/* This file is part of the OpenLB library
*
* Copyright (C) 2019 Adrian Kummerlaender
* E-mail contact: info@openlb.net
* The most recent release of OpenLB can be downloaded at
*
*
* 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
* DESCRIPTORBASE for all types of 2D and 3D lattices. In principle, thanks
* to the fact that the OpenLB code is generic, it is sufficient to
* write a new descriptor when a new type of lattice is to be used.
* -- header file
*/
#ifndef MRT_LATTICE_DESCRIPTORS_H
#define MRT_LATTICE_DESCRIPTORS_H
#include "latticeDescriptors.h"
namespace olb {
/// Descriptors for the 2D and 3D lattices.
/** \warning Attention: The lattice directions must always be ordered in
* such a way that c[i] = -c[i+(q-1)/2] for i=1..(q-1)/2, and c[0] = 0 must
* be the rest velocity. Furthermore, the velocities c[i] for i=1..(q-1)/2
* must verify
* - in 2D: (c[i][0]<0) || (c[i][0]==0 && c[i][1]<0)
* - in 3D: (c[i][0]<0) || (c[i][0]==0 && c[i][1]<0)
* || (c[i][0]==0 && c[i][1]==0 && c[i][2]<0)
* Otherwise some of the code will work erroneously, because the
* aformentioned relations are taken as given to enable a few
* optimizations.
*/
namespace descriptors {
namespace tag {
struct MRT : public CATEGORY, public DESCRIPTOR_TAG { };
}
using MRTD2Q5Descriptor = D2Q5;
/// Advection Diffusion MRT D2Q5
/**
* Based on: Liu, Q., & He, Y. L. (2015). Double multiple-relaxation-time lattice Boltzmann model
* for solid–liquid phase change with natural convection in porous media.
* Physica A: Statistical Mechanics and its Applications, 438, 94-106.
**/
using AdvectionDiffusionMRTD2Q5Descriptor = D2Q5;
/// MRT D2Q9 lattice. The numbering follows the one in "Viscous flow computations
/// with the method of lattice Boltzmann equation", D. Yu, L.-S. Luo, W. Shi,
/// Progress in Aerospace Sciences 39, (2003), p. 329-367
using MRTD2Q9Descriptor = D2Q9;
using ForcedMRTD2Q9Descriptor = D2Q9;
using MRTD3Q7Descriptor = D3Q7;
/// Advection Diffusion MRT D3Q7
/**
* Based on: Wu, H., Wang, J., & Tao, Z. (2011). Passive heat transfer in a turbulent
* channel flow simulation using large eddy simulation based on the lattice
* Boltzmann method framework.
* International Journal of Heat and Fluid Flow, 32(6), 1111-1119.
*
* There are some differences in respect to the order of the columns based on the lattice directions
**/
using AdvectionDiffusionMRTD3Q7Descriptor = D3Q7;
/// MRT D3Q19 lattice. The numbering follows the one in "Multiple-relaxation-
/// time lattice Boltzmann models in three dimensions", D. D'Humières,
/// I. Ginzburg, M. Krafzcyk, P. Lallemand, L.-S. Luo,
/// Phil. Trans. R. Soc. Lond. A (2002) 660, p. 437-451
using MRTD3Q19Descriptor = D3Q19;
using ForcedMRTD3Q19Descriptor = D3Q19;
namespace mrt_data {
using utilities::Fraction;
// Matrix of base change between f and moments : moments=M.f
template
constexpr Fraction M[Q][Q] = {};
// inverse of base change matrix : f=invM.moments
template
constexpr Fraction invM[Q][Q] = {};
// relaxation times
template
constexpr Fraction s[Q] = {};
// relaxation times
template
constexpr Fraction s_2[Q] = {};
template
constexpr int shearIndexes = {};
// relevant indexes of r. t. for shear viscosity
template
constexpr int shearViscIndexes[shearIndexes] = {};
// relevant index of r. t. for bulk viscosity
template
constexpr int bulkViscIndex = {};
template <>
constexpr Fraction M<2,5>[5][5] = {
{ 1, 1, 1, 1, 1},
{ 0,-1, 0, 1, 0},
{ 0, 0,-1, 0, 1},
{-4, 1, 1, 1, 1},
{ 0, 1,-1, 1,-1}
};
template <>
constexpr Fraction M<2,9>[9][9] = {
{ 1, 1, 1, 1, 1, 1, 1, 1, 1},
{-4, 2, -1, 2, -1, 2, -1, 2, -1},
{ 4, 1, -2, 1, -2, 1, -2, 1, -2},
{ 0, -1, -1, -1, 0, 1, 1, 1, 0},
{ 0, -1, 2, -1, 0, 1, -2, 1, 0},
{ 0, 1, 0, -1, -1, -1, 0, 1, 1},
{ 0, 1, 0, -1, 2, -1, 0, 1, -2},
{ 0, 0, 1, 0, -1, 0, 1, 0, -1},
{ 0, -1, 0, 1, 0, -1, 0, 1, 0}
};
template <>
constexpr Fraction M<3,7>[7][7] = {
// Li, Yang et al 2016: The directions are modified for the OpenLB definition
{1, 1, 1, 1, 1, 1, 1},
{0, 1, 0, -1, 0, 0, 0},
{0, 0, -1, 0, 0, 1, 0},
{0, 0, 0, 0, 1, 0, -1},
{6, -1, -1, -1, -1, -1, -1},
{0, 2, -1, 2, -1, -1, -1},
{0, 0, 1, 0, -1, 1, -1}
};
template <>
constexpr Fraction M<3,19>[19][19] = {
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1},
{-30,-11,-11,-11, 8, 8, 8, 8, 8, 8,-11,-11,-11, 8, 8, 8, 8, 8, 8},
{ 12, -4, -4, -4, 1, 1, 1, 1, 1, 1, -4, -4, -4, 1, 1, 1, 1, 1, 1},
{ 0, -1, 0, 0, -1, -1, -1, -1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0},
{ 0, 4, 0, 0, -1, -1, -1, -1, 0, 0, -4, 0, 0, 1, 1, 1, 1, 0, 0},
{ 0, 0, -1, 0, -1, 1, 0, 0, -1, -1, 0, 1, 0, 1, -1, 0, 0, 1, 1},
{ 0, 0, 4, 0, -1, 1, 0, 0, -1, -1, 0, -4, 0, 1, -1, 0, 0, 1, 1},
{ 0, 0, 0, -1, 0, 0, -1, 1, -1, 1, 0, 0, 1, 0, 0, 1, -1, 1, -1},
{ 0, 0, 0, 4, 0, 0, -1, 1, -1, 1, 0, 0, -4, 0, 0, 1, -1, 1, -1},
{ 0, 2, -1, -1, 1, 1, 1, 1, -2, -2, 2, -1, -1, 1, 1, 1, 1, -2, -2},
{ 0, -4, 2, 2, 1, 1, 1, 1, -2, -2, -4, 2, 2, 1, 1, 1, 1, -2, -2},
{ 0, 0, 1, -1, 1, 1, -1, -1, 0, 0, 0, 1, -1, 1, 1, -1, -1, 0, 0},
{ 0, 0, -2, 2, 1, 1, -1, -1, 0, 0, 0, -2, 2, 1, 1, -1, -1, 0, 0},
{ 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1, -1},
{ 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0},
{ 0, 0, 0, 0, -1, -1, 1, 1, 0, 0, 0, 0, 0, 1, 1, -1, -1, 0, 0},
{ 0, 0, 0, 0, 1, -1, 0, 0, -1, -1, 0, 0, 0, -1, 1, 0, 0, 1, 1},
{ 0, 0, 0, 0, 0, 0, -1, 1, 1, -1, 0, 0, 0, 0, 0, 1, -1, -1, 1}
};
template <>
constexpr Fraction invM<2,5>[5][5] = {
{{1, 5}, 0, 0, {-1, 5}, 0},
{{1, 5}, {-1, 2}, 0, { 1, 20}, { 1, 4}},
{{1, 5}, 0, {-1, 2}, { 1, 20}, {-1, 4}},
{{1, 5}, { 1, 2}, 0, { 1, 20}, { 1, 4}},
{{1, 5}, 0, { 1, 2}, { 1, 20}, {-1, 4}}
};
template <>
constexpr Fraction invM<2,9>[9][9] = {
{{1, 9}, {-1, 9}, { 1, 9}, 0, 0, 0, 0, 0, 0},
{{1, 9}, { 1, 18}, { 1, 36}, {-1, 6}, {-1, 12}, { 1, 6}, { 1, 12}, 0, {-1, 4}},
{{1, 9}, {-1, 36}, {-1, 18}, {-1, 6}, { 1, 6}, 0, 0, { 1, 4}, 0},
{{1, 9}, { 1, 18}, { 1, 36}, {-1, 6}, {-1, 12}, {-1, 6}, {-1, 12}, 0, { 1, 4}},
{{1, 9}, {-1, 36}, {-1, 18}, 0, 0, {-1, 6}, { 1, 6}, {-1, 4}, 0},
{{1, 9}, { 1, 18}, { 1, 36}, { 1, 6}, { 1, 12}, {-1, 6}, {-1, 12}, 0, {-1, 4}},
{{1, 9}, {-1, 36}, {-1, 18}, { 1, 6}, {-1, 6}, 0, 0, { 1, 4}, 0},
{{1, 9}, { 1, 18}, { 1, 36}, { 1, 6}, { 1, 12}, { 1, 6}, { 1, 12}, 0, { 1, 4}},
{{1, 9}, {-1, 36}, {-1, 18}, 0, 0, { 1, 6}, {-1, 6}, {-1, 4}, 0}
};
template <>
constexpr Fraction invM<3,7>[7][7] = {
// Li, Yang et al 2016: The directions are modified for the OpenLB definition
{{1, 7}, 0, 0, 0, { 1, 7}, 0, 0},
{{1, 7}, { 1, 2}, 0, 0, {-1, 42}, { 1, 6}, 0},
{{1, 7}, 0, {-1, 2}, 0, {-1, 42}, {-1, 12}, { 1, 4}},
{{1, 7}, {-1, 2}, 0, 0, {-1, 42}, { 1, 6}, 0},
{{1, 7}, 0, 0, { 1, 2}, {-1, 42}, {-1, 12}, {-1, 4}},
{{1, 7}, 0, { 1, 2}, 0, {-1, 42}, {-1, 12}, { 1, 4}},
{{1, 7}, 0, 0, {-1, 2}, {-1, 42}, {-1, 12}, {-1, 4}}
};
template <>
constexpr Fraction invM<3,19>[19][19] = {
{{1,19}, { -5, 399}, { 1, 21}, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0},/*0*/
{{1,19}, {-11, 2394}, {-1, 63}, {-1, 10}, { 1, 10}, 0, 0,
0, 0, { 1, 18}, {-1, 18}, 0, 0,
0, 0, 0, 0, 0, 0},/*1*/
{{1,19}, {-11, 2394}, {-1, 63}, 0, 0, {-1, 10}, { 1, 10},
0, 0, {-1, 36}, { 1, 36}, { 1, 12}, {-1, 12},
0, 0, 0, 0, 0, 0},/*2*/
{{1,19}, {-11, 2394}, {-1, 63}, 0, 0, 0, 0,
{ -1, 10}, { 1, 10}, {-1, 36}, { 1, 36}, {-1, 12}, { 1, 12},
0, 0, 0, 0, 0, 0},/*3*/
{{1,19}, { 4, 1197}, { 1, 252}, {-1, 10}, {-1, 40}, {-1, 10}, {-1, 40},
0, 0, { 1, 36}, { 1, 72}, { 1, 12}, { 1, 24},
{ 1, 4}, 0, 0, {-1, 8}, { 1, 8}, 0},/*4*/
{{1,19}, { 4, 1197}, { 1, 252}, {-1, 10}, {-1, 40}, { 1, 10}, { 1, 40},
0, 0, { 1, 36}, { 1, 72}, { 1, 12}, { 1, 24},
{ -1, 4}, 0, 0, {-1, 8}, {-1, 8}, 0},/*5*/
{{1,19}, { 4, 1197}, { 1, 252}, {-1, 10}, {-1, 40}, 0, 0,
{ -1, 10}, {-1, 40}, { 1, 36}, { 1, 72}, {-1, 12}, {-1, 24},
0, 0, { 1, 4}, { 1, 8}, 0, {-1, 8}},/*6*/
{{1,19}, { 4, 1197}, { 1, 252}, {-1, 10}, {-1, 40}, 0, 0,
{ 1, 10}, { 1, 40}, { 1, 36}, { 1, 72}, {-1, 12}, {-1, 24},
0, 0, {-1, 4}, { 1, 8}, 0, { 1, 8}},/*7*/
{{1,19}, { 4, 1197}, { 1, 252}, 0, 0, {-1, 10}, {-1, 40},
{ -1, 10}, {-1, 40}, {-1, 18}, {-1, 36}, 0, 0,
0, { 1, 4}, 0, 0, {-1, 8}, { 1, 8}},/*8*/
{{1,19}, { 4, 1197}, { 1, 252}, 0, 0, {-1, 10}, {-1, 40},
{ 1, 10}, { 1, 40}, {-1, 18}, {-1, 36}, 0, 0,
0, {-1, 4}, 0, 0, {-1, 8}, {-1, 8}},/*9*/
{{1,19}, {-11, 2394}, {-1, 63}, { 1, 10}, {-1, 10}, 0, 0,
0, 0, { 1, 18}, {-1, 18}, 0, 0,
0, 0, 0, 0, 0, 0},/*10*/
{{1,19}, {-11, 2394}, {-1, 63}, 0, 0, { 1, 10}, {-1, 10},
0, 0, {-1, 36}, { 1, 36}, { 1, 12}, {-1, 12},
0, 0, 0, 0, 0, 0},/*11*/
{{1,19}, {-11, 2394}, {-1, 63}, 0, 0, 0, 0,
{ 1, 10}, {-1, 10}, {-1, 36}, { 1, 36}, {-1, 12}, { 1, 12},
0, 0, 0, 0, 0, 0},/*12*/
{{1,19}, { 4, 1197}, { 1, 252}, { 1, 10}, { 1, 40}, { 1, 10}, { 1, 40},
0, 0, { 1, 36}, { 1, 72}, { 1, 12}, { 1, 24},
{ 1, 4}, 0, 0, { 1, 8}, {-1, 8}, 0},/*13*/
{{1,19}, { 4, 1197}, { 1, 252}, { 1, 10}, { 1, 40}, {-1, 10}, {-1, 40},
0, 0, { 1, 36}, { 1, 72}, { 1, 12}, { 1, 24},
{ -1, 4}, 0, 0, { 1, 8}, { 1, 8}, 0},/*14*/
{{1,19}, { 4, 1197}, { 1, 252}, { 1, 10}, { 1, 40}, 0, 0,
{ 1, 10}, { 1, 40}, { 1, 36}, { 1, 72}, {-1, 12}, {-1, 24},
0, 0, { 1, 4}, {-1, 8}, 0, { 1, 8}},/*15*/
{{1,19}, { 4, 1197}, { 1, 252}, { 1, 10}, { 1, 40}, 0, 0,
{ -1, 10}, {-1, 40}, { 1, 36}, { 1, 72}, {-1, 12}, {-1, 24},
0, 0, {-1, 4}, {-1, 8}, 0, {-1, 8}},/*16*/
{{1,19}, { 4, 1197}, { 1, 252}, 0, 0, { 1, 10}, { 1, 40},
{ 1, 10}, { 1, 40}, {-1, 18}, {-1, 36}, 0, 0,
0, { 1, 4}, 0, 0, { 1, 8}, {-1, 8}},/*17*/
{{1,19}, { 4, 1197}, { 1, 252}, 0, 0, { 1, 10}, { 1, 40},
{ -1, 10}, {-1, 40}, {-1, 18}, {-1, 36}, 0, 0,
0, {-1, 4}, 0, 0, { 1, 8}, { 1, 8}}/*18*/
};
template <>
constexpr Fraction s<2,5>[5] = {
0, 0, 0, {3, 2}, {3, 2}
};
// s7=s8 to have a shear viscosity nu
// and the bulk viscosity depends on s2.
template <>
constexpr Fraction s<2,9>[9] = {
0, {11, 10}, {11, 10}, 0, {11, 10}, 0, {11, 10}, 0, 0
};
template <>
constexpr Fraction s<3,7>[7] = {
// Original MRT Relaxation times
/*s0*/ 0, // rho (conserved)
/*s1*/ 0, // Function of the thermal diffusivity: S_a = 1/t_a = 1/(4*a + 1/2)
/*s2*/ 0, // Function of the thermal diffusivity: S_a = 1/t_a = 1/(4*a + 1/2)
/*s3*/ 0, // Function of the thermal diffusivity: S_a = 1/t_a = 1/(4*a + 1/2)
/*s4*/ {19, 10},
/*s5*/ {19, 10},
/*s6*/ {19, 10}
};
// Original MRT Relaxation times
template <>
constexpr Fraction s<3,19>[19] = {
/*s0*/ 0, // rho (conserved)
/*s1*/ { 119, 100},
/*s2*/ { 7, 5},
/*s3*/ 0, // rho*ux (conserved)
/*s4*/ { 6, 5},
/*s5*/ 0, // rho*uy (conserved)
/*s6*/ { 6, 5}, // = s4
/*s7*/ 0, // rho*uz (conserved)
/*s8*/ { 6, 5}, // = s4
/*s9*/ 0, //should be equal to s13, used to define nu
/*s10*/ { 7, 5},
/*s11*/ 0, // = s9,
/*s12*/ { 7, 5},
/*s13*/ 0, //should be equal to s9, used to define nu
/*s14*/ 0, // = s13,
/*s15*/ 0, // = s13,
/*s16*/ { 99, 50},
/*s17*/ { 99, 50}, // = s16,
/*s18*/ { 99, 50} // = s16,
};
// Use these relaxation time for higher stability
template <>
constexpr Fraction s_2<3,19>[19] = {
/*s0*/ 0, // rho (conserved)
/*s1*/ 1,
/*s2*/ 1,
/*s3*/ 0, // rho*ux (conserved)
/*s4*/ 1,
/*s5*/ 0, // rho*uy (conserved)
/*s6*/ 1, // = s4
/*s7*/ 0, // rho*uz (conserved)
/*s8*/ 1, // = s4
/*s9*/ 0, //should be equal to s13, used to define nu
/*s10*/ 1,
/*s11*/ 0, // = s9,
/*s12*/ 1,
/*s13*/ 0, //should be equal to s9, used to define nu
/*s14*/ 0, // = s13,
/*s15*/ 0, // = s13,
/*s16*/ 1,
/*s17*/ 1, // = s16,
/*s18*/ 1 // = s16,
};
template <>
constexpr int shearIndexes<2,5> = 2;
template <>
constexpr int shearIndexes<2,9> = 2;
template <>
constexpr int shearIndexes<3,7> = 3;
template <>
constexpr int shearIndexes<3,19> = 5;
template <>
constexpr int shearViscIndexes<2,5>[shearIndexes<2,5>] = { 1, 2 };
template <>
constexpr int shearViscIndexes<2,9>[shearIndexes<2,9>] = { 7, 8 };
template <>
constexpr int shearViscIndexes<3,7>[shearIndexes<3,7>] = { 1, 2, 3 };
template <>
constexpr int shearViscIndexes<3,19>[shearIndexes<3,19>] = { 9, 11, 13, 14, 15 };
template <>
constexpr int bulkViscIndex<2,9> = 2;
template <>
constexpr int bulkViscIndex<3,19> = 1;
} // mrt_data
template
constexpr T t(unsigned iPop, tag::MRT)
{
return data::t[iPop].template as();
}
template
constexpr T m(unsigned iPop, unsigned jPop, tag::MRT)
{
return mrt_data::M[iPop][jPop].template as();
}
template
constexpr T m(unsigned iPop, unsigned jPop)
{
return m(iPop, jPop, typename DESCRIPTOR::category_tag());
}
template
constexpr T invM(unsigned iPop, unsigned jPop, tag::MRT)
{
return mrt_data::invM[iPop][jPop].template as();
}
template
constexpr T invM(unsigned iPop, unsigned jPop)
{
return invM(iPop, jPop, typename DESCRIPTOR::category_tag());
}
template
constexpr T s(unsigned iPop, tag::MRT)
{
return mrt_data::s[iPop].template as();
}
template
constexpr T s(unsigned iPop)
{
return s(iPop, typename DESCRIPTOR::category_tag());
}
template
constexpr T s_2(unsigned iPop, tag::MRT)
{
return mrt_data::s_2[iPop].template as();
}
template
constexpr T s_2(unsigned iPop)
{
return s_2(iPop, typename DESCRIPTOR::category_tag());
}
template
constexpr int shearIndexes(tag::MRT)
{
return mrt_data::shearIndexes;
}
template
constexpr int shearIndexes()
{
return shearIndexes(typename DESCRIPTOR::category_tag());
}
template
constexpr int shearViscIndexes(unsigned iPop, tag::MRT)
{
return mrt_data::shearViscIndexes[iPop];
}
template
constexpr int shearViscIndexes(unsigned iPop)
{
return shearViscIndexes(iPop, typename DESCRIPTOR::category_tag());
}
template
constexpr int bulkViscIndex(tag::MRT)
{
return mrt_data::bulkViscIndex;
}
template
constexpr int bulkViscIndex()
{
return bulkViscIndex(typename DESCRIPTOR::category_tag());
}
} // namespace descriptors
} // namespace olb
#endif