell.takesStatistics()) {
        statistics.gatherStats(rho, uSqr);
    }
}

template<typename T, template<typename U> class Lattice>
void EntropicDynamics<T,Lattice>::staticCollide (
        Cell<T,Lattice>& cell,
        const T u[Lattice<T>::d],
        LatticeStatistics<T>& statistics )
{
    typedef Lattice<T> L;
    typedef entropicLbHelpers<T,Lattice> eLbH;
    
    T rho = this->momenta.computeRho(cell);
    T uSqr = util::normSqr<T,L::d>(u);
    
    T f[L::q], fEq[L::q], fNeq[L::q];
    for (int iPop = 0; iPop < L::q; ++iPop)
    {
        fEq[iPop]  = eLbH::equilibrium(iPop,rho,u);
        fNeq[iPop] = cell[iPop] - fEq[iPop];
        f[iPop]    = cell[iPop] + L::t[iPop];
        fEq[iPop] += L::t[iPop];
    }
    //==============================================================================//
    //============= Evaluation of alpha using a Newton Raphson algorithm ===========//
    //==============================================================================//

    T alpha = 2.0;
    bool converged = getAlpha(alpha,f,fNeq);
    if (!converged)
    {
        std::cout << "Newton-Raphson failed to converge.\n";
        exit(1);
    }
    
    OLB_ASSERT(converged,"Entropy growth failed to converge!");
    
    T omegaTot = omega / 2.0 * alpha;
    for (int iPop=0; iPop < Lattice<T>::q; ++iPop) 
    {
        cell[iPop] *= (T)1-omegaTot;
        cell[iPop] += omegaTot * (fEq[iPop]-L::t[iPop]);
    }
    
    if (cell.takesStatistics()) {
        statistics.gatherStats(rho, uSqr);
    }
}

template<typename T, template<typename U> class Lattice>
T EntropicDynamics<T,Lattice>::getOmega() const {
    return omega;
}

template<typename T, template<typename U> class Lattice>
void EntropicDynamics<T,Lattice>::setOmega(T omega_) {
    omega = omega_;
}

template<typename T, template<typename U> class Lattice>
T EntropicDynamics<T,Lattice>::computeEntropy(const T f[])
{
    typedef Lattice<T> L;
    T entropy = T();
    for (int iPop = 0; iPop < L::q; ++iPop)
    {
        OLB_ASSERT(f[iPop] > T(), "f[iPop] <= 0");
        entropy += f[iPop]*log(f[iPop]/L::t[iPop]);
    }

    return entropy;
}

template<typename T, template<typename U> class Lattice>
T EntropicDynamics<T,Lattice>::computeEntropyGrowth(const T f[], const T fNeq[], const T &alpha)
{
    typedef Lattice<T> L;
    
    T fAlphaFneq[L::q];
    for (int iPop = 0; iPop < L::q; ++iPop)
    {
        fAlphaFneq[iPop] = f[iPop] - alpha*fNeq[iPop];
    }

    return computeEntropy(f) - computeEntropy(fAlphaFneq);
}

template<typename T, template<typename U> class Lattice>
T EntropicDynamics<T,Lattice>::computeEntropyGrowthDerivative(const T f[], const T fNeq[], const T &alpha)
{
    typedef Lattice<T> L;
    
    T entropyGrowthDerivative = T();
    for (int iPop = 0; iPop < L::q; ++iPop)
    {
        T tmp = f[iPop] - alpha*fNeq[iPop];
        OLB_ASSERT(tmp > T(), "f[iPop] - alpha*fNeq[iPop] <= 0");
        entropyGrowthDerivative += fNeq[iPop]*(log(tmp/L::t[iPop]));
    }

    return entropyGrowthDerivative;
}

template<typename T, template<typename U> class Lattice>
bool EntropicDynamics<T,Lattice>::getAlpha(T &alpha, const T f[], const T fNeq[])
{
    const T epsilon = std::numeric_limits<T>::epsilon();

    T alphaGuess = T();
    const T var = 100.0;
    const T errorMax = epsilon*var;
    T error = 1.0;
    int count = 0;
    for (count = 0; count < 10000; ++count)
    {
        T entGrowth = computeEntropyGrowth(f,fNeq,alpha);
        T entGrowthDerivative = computeEntropyGrowthDerivative(f,fNeq,alpha);
        if ((error < errorMax) || (fabs(entGrowth) < var*epsilon))
        {
            return true;
        }
        alphaGuess = alpha - entGrowth /
                entGrowthDerivative;
        error = fabs(alpha-alphaGuess);
        alpha = alphaGuess;
    }
    return false;
}

//====================================================================//
//////////////////// Class ForcedEntropicDynamics //////////////////////
//====================================================================//

/** \param omega_ relaxation parameter, related to the dynamic viscosity
 */
template<typename T, template<typename U> class Lattice>
ForcedEntropicDynamics<T,Lattice>::ForcedEntropicDynamics (
        T omega_, Momenta<T,Lattice>& momenta_ )
    : BasicDynamics<T,Lattice>(momenta_),
      omega(omega_)
{ }

template<typename T, template<typename U> class Lattice>
ForcedEntropicDynamics<T,Lattice>* ForcedEntropicDynamics<T,Lattice>::clone() const {
    return new ForcedEntropicDynamics<T,Lattice>(*this);
}

template<typename T, template<typename U> class Lattice>
T ForcedEntropicDynamics<T,Lattice>::computeEquilibrium(int iPop, T rho, const T u[Lattice<T>::d], T uSqr) const
{
    return entropicLbHelpers<T,Lattice>::equilibrium(iPop,rho,u);
}


template<typename T, template<typename U> class Lattice>
void ForcedEntropicDynamics<T,Lattice>::collide (
        Cell<T,Lattice>& cell,
        LatticeStatistics<T>& statistics )
{
    typedef Lattice<T> L;
    typedef entropicLbHelpers<T,Lattice> eLbH;

    T rho, u[Lattice<T>::d];
    this->momenta.computeRhoU(cell, rho, u);
    T uSqr = util::normSqr<T,L::d>(u);

    T f[L::q], fEq[L::q], fNeq[L::q];
    for (int iPop = 0; iPop < L::q; ++iPop)
    {
        fEq[iPop]  = eLbH::equilibrium(iPop,rho,u);
        fNeq[iPop] = cell[iPop] - fEq[iPop];
        f[iPop]    = cell[iPop] + L::t[iPop];
        fEq[iPop] += L::t[iPop];
    }
    //==============================================================================//
    //============= Evaluation of alpha using a Newton Raphson algorithm ===========//
    //==============================================================================//

    T alpha = 2.0;
    bool converged = getAlpha(alpha,f,fNeq);
    if (!converged)
    {
        std::cout << "Newton-Raphson failed to converge.\n";
        exit(1);
    }

    OLB_ASSERT(converged,"Entropy growth failed to converge!");
    
    T* force = cell.getExternal(forceBeginsAt);
    for (int iDim=0; iDim<Lattice<T>::d; ++iDim)
    {
        u[iDim] += force[iDim] / (T)2.;
    }
    uSqr = util::normSqr<T,L::d>(u);
    T omegaTot = omega / 2.0 * alpha;
    for (int iPop=0; iPop < Lattice<T>::q; ++iPop) 
    {
        cell[iPop] *= (T)1-omegaTot;
        cell[iPop] += omegaTot * eLbH::equilibrium(iPop,rho,u);
    }
    lbHelpers<T,Lattice>::addExternalForce(cell, u, omegaTot);
    
    if (cell.takesStatistics())
    {
        statistics.gatherStats(rho, uSqr);
    }
}

template<typename T, template<typename U> class Lattice>
void ForcedEntropicDynamics<T,Lattice>::staticCollide (
        Cell<T,Lattice>& cell,
        const T u[Lattice<T>::d],
        LatticeStatistics<T>& statistics )
{
    typedef Lattice<T> L;
    typedef entropicLbHelpers<T,Lattice> eLbH;
    
    T rho;
    rho = this->momenta.computeRho(cell);
    T uSqr = util::normSqr<T,L::d>(u);
    
    T f[L::q], fEq[L::q], fNeq[L::q];
    for (int iPop = 0; iPop < L::q; ++iPop)
    {
        fEq[iPop]  = eLbH::equilibrium(iPop,rho,u);
        fNeq[iPop] = cell[iPop] - fEq[iPop];
        f[iPop]    = cell[iPop] + L::t[iPop];
        fEq[iPop] += L::t[iPop];
    }
    //==============================================================================//
    //============= Evaluation of alpha using a Newton Raphson algorithm ===========//
    //==============================================================================//

    T alpha = 2.0;
    bool converged = getAlpha(alpha,f,fNeq);
    if (!converged)
    {
        std::cout << "Newton-Raphson failed to converge.\n";
        exit(1);
    }
    
    OLB_ASSERT(converged,"Entropy growth failed to converge!");
    
    T omegaTot = omega / 2.0 * alpha;
    for (int iPop=0; iPop < Lattice<T>::q; ++iPop) 
    {
        cell[iPop] *= (T)1-omegaTot;
        cell[iPop] += omegaTot * (fEq[iPop]-L::t[iPop]);
    }
    lbHelpers<T,Lattice>::addExternalForce(cell, u, omegaTot);
    
    if (cell.takesStatistics()) {
        statistics.gatherStats(rho, uSqr);
    }
}

template<typename T, template<typename U> class Lattice>
T ForcedEntropicDynamics<T,Lattice>::getOmega() const {
    return omega;
}

template<typename T, template<typename U> class Lattice>
void ForcedEntropicDynamics<T,Lattice>::setOmega(T omega_) {
    omega = omega_;
}

template<typename T, template<typename U> class Lattice>
T ForcedEntropicDynamics<T,Lattice>::computeEntropy(const T f[])
{
    typedef Lattice<T> L;
    T entropy = T();
    for (int iPop = 0; iPop < L::q; ++iPop)
    {
        OLB_ASSERT(f[iPop] > T(), "f[iPop] <= 0");
        entropy += f[iPop]*log(f[iPop]/L::t[iPop]);
    }

    return entropy;
}

template<typename T, template<typename U> class Lattice>
T ForcedEntropicDynamics<T,Lattice>::computeEntropyGrowth(const T f[], const T fNeq[], const T &alpha)
{
    typedef Lattice<T> L;
    
    T fAlphaFneq[L::q];
    for (int iPop = 0; iPop < L::q; ++iPop)
    {
        fAlphaFneq[iPop] = f[iPop] - alpha*fNeq[iPop];
    }

    return computeEntropy(f) - computeEntropy(fAlphaFneq);
}

template<typename T, template<typename U> class Lattice>
T ForcedEntropicDynamics<T,Lattice>::computeEntropyGrowthDerivative(const T f[], const T fNeq[], const T &alpha)
{
    typedef Lattice<T> L;
    
    T entropyGrowthDerivative = T();
    for (int iPop = 0; iPop < L::q; ++iPop)
    {
        T tmp = f[iPop] - alpha*fNeq[iPop];
        OLB_ASSERT(tmp > T(), "f[iPop] - alpha*fNeq[iPop] <= 0");
        entropyGrowthDerivative += fNeq[iPop]*log(tmp/L::t[iPop]);
    }

    return entropyGrowthDerivative;
}

template<typename T, template<typename U> class Lattice>
bool ForcedEntropicDynamics<T,Lattice>::getAlpha(T &alpha, const T f[], const T fNeq[])
{
    const T epsilon = std::numeric_limits<T>::epsilon();

    T alphaGuess = T();
    const T var = 100.0;
    const T errorMax = epsilon*var;
    T error = 1.0;
    int count = 0;
    for (count = 0; count < 10000; ++count)
    {
        T entGrowth = computeEntropyGrowth(f,fNeq,alpha);
        T entGrowthDerivative = computeEntropyGrowthDerivative(f,fNeq,alpha);
        if ((error < errorMax) || (fabs(entGrowth) < var*epsilon))
        {
            return true;
        }
        alphaGuess = alpha - entGrowth /
                entGrowthDerivative;
        error = fabs(alpha-alphaGuess);
        alpha = alphaGuess;
    }
    return false;
}

}

#endif