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Anna Wellmann authoredAnna Wellmann authored
CumulantChimera.cpp 26.09 KiB
#include "CumulantChimera.h"
#include <cmath>
#include <basics/Core/DataTypes.h>
#include <basics/Core/RealConstants.h>
#include "constants/NumericConstants.h"
#include "constants/D3Q27.h"
#include "Chimera.h"
#include "MacroscopicQuantities.h"
namespace vf
{
namespace lbm
{
using namespace constant;
////////////////////////////////////////////////////////////////////////////////////
//! - Setting relaxation rates for non-hydrodynamic cumulants (default values). Variable names and equations according to
//! <a href="https://doi.org/10.1016/j.jcp.2017.05.040"><b>[ M. Geier et al. (2017), DOI:10.1016/j.jcp.2017.05 040 ]</b></a>
//! => [NAME IN PAPER]=[NAME IN CODE]=[DEFAULT VALUE].
//! - Trace of second order cumulants \f$ C_{200}+C_{020}+C_{002} \f$ used to adjust bulk viscosity:\f$\omega_2=OxxPyyPzz=1.0 \f$.
//! - Third order cumulants \f$ C_{120}+C_{102}, C_{210}+C_{012}, C_{201}+C_{021} \f$: \f$ \omega_3=OxyyPxzz \f$ set according to Eq. (111) with simplifications assuming \f$ \omega_2=1.0\f$.
//! - Third order cumulants \f$ C_{120}-C_{102}, C_{210}-C_{012}, C_{201}-C_{021} \f$: \f$ \omega_4 = OxyyMxzz \f$ set according to Eq. (112) with simplifications assuming \f$ \omega_2 = 1.0\f$.
//! - Third order cumulants \f$ C_{111} \f$: \f$ \omega_5 = Oxyz \f$ set according to Eq. (113) with simplifications assuming \f$ \omega_2 = 1.0\f$ (modify for different bulk viscosity).
//! - Fourth order cumulants \f$ C_{220}, C_{202}, C_{022}, C_{211}, C_{121}, C_{112} \f$: for simplification all set to the same default value \f$ \omega_6=\omega_7=\omega_8=O4=1.0 \f$.
//! - Fifth order cumulants \f$ C_{221}, C_{212}, C_{122}\f$: \f$\omega_9=O5=1.0\f$.
//! - Sixth order cumulant \f$ C_{222}\f$: \f$\omega_{10}=O6=1.0\f$.
//////////////////////////////////////////////////////////////////////////
__host__ __device__ void setRelaxationRatesK17(real omega, real &OxxPyyPzz, real &OxyyPxzz, real &OxyyMxzz, real &Oxyz,
real &O4, real &O5, real &O6)
{
OxxPyyPzz = c1o1;
OxyyPxzz = c8o1 * (-c2o1 + omega) * (c1o1 + c2o1 * omega) / (-c8o1 - c14o1 * omega + c7o1 * omega * omega);
OxyyMxzz = c8o1 * (-c2o1 + omega) * (-c7o1 + c4o1 * omega) / (c56o1 - c50o1 * omega + c9o1 * omega * omega);
Oxyz = c24o1 * (-c2o1 + omega) * (-c2o1 - c7o1 * omega + c3o1 * omega * omega) /
(c48o1 + c152o1 * omega - c130o1 * omega * omega + c29o1 * omega * omega * omega);
O4 = c1o1;
O5 = c1o1;
O6 = c1o1;
}
__host__ __device__ void setRelaxationRatesK15(real omega, real &OxxPyyPzz, real &OxyyPxzz, real &OxyyMxzz, real &Oxyz,
real &O4, real &O5, real &O6)
{
OxxPyyPzz = c1o1;
OxyyPxzz = c1o1;
OxyyMxzz = c1o1;
Oxyz = c1o1;
O4 = c1o1;
O5 = c1o1;
O6 = c1o1;
}
//////////////////////////////////////////////////////////////////////////
//! Cumulant K17 Kernel is based on \ref
//! <a href="https://doi.org/10.1016/j.jcp.2017.05.040"><b>[ M. Geier et al. (2017), DOI:10.1016/j.jcp.2017.05.040 ]</b></a>//! and \ref
//! <a href="https://doi.org/10.1016/j.jcp.2017.07.004"><b>[ M. Geier et al. (2017), DOI:10.1016/j.jcp.2017.07.004 ]</b></a>
//////////////////////////////////////////////////////////////////////////
__host__ __device__ void cumulantChimera(KernelParameter parameter, RelaxationRatesFunctor setRelaxationRates)
{
auto& distribution = parameter.distribution;
const auto omega = parameter.omega;
const auto* forces = parameter.forces;
////////////////////////////////////////////////////////////////////////////////////
//! - Read distributions: style of reading and writing the distributions from/to
//! stored arrays dependent on timestep is based on the esoteric twist algorithm
//! <a href="https://doi.org/10.3390/computation5020019"><b>[ M. Geier et al. (2017), DOI:10.3390/computation5020019 ]</b></a>
//!
real mfcbb = distribution.f[dir::PZZ];
real mfabb = distribution.f[dir::MZZ];
real mfbcb = distribution.f[dir::ZPZ];
real mfbab = distribution.f[dir::ZMZ];
real mfbbc = distribution.f[dir::ZZP];
real mfbba = distribution.f[dir::ZZM];
real mfccb = distribution.f[dir::PPZ];
real mfaab = distribution.f[dir::MMZ];
real mfcab = distribution.f[dir::PMZ];
real mfacb = distribution.f[dir::MPZ];
real mfcbc = distribution.f[dir::PZP];
real mfaba = distribution.f[dir::MZM];
real mfcba = distribution.f[dir::PZM];
real mfabc = distribution.f[dir::MZP];
real mfbcc = distribution.f[dir::ZPP];
real mfbaa = distribution.f[dir::ZMM];
real mfbca = distribution.f[dir::ZPM];
real mfbac = distribution.f[dir::ZMP];
real mfccc = distribution.f[dir::PPP];
real mfacc = distribution.f[dir::MPP];
real mfcac = distribution.f[dir::PMP];
real mfaac = distribution.f[dir::MMP];
real mfcca = distribution.f[dir::PPM];
real mfaca = distribution.f[dir::MPM];
real mfcaa = distribution.f[dir::PMM];
real mfaaa = distribution.f[dir::MMM];
real mfbbb = distribution.f[dir::ZZZ];
const real drho = getDensity(distribution.f);
const real OOrho = c1o1 / (c1o1 + drho);
////////////////////////////////////////////////////////////////////////////////////
//! - Add half of the acceleration (body force) to the velocity as in Eq. (42) \ref
//! <a href="https://doi.org/10.1016/j.camwa.2015.05.001"><b>[ M. Geier et al. (2015), DOI:10.1016/j.camwa 2015.05.001 ]</b></a>
//!
const real vvx = getIncompressibleVelocityX1(distribution.f) * OOrho + forces[0] * c1o2;
const real vvy = getIncompressibleVelocityX2(distribution.f) * OOrho + forces[0] * c1o2;
const real vvz = getIncompressibleVelocityX3(distribution.f) * OOrho + forces[0] * c1o2;
////////////////////////////////////////////////////////////////////////////////////
// calculate the square of velocities for this lattice node
const real vx2 = vvx*vvx;
const real vy2 = vvy*vvy;
const real vz2 = vvz*vvz;
////////////////////////////////////////////////////////////////////////////////////
//! - Chimera transform from well conditioned distributions to central moments as defined in Appendix J in \ref
//! <a href="https://doi.org/10.1016/j.camwa.2015.05.001"><b>[ M. Geier et al. (2015), DOI:10.1016/j.camwa 2015.05.001 ]</b></a>
//! see also Eq. (6)-(14) in \ref
//! <a href="https://doi.org/10.1016/j.jcp.2017.05.040"><b>[ M. Geier et al. (2017), DOI:10.1016/j.jcp.2017.05 040 ]</b></a>
//!
////////////////////////////////////////////////////////////////////////////////////
// Z - Dir
vf::lbm::forwardInverseChimeraWithK(mfaaa, mfaab, mfaac, vvz, vz2, c36o1, c1o36);
vf::lbm::forwardInverseChimeraWithK(mfaba, mfabb, mfabc, vvz, vz2, c9o1, c1o9); vf::lbm::forwardInverseChimeraWithK(mfaca, mfacb, mfacc, vvz, vz2, c36o1, c1o36);
vf::lbm::forwardInverseChimeraWithK(mfbaa, mfbab, mfbac, vvz, vz2, c9o1, c1o9);
vf::lbm::forwardInverseChimeraWithK(mfbba, mfbbb, mfbbc, vvz, vz2, c9o4, c4o9);
vf::lbm::forwardInverseChimeraWithK(mfbca, mfbcb, mfbcc, vvz, vz2, c9o1, c1o9);
vf::lbm::forwardInverseChimeraWithK(mfcaa, mfcab, mfcac, vvz, vz2, c36o1, c1o36);
vf::lbm::forwardInverseChimeraWithK(mfcba, mfcbb, mfcbc, vvz, vz2, c9o1, c1o9);
vf::lbm::forwardInverseChimeraWithK(mfcca, mfccb, mfccc, vvz, vz2, c36o1, c1o36);
////////////////////////////////////////////////////////////////////////////////////
// Y - Dir
vf::lbm::forwardInverseChimeraWithK(mfaaa, mfaba, mfaca, vvy, vy2, c6o1, c1o6);
vf::lbm::forwardChimera( mfaab, mfabb, mfacb, vvy, vy2);
vf::lbm::forwardInverseChimeraWithK(mfaac, mfabc, mfacc, vvy, vy2, c18o1, c1o18);
vf::lbm::forwardInverseChimeraWithK(mfbaa, mfbba, mfbca, vvy, vy2, c3o2, c2o3);
vf::lbm::forwardChimera( mfbab, mfbbb, mfbcb, vvy, vy2);
vf::lbm::forwardInverseChimeraWithK(mfbac, mfbbc, mfbcc, vvy, vy2, c9o2, c2o9);
vf::lbm::forwardInverseChimeraWithK(mfcaa, mfcba, mfcca, vvy, vy2, c6o1, c1o6);
vf::lbm::forwardChimera( mfcab, mfcbb, mfccb, vvy, vy2);
vf::lbm::forwardInverseChimeraWithK(mfcac, mfcbc, mfccc, vvy, vy2, c18o1, c1o18);
////////////////////////////////////////////////////////////////////////////////////
// X - Dir
vf::lbm::forwardInverseChimeraWithK(mfaaa, mfbaa, mfcaa, vvx, vx2, c1o1, c1o1);
vf::lbm::forwardChimera( mfaba, mfbba, mfcba, vvx, vx2);
vf::lbm::forwardInverseChimeraWithK(mfaca, mfbca, mfcca, vvx, vx2, c3o1, c1o3);
vf::lbm::forwardChimera( mfaab, mfbab, mfcab, vvx, vx2);
vf::lbm::forwardChimera( mfabb, mfbbb, mfcbb, vvx, vx2);
vf::lbm::forwardChimera( mfacb, mfbcb, mfccb, vvx, vx2);
vf::lbm::forwardInverseChimeraWithK(mfaac, mfbac, mfcac, vvx, vx2, c3o1, c1o3);
vf::lbm::forwardChimera( mfabc, mfbbc, mfcbc, vvx, vx2);
vf::lbm::forwardInverseChimeraWithK(mfacc, mfbcc, mfccc, vvx, vx2, c3o1, c1o9);
////////////////////////////////////////////////////////////////////////////////////
//! - Setting relaxation rates for non-hydrodynamic cumulants (default values). Variable names and equations
real OxxPyyPzz;
real OxyyPxzz;
real OxyyMxzz;
real Oxyz;
real O4;
real O5;
real O6;
setRelaxationRates(omega, OxxPyyPzz, OxyyPxzz, OxyyMxzz, Oxyz, O4, O5, O6);
////////////////////////////////////////////////////////////////////////////////////
//! - A and B: parameters for fourth order convergence of the diffusion term according to Eq. (115) and (116)
//! <a href="https://doi.org/10.1016/j.jcp.2017.05.040"><b>[ M. Geier et al. (2017), DOI:10.1016/j.jcp.2017.05 040 ]</b></a>
//! with simplifications assuming \f$ \omega_2 = 1.0 \f$ (modify for different bulk viscosity).
//!
const real A = (c4o1 + c2o1*omega - c3o1*omega*omega) / (c2o1 - c7o1*omega + c5o1*omega*omega);
const real B = (c4o1 + c28o1*omega - c14o1*omega*omega) / (c6o1 - c21o1*omega + c15o1*omega*omega);
////////////////////////////////////////////////////////////////////////////////////
//! - Compute cumulants from central moments according to Eq. (20)-(23) in
//! <a href="https://doi.org/10.1016/j.jcp.2017.05.040"><b>[ M. Geier et al. (2017), DOI:10.1016/j.jcp.2017.05 040 ]</b></a>
//!
////////////////////////////////////////////////////////////
//4.
real CUMcbb = mfcbb - ((mfcaa + c1o3) * mfabb + c2o1 * mfbba * mfbab) * OOrho;
real CUMbcb = mfbcb - ((mfaca + c1o3) * mfbab + c2o1 * mfbba * mfabb) * OOrho;
real CUMbbc = mfbbc - ((mfaac + c1o3) * mfbba + c2o1 * mfbab * mfabb) * OOrho;
real CUMcca = mfcca - (((mfcaa * mfaca + c2o1 * mfbba * mfbba) + c1o3 * (mfcaa + mfaca)) * OOrho - c1o9*(drho * OOrho));
real CUMcac = mfcac - (((mfcaa * mfaac + c2o1 * mfbab * mfbab) + c1o3 * (mfcaa + mfaac)) * OOrho - c1o9*(drho * OOrho));
real CUMacc = mfacc - (((mfaac * mfaca + c2o1 * mfabb * mfabb) + c1o3 * (mfaac + mfaca)) * OOrho - c1o9*(drho * OOrho));
////////////////////////////////////////////////////////////
//5.
real CUMbcc = mfbcc - ((mfaac * mfbca + mfaca * mfbac + c4o1 * mfabb * mfbbb + c2o1 * (mfbab * mfacb + mfbba * mfabc)) + c1o3 * (mfbca + mfbac)) * OOrho;
real CUMcbc = mfcbc - ((mfaac * mfcba + mfcaa * mfabc + c4o1 * mfbab * mfbbb + c2o1 * (mfabb * mfcab + mfbba * mfbac)) + c1o3 * (mfcba + mfabc)) * OOrho;
real CUMccb = mfccb - ((mfcaa * mfacb + mfaca * mfcab + c4o1 * mfbba * mfbbb + c2o1 * (mfbab * mfbca + mfabb * mfcba)) + c1o3 * (mfacb + mfcab)) * OOrho;
////////////////////////////////////////////////////////////
//6.
real CUMccc = mfccc + ((-c4o1 * mfbbb * mfbbb
- (mfcaa * mfacc + mfaca * mfcac + mfaac * mfcca) - c4o1 * (mfabb * mfcbb + mfbab * mfbcb + mfbba * mfbbc)
- c2o1 * (mfbca * mfbac + mfcba * mfabc + mfcab * mfacb)) * OOrho
+ (c4o1 * (mfbab * mfbab * mfaca + mfabb * mfabb * mfcaa + mfbba * mfbba * mfaac)
+ c2o1 * (mfcaa * mfaca * mfaac)
+ c16o1 * mfbba * mfbab * mfabb) * OOrho * OOrho
- c1o3 * (mfacc + mfcac + mfcca) * OOrho
- c1o9 * (mfcaa + mfaca + mfaac) * OOrho
+ (c2o1 * (mfbab * mfbab + mfabb * mfabb + mfbba * mfbba)
+ (mfaac * mfaca + mfaac * mfcaa + mfaca * mfcaa) + c1o3 *(mfaac + mfaca + mfcaa)) * OOrho * OOrho * c2o3
+ c1o27*((drho * drho - drho) * OOrho * OOrho));
////////////////////////////////////////////////////////////////////////////////////
//! - Compute linear combinations of second and third order cumulants
//!
////////////////////////////////////////////////////////////
//2.
real mxxPyyPzz = mfcaa + mfaca + mfaac;
real mxxMyy = mfcaa - mfaca;
real mxxMzz = mfcaa - mfaac;
////////////////////////////////////////////////////////////
//3.
real mxxyPyzz = mfcba + mfabc;
real mxxyMyzz = mfcba - mfabc;
real mxxzPyyz = mfcab + mfacb;
real mxxzMyyz = mfcab - mfacb;
real mxyyPxzz = mfbca + mfbac;
real mxyyMxzz = mfbca - mfbac;
////////////////////////////////////////////////////////////////////////////////////
//incl. correction
////////////////////////////////////////////////////////////
//! - Compute velocity gradients from second order cumulants according to Eq. (27)-(32)
//! <a href="https://doi.org/10.1016/j.jcp.2017.05.040"><b>[ M. Geier et al. (2017), DOI:10.1016/j.jcp.2017.05 040 ]</b></a>
//! Further explanations of the correction in viscosity in Appendix H of
//! <a href="https://doi.org/10.1016/j.camwa.2015.05.001"><b>[ M. Geier et al. (2015), DOI:10.1016/j.camwa 2015.05.001 ]</b></a>
//! Note that the division by rho is omitted here as we need rho times the gradients later.
//!
const real Dxy = -c3o1*omega*mfbba;
const real Dxz = -c3o1*omega*mfbab;
const real Dyz = -c3o1*omega*mfabb;
const real dxux = c1o2 * (-omega) *(mxxMyy + mxxMzz) + c1o2 * OxxPyyPzz * (mfaaa - mxxPyyPzz);
const real dyuy = dxux + omega * c3o2 * mxxMyy;
const real dzuz = dxux + omega * c3o2 * mxxMzz;
////////////////////////////////////////////////////////////
//! - Relaxation of second order cumulants with correction terms according to Eq. (33)-(35) in
//! <a href="https://doi.org/10.1016/j.jcp.2017.05.040"><b>[ M. Geier et al. (2017), DOI:10.1016/j.jcp.2017.05 040 ]</b></a>
//!
mxxPyyPzz += OxxPyyPzz*(mfaaa - mxxPyyPzz) - c3o1 * (c1o1 - c1o2 * OxxPyyPzz) * (vx2 * dxux + vy2 * dyuy + vz2 * dzuz);
mxxMyy += omega * (-mxxMyy) - c3o1 * (c1o1 + c1o2 * (-omega)) * (vx2 * dxux - vy2 * dyuy);
mxxMzz += omega * (-mxxMzz) - c3o1 * (c1o1 + c1o2 * (-omega)) * (vx2 * dxux - vz2 * dzuz);
////////////////////////////////////////////////////////////////////////////////////
////no correction
//mxxPyyPzz += OxxPyyPzz*(mfaaa - mxxPyyPzz);
//mxxMyy += -(-omega) * (-mxxMyy);
//mxxMzz += -(-omega) * (-mxxMzz);
//////////////////////////////////////////////////////////////////////////
mfabb += omega * (-mfabb);
mfbab += omega * (-mfbab);
mfbba += omega * (-mfbba);
////////////////////////////////////////////////////////////////////////////////////
//relax
//////////////////////////////////////////////////////////////////////////
// incl. limiter
//! Set relaxation limiters for third order cumulants to default value \f$ \lambda=0.001 \f$ according to section 6 in \ref
//! - Relaxation of third order cumulants including limiter according to Eq. (116)-(123)
//! <a href="https://doi.org/10.1016/j.jcp.2017.05.040"><b>[ M. Geier et al. (2017), DOI:10.1016/j.jcp.2017.05 040 ]</b></a>
//!
const real qudricLimitP = c1o100;
const real qudricLimitM = c1o100;
const real qudricLimitD = c1o100;
real wadjust = Oxyz + (c1o1 - Oxyz)*abs_internal(mfbbb) / (abs_internal(mfbbb) + qudricLimitD);
mfbbb += wadjust * (-mfbbb);
wadjust = OxyyPxzz + (c1o1 - OxyyPxzz)*abs_internal(mxxyPyzz) / (abs_internal(mxxyPyzz) + qudricLimitP);
mxxyPyzz += wadjust * (-mxxyPyzz);
wadjust = OxyyMxzz + (c1o1 - OxyyMxzz)*abs_internal(mxxyMyzz) / (abs_internal(mxxyMyzz) + qudricLimitM);
mxxyMyzz += wadjust * (-mxxyMyzz);
wadjust = OxyyPxzz + (c1o1 - OxyyPxzz)*abs_internal(mxxzPyyz) / (abs_internal(mxxzPyyz) + qudricLimitP);
mxxzPyyz += wadjust * (-mxxzPyyz);
wadjust = OxyyMxzz + (c1o1 - OxyyMxzz)*abs_internal(mxxzMyyz) / (abs_internal(mxxzMyyz) + qudricLimitM);
mxxzMyyz += wadjust * (-mxxzMyyz);
wadjust = OxyyPxzz + (c1o1 - OxyyPxzz)*abs_internal(mxyyPxzz) / (abs_internal(mxyyPxzz) + qudricLimitP);
mxyyPxzz += wadjust * (-mxyyPxzz);
wadjust = OxyyMxzz + (c1o1 - OxyyMxzz)*abs_internal(mxyyMxzz) / (abs_internal(mxyyMxzz) + qudricLimitM);
mxyyMxzz += wadjust * (-mxyyMxzz);
//////////////////////////////////////////////////////////////////////////
// no limiter
//mfbbb += OxyyMxzz * (-mfbbb);
//mxxyPyzz += OxyyPxzz * (-mxxyPyzz);
//mxxyMyzz += OxyyMxzz * (-mxxyMyzz);
//mxxzPyyz += OxyyPxzz * (-mxxzPyyz);
//mxxzMyyz += OxyyMxzz * (-mxxzMyyz);
//mxyyPxzz += OxyyPxzz * (-mxyyPxzz);
//mxyyMxzz += OxyyMxzz * (-mxyyMxzz);
////////////////////////////////////////////////////////////////////////////////////
//! - Compute inverse linear combinations of second and third order cumulants
//!
mfcaa = c1o3 * (mxxMyy + mxxMzz + mxxPyyPzz);
mfaca = c1o3 * (-c2o1* mxxMyy + mxxMzz + mxxPyyPzz);
mfaac = c1o3 * (mxxMyy - c2o1* mxxMzz + mxxPyyPzz);
mfcba = ( mxxyMyzz + mxxyPyzz) * c1o2;
mfabc = (-mxxyMyzz + mxxyPyzz) * c1o2;
mfcab = ( mxxzMyyz + mxxzPyyz) * c1o2;
mfacb = (-mxxzMyyz + mxxzPyyz) * c1o2;
mfbca = ( mxyyMxzz + mxyyPxzz) * c1o2;
mfbac = (-mxyyMxzz + mxyyPxzz) * c1o2;
//////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////
//4.
// no limiter
//! - Relax fourth order cumulants to modified equilibrium for fourth order convergence of diffusion according to Eq. (43)-(48)
//! <a href="https://doi.org/10.1016/j.jcp.2017.05.040"><b>[ M. Geier et al. (2017), DOI:10.1016/j.jcp.2017.05 040 ]</b></a>
//!
CUMacc = -O4*(c1o1 / omega - c1o2) * (dyuy + dzuz) * c2o3 * A + (c1o1 - O4) * (CUMacc);
CUMcac = -O4*(c1o1 / omega - c1o2) * (dxux + dzuz) * c2o3 * A + (c1o1 - O4) * (CUMcac);
CUMcca = -O4*(c1o1 / omega - c1o2) * (dyuy + dxux) * c2o3 * A + (c1o1 - O4) * (CUMcca);
CUMbbc = -O4*(c1o1 / omega - c1o2) * Dxy * c1o3 * B + (c1o1 - O4) * (CUMbbc);
CUMbcb = -O4*(c1o1 / omega - c1o2) * Dxz * c1o3 * B + (c1o1 - O4) * (CUMbcb);
CUMcbb = -O4*(c1o1 / omega - c1o2) * Dyz * c1o3 * B + (c1o1 - O4) * (CUMcbb);
//////////////////////////////////////////////////////////////////////////
//5.
CUMbcc += O5 * (-CUMbcc);
CUMcbc += O5 * (-CUMcbc);
CUMccb += O5 * (-CUMccb);
//////////////////////////////////////////////////////////////////////////
//6.
CUMccc += O6 * (-CUMccc);
////////////////////////////////////////////////////////////////////////////////////
//! - Compute central moments from post collision cumulants according to Eq. (53)-(56) in
//! <a href="https://doi.org/10.1016/j.jcp.2017.05.040"><b>[ M. Geier et al. (2017), DOI:10.1016/j.jcp.2017.05 040 ]</b></a>
//!
//////////////////////////////////////////////////////////////////////////
//4.
mfcbb = CUMcbb + c1o3*((c3o1*mfcaa + c1o1) * mfabb + c6o1 * mfbba * mfbab) * OOrho;
mfbcb = CUMbcb + c1o3*((c3o1*mfaca + c1o1) * mfbab + c6o1 * mfbba * mfabb) * OOrho;
mfbbc = CUMbbc + c1o3*((c3o1*mfaac + c1o1) * mfbba + c6o1 * mfbab * mfabb) * OOrho;
mfcca = CUMcca + (((mfcaa * mfaca + c2o1 * mfbba * mfbba)*c9o1 + c3o1 * (mfcaa + mfaca)) * OOrho - (drho * OOrho))*c1o9;
mfcac = CUMcac + (((mfcaa * mfaac + c2o1 * mfbab * mfbab)*c9o1 + c3o1 * (mfcaa + mfaac)) * OOrho - (drho * OOrho))*c1o9;
mfacc = CUMacc + (((mfaac * mfaca + c2o1 * mfabb * mfabb)*c9o1 + c3o1 * (mfaac + mfaca)) * OOrho - (drho * OOrho))*c1o9;
//////////////////////////////////////////////////////////////////////////
//5. mfbcc = CUMbcc + c1o3 *(c3o1*(mfaac * mfbca + mfaca * mfbac + c4o1 * mfabb * mfbbb + c2o1 * (mfbab * mfacb + mfbba * mfabc)) + (mfbca + mfbac)) * OOrho;
mfcbc = CUMcbc + c1o3 *(c3o1*(mfaac * mfcba + mfcaa * mfabc + c4o1 * mfbab * mfbbb + c2o1 * (mfabb * mfcab + mfbba * mfbac)) + (mfcba + mfabc)) * OOrho;
mfccb = CUMccb + c1o3 *(c3o1*(mfcaa * mfacb + mfaca * mfcab + c4o1 * mfbba * mfbbb + c2o1 * (mfbab * mfbca + mfabb * mfcba)) + (mfacb + mfcab)) * OOrho;
//////////////////////////////////////////////////////////////////////////
//6.
mfccc = CUMccc - ((-c4o1 * mfbbb * mfbbb
- (mfcaa * mfacc + mfaca * mfcac + mfaac * mfcca)
- c4o1 * (mfabb * mfcbb + mfbab * mfbcb + mfbba * mfbbc)
- c2o1 * (mfbca * mfbac + mfcba * mfabc + mfcab * mfacb)) * OOrho
+ (c4o1 * (mfbab * mfbab * mfaca + mfabb * mfabb * mfcaa + mfbba * mfbba * mfaac)
+ c2o1 * (mfcaa * mfaca * mfaac)
+ c16o1 * mfbba * mfbab * mfabb) * OOrho * OOrho
- c1o3 * (mfacc + mfcac + mfcca) * OOrho
- c1o9 * (mfcaa + mfaca + mfaac) * OOrho
+ (c2o1 * (mfbab * mfbab + mfabb * mfabb + mfbba * mfbba)
+ (mfaac * mfaca + mfaac * mfcaa + mfaca * mfcaa) + c1o3 *(mfaac + mfaca + mfcaa)) * OOrho * OOrho * c2o3
+ c1o27*((drho * drho - drho) * OOrho * OOrho));
////////////////////////////////////////////////////////////////////////////////////
//! - Add acceleration (body force) to first order cumulants according to Eq. (85)-(87) in
//! <a href="https://doi.org/10.1016/j.camwa.2015.05.001"><b>[ M. Geier et al. (2015), DOI:10.1016/j.camwa 2015.05.001 ]</b></a>
//!
mfbaa = -mfbaa;
mfaba = -mfaba;
mfaab = -mfaab;
////////////////////////////////////////////////////////////////////////////////////
//! - Chimera transform from central moments to well conditioned distributions as defined in Appendix J in
//! <a href="https://doi.org/10.1016/j.camwa.2015.05.001"><b>[ M. Geier et al. (2015), DOI:10.1016/j.camwa 2015.05.001 ]</b></a>
//! see also Eq. (88)-(96) in
//! <a href="https://doi.org/10.1016/j.jcp.2017.05.040"><b>[ M. Geier et al. (2017), DOI:10.1016/j.jcp.2017.05 040 ]</b></a>
//!
////////////////////////////////////////////////////////////////////////////////////
// X - Dir
vf::lbm::backwardInverseChimeraWithK(mfaaa, mfbaa, mfcaa, vvx, vx2, c1o1, c1o1);
vf::lbm::backwardChimera( mfaba, mfbba, mfcba, vvx, vx2);
vf::lbm::backwardInverseChimeraWithK(mfaca, mfbca, mfcca, vvx, vx2, c3o1, c1o3);
vf::lbm::backwardChimera( mfaab, mfbab, mfcab, vvx, vx2);
vf::lbm::backwardChimera( mfabb, mfbbb, mfcbb, vvx, vx2);
vf::lbm::backwardChimera( mfacb, mfbcb, mfccb, vvx, vx2);
vf::lbm::backwardInverseChimeraWithK(mfaac, mfbac, mfcac, vvx, vx2, c3o1, c1o3);
vf::lbm::backwardChimera( mfabc, mfbbc, mfcbc, vvx, vx2);
vf::lbm::backwardInverseChimeraWithK(mfacc, mfbcc, mfccc, vvx, vx2, c9o1, c1o9);
////////////////////////////////////////////////////////////////////////////////////
// Y - Dir
vf::lbm::backwardInverseChimeraWithK(mfaaa, mfaba, mfaca, vvy, vy2, c6o1, c1o6);
vf::lbm::backwardChimera( mfaab, mfabb, mfacb, vvy, vy2);
vf::lbm::backwardInverseChimeraWithK(mfaac, mfabc, mfacc, vvy, vy2, c18o1, c1o18);
vf::lbm::backwardInverseChimeraWithK(mfbaa, mfbba, mfbca, vvy, vy2, c3o2, c2o3);
vf::lbm::backwardChimera( mfbab, mfbbb, mfbcb, vvy, vy2);
vf::lbm::backwardInverseChimeraWithK(mfbac, mfbbc, mfbcc, vvy, vy2, c9o2, c2o9);
vf::lbm::backwardInverseChimeraWithK(mfcaa, mfcba, mfcca, vvy, vy2, c6o1, c1o6);
vf::lbm::backwardChimera( mfcab, mfcbb, mfccb, vvy, vy2);
vf::lbm::backwardInverseChimeraWithK(mfcac, mfcbc, mfccc, vvy, vy2, c18o1, c1o18);
////////////////////////////////////////////////////////////////////////////////////
// Z - Dir
vf::lbm::backwardInverseChimeraWithK(mfaaa, mfaab, mfaac, vvz, vz2, c36o1, c1o36);
vf::lbm::backwardInverseChimeraWithK(mfaba, mfabb, mfabc, vvz, vz2, c9o1, c1o9);
vf::lbm::backwardInverseChimeraWithK(mfaca, mfacb, mfacc, vvz, vz2, c36o1, c1o36);
vf::lbm::backwardInverseChimeraWithK(mfbaa, mfbab, mfbac, vvz, vz2, c9o1, c1o9);
vf::lbm::backwardInverseChimeraWithK(mfbba, mfbbb, mfbbc, vvz, vz2, c9o4, c4o9);
vf::lbm::backwardInverseChimeraWithK(mfbca, mfbcb, mfbcc, vvz, vz2, c9o1, c1o9);
vf::lbm::backwardInverseChimeraWithK(mfcaa, mfcab, mfcac, vvz, vz2, c36o1, c1o36);
vf::lbm::backwardInverseChimeraWithK(mfcba, mfcbb, mfcbc, vvz, vz2, c9o1, c1o9);
vf::lbm::backwardInverseChimeraWithK(mfcca, mfccb, mfccc, vvz, vz2, c36o1, c1o36);
////////////////////////////////////////////////////////////////////////////////////
//! - Write distributions: style of reading and writing the distributions from/to
//! stored arrays dependent on timestep is based on the esoteric twist algorithm
//! <a href="https://doi.org/10.3390/computation5020019"><b>[ M. Geier et al. (2017), DOI:10.3390/computation5020019 ]</b></a>
//! distribution.f[dir::MZZ] = mfcbb;
distribution.f[dir::PZZ] = mfabb;
distribution.f[dir::ZMZ] = mfbcb;
distribution.f[dir::ZPZ] = mfbab;
distribution.f[dir::ZZM] = mfbbc;
distribution.f[dir::ZZP] = mfbba;
distribution.f[dir::MMZ] = mfccb;
distribution.f[dir::PPZ] = mfaab;
distribution.f[dir::MPZ] = mfcab;
distribution.f[dir::PMZ] = mfacb;
distribution.f[dir::MZM] = mfcbc;
distribution.f[dir::PZP] = mfaba;
distribution.f[dir::MZP] = mfcba;
distribution.f[dir::PZM] = mfabc;
distribution.f[dir::ZMM] = mfbcc;
distribution.f[dir::ZPP] = mfbaa;
distribution.f[dir::ZMP] = mfbca;
distribution.f[dir::ZPM] = mfbac;
distribution.f[dir::MMM] = mfccc;
distribution.f[dir::PMM] = mfacc;
distribution.f[dir::MPM] = mfcac;
distribution.f[dir::PPM] = mfaac;
distribution.f[dir::MMP] = mfcca;
distribution.f[dir::PMP] = mfaca;
distribution.f[dir::MPP] = mfcaa;
distribution.f[dir::PPP] = mfaaa;
distribution.f[dir::ZZZ] = mfbbb;
}
}
}