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lbm.hpp
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lbm.hpp
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#ifndef LBM_HPP
#define LBM_HPP
#include "grid.h"
#include "settings.hpp"
#include <QThread>
#include <Eigen/Dense>
#include <array>
#include <fstream>
#include <iostream>
#include <cmath>
#include <chrono>
#include "Debug.hpp"
class catchGridSignal: public QObject
{
Q_OBJECT
public slots:
virtual void compute(unsigned int nIter) = 0;
signals:
void endCompute();
void colorUpdated();
};
template <const unsigned int jMax, const unsigned int iMax>
class LBM: public catchGridSignal
{
public:
EIGEN_MAKE_ALIGNED_OPERATOR_NEW
LBM(Eigen::Array<int,Eigen::Dynamic,Eigen::Dynamic>& grid,Eigen::Array<Eigen::Array3f,Eigen::Dynamic,Eigen::Dynamic>& result);
void compute(unsigned int nIter){Iterate(nIter);}
protected:
void saveVtk(std::string fileName) const;
void Iterate(int nIter);
void Init();
private:
Eigen::Array2f mRescalerU;
Eigen::Array2f mRescalerR;
void updateColor();
Eigen::Array<int,Eigen::Dynamic,Eigen::Dynamic>& mObstacle;
Eigen::Array<Eigen::Array3f,Eigen::Dynamic,Eigen::Dynamic>& mResultGrid;
Eigen::Array<float,iMax,jMax> mRho;
Eigen::Matrix<Eigen::Vector2f,iMax,jMax> mU;
//Viscosity and Boltzman entry speed
static constexpr float sNu=0.01, sUin=0.4;
//Lattice Boltzman D2Q9 uses 9 speeds
static constexpr int sQMax = 9;
//Just because I never know when to stop...
static constexpr float sC = 1.73205080756887729352744634150587236694280525381038062805580, sEps = 0.2; //sqrt(3)
static constexpr float sDx = 2./jMax, sDt=sDx*sEps/sC;
static constexpr float sEta = 1./(sEps*sEps*sNu/sDt+0.5);
static constexpr float sCfl = sDt*sNu/(sDx*sDx);
#ifndef DYNAMIC_ALLOCATION
Eigen::Array<Eigen::Array<float,sQMax,1>,iMax+2,jMax+2> mGn;
Eigen::Array<Eigen::Array<float,sQMax,1>,iMax+2,jMax+2> mGnp;
Eigen::Array<Eigen::Array<float,sQMax,1>,iMax,jMax> mGeq;
#else
Eigen::Array<Eigen::Array<float,sQMax,1>,Eigen::Dynamic,Eigen::Dynamic> mGn;
Eigen::Array<Eigen::Array<float,sQMax,1>,Eigen::Dynamic,Eigen::Dynamic> mGnp;
Eigen::Array<Eigen::Array<float,sQMax,1>,Eigen::Dynamic,Eigen::Dynamic> mGeq;
#endif
Eigen::Matrix<Eigen::Array<float,sQMax,1>,2,1> mSpeeds;
Eigen::Array<float,sQMax,1> mOmega;
static constexpr float Xc(unsigned int i)
{
ONLYDEBUG(return i<iMax ? (2*i+1)*sDx/2:0;)
ONLYRELEASE(return (2*i+1)*sDx/2;)
}
static constexpr float X(unsigned int i)
{
ONLYDEBUG(return i<iMax ? i*sDx:0;)
ONLYRELEASE(return i*sDx;)
}
static constexpr float Yc(unsigned int j)
{
ONLYDEBUG(return j<jMax ? (2*j+1)*sDx/2 -1:0;)
ONLYRELEASE(return (2*j+1)*sDx/2 -1;)
}
static constexpr float Y(unsigned int j)
{
ONLYDEBUG(return j<jMax ? j*sDx-1:0;)
ONLYRELEASE(return j*sDx;)
}
};
// unary functors
template <typename Derived>
struct sumCoef
{
typedef typename Eigen::DenseBase<Derived>::Scalar result_type;
result_type operator()(const Eigen::DenseBase<Derived>& m) const { return m.sum(); }
};
struct computeSpeed
{
typedef Eigen::Vector2f result_type;
Eigen::Vector2f operator()(const Eigen::Array<float,9,1>& gn) const
{
float x = (gn(1)-gn(3)+gn(5)-gn(6)-gn(7)+gn(8));
float y = (gn(2)-gn(4)+gn(5)+gn(6)-gn(7)-gn(8));
return Eigen::Vector2f(x,y);
}
};
struct computeEquilibriumDistribution
{
typedef Eigen::Array<float,9,1> result_type;
result_type operator()(const Eigen::Vector2f& U) const
{
Eigen::Array<float,9,1> dotProd;
float C = 1.73205080756887729352744634150587236694280525381038062805580;
float UC0 = U(0)*C;
float UC1 = U(1)*C;
float UC0pUC1 = UC0+UC1;
float UC0mUC1 = UC0-UC1;
float USNo2m1 = 0.5*U.squaredNorm()-1;
dotProd(0) = 0;
dotProd(1) = UC0;
dotProd(2) = UC1;
dotProd(3) = -UC0;
dotProd(4) = -UC1;
dotProd(5) = UC0pUC1;
dotProd(6) = -UC0mUC1;
dotProd(7) = -UC0pUC1;
dotProd(8) = UC0mUC1;
#ifdef STOKES
return (Eigen::VectorXf::Ones(9)+ dotProd);
#else
#ifdef NAVIERSTOKES
return (dotProd- USNo2m1 + 0.5*dotProd*dotProd);
#endif
#endif
}
};
template<const unsigned int jMax, const unsigned int iMax>
void LBM<jMax, iMax>::Init()
{
#ifdef DYNAMIC_ALLOCATION
mGn.resize(iMax+2,jMax+2);
mGnp.resize(iMax+2,jMax+2);
mGeq.resize(iMax,jMax);
#endif
float sCTemp = sC;
// (0,0), (1,0), (2,0), (3,0), (4,0), (5,0), (6,0), (7,0), (8,0)
mSpeeds(0) << 0, sCTemp, 0, -sCTemp, 0, sCTemp, -sCTemp, -sCTemp, sCTemp;
// (0,1), (1,1), (2,1), (3,1), (4,1), (5,1), (6,1), (7,1), (8,1)
mSpeeds(1) << 0, 0, sCTemp, 0, -sCTemp, sCTemp, sCTemp, -sCTemp, -sCTemp;
// 0, 1, 2, 3, 4, 5, 6, 7, 8
mOmega << 4./9, 1./9, 1./9, 1./9, 1./9, 1./36, 1./36, 1./36, 1./36;
// mU.setZero();
mRho.setOnes();
for(unsigned i = 1; i<iMax+1; i++)
{
for (unsigned j = 1; j<jMax+1; j++)
{
mU(i-1,j-1).setZero();
if (mObstacle(i,j)==0)
{
mU(i-1,j-1)(0) = 0;
}else
{
mU(i-1,j-1)(0) = (1. - Yc(j-1)* Yc(j-1))*sUin;
}
mGn(i,j)(0) = mOmega(0)*mRho(i-1,j-1);
mGn(i,j)(1) = mOmega(1)*mRho(i-1,j-1)*(1+sC*mU(i-1,j-1)(0));
mGn(i,j)(2) = mOmega(2)*mRho(i-1,j-1)*(1+sC*mU(i-1,j-1)(1));
mGn(i,j)(3) = mOmega(3)*mRho(i-1,j-1)*(1-sC*mU(i-1,j-1)(0));
mGn(i,j)(4) = mOmega(4)*mRho(i-1,j-1)*(1-sC*mU(i-1,j-1)(1));
mGn(i,j)(5) = mOmega(5)*mRho(i-1,j-1)*(1+sC*(mU(i-1,j-1)(0)+mU(i-1,j-1)(1)));
mGn(i,j)(6) = mOmega(6)*mRho(i-1,j-1)*(1-sC*(mU(i-1,j-1)(0)-mU(i-1,j-1)(1)));
mGn(i,j)(7) = mOmega(7)*mRho(i-1,j-1)*(1-sC*(mU(i-1,j-1)(0)+mU(i-1,j-1)(1)));
mGn(i,j)(8) = mOmega(8)*mRho(i-1,j-1)*(1+sC*(mU(i-1,j-1)(0)-mU(i-1,j-1)(1)));
mGnp(i,j) = mGn(i,j);
}
}
}
template<const unsigned int jMax, const unsigned int iMax>
void LBM<jMax, iMax>::Iterate(int nIter)
{
std::chrono::time_point<std::chrono::system_clock> t1 = std::chrono::system_clock::now();
std::stringstream buf;
for (int iter = 1; iter<nIter; iter++) // time loop
{
//const auto& centerGn = mGn.block<iMax,jMax>(1,1);
const auto& centerGn = mGn.block(1, 1, iMax, jMax);
//integrate density to get pressure:
mRho = centerGn.unaryExpr(sumCoef<Eigen::Array<float,sQMax,1> >());
//Compute macroscopic speeds
mU = centerGn.unaryExpr(computeSpeed());
// normalize
for (size_t i = 0, sizeRho = mRho.size(); i<sizeRho; i++)
{mU(i) *= sC/mRho(i);}
//Compute equilibrium distribution
mGeq = mU.unaryExpr(computeEquilibriumDistribution());
// normalize
for (size_t i = 0, sizeRho = mRho.size(); i<sizeRho; i++)
{mGeq(i) *= mOmega*mRho(i);}
//-- collision
for (unsigned int j = 0; j<jMax; j++)
{
for (unsigned int i = 0; i<iMax; i++)
{
if (mObstacle(i,j) == 1)
{
Eigen::Matrix<float,sQMax,1> temp;
temp = (1 - sEta)*mGn(i+1,j+1) + sEta*mGeq(i,j);
//-- interior nodes transport (this is why Gnp is allocated to size (iMax+2, jMax+2)
//-- so border nodes are treated the same way than the others
mGnp(i+1,j+1)(0) = temp(0);
mGnp(i+2,j+1)(1) = temp(1);
mGnp(i+1,j+2)(2) = temp(2);
mGnp(i,j+1) (3) = temp(3);
mGnp(i+1,j) (4) = temp(4);
mGnp(i+2,j+2)(5) = temp(5);
mGnp(i,j+2) (6) = temp(6);
mGnp(i,j) (7) = temp(7);
mGnp(i+2,j) (8) = temp(8);
}else //obst(i,j) == 0
{
mGnp(i+1,j+1)(0) = mGn(i+1,j+1)(0);
mGnp(i+2,j+1)(1) = mGn(i+1,j+1)(3);
mGnp(i+1,j+2)(2) = mGn(i+1,j+1)(4);
mGnp(i,j+1)(3) = mGn(i+1,j+1)(1);
mGnp(i+1,j)(4) = mGn(i+1,j+1)(2);
mGnp(i+2,j+2)(5) = mGn(i+1,j+1)(7);
mGnp(i,j+2)(6) = mGn(i+1,j+1)(8);
mGnp(i,j)(7) = mGn(i+1,j+1)(5);
mGnp(i+2,j)(8) = mGn(i+1,j+1)(6);
}
}
}
//-- CL Est : Neumann
mGnp.row(iMax) = mGnp.row(iMax-1);
//-- CL Ouest : Dirichlet
for (unsigned int j =0; j<jMax; j++)
{
mGnp(1,j+1) = mOmega*mRho(0,j)*(1+(1-Yc(j)*Yc(j))*sUin*mSpeeds(0));
}
mGn.swap(mGnp);
//~ //--- sorties fichiers
if(iter%(iterPerCall-1) == 0)
{
// buf.str("");
// buf << "u_" << iter <<".vtk";
// saveVtk(buf.str());
// std::cout << "Rescale x" << mRescalerU(0) << " -" << mRescalerU(1) << '\n';
// std::cout << "Total mass: " << mRho.sum() << '\n';
if (std::isnan(mRho.sum()))
this->Init();
updateColor();
}
}// end of time loop
std::chrono::time_point<std::chrono::system_clock> t2 = std::chrono::system_clock::now();
std::chrono::duration<float> elapsed_seconds = t2-t1;
// std::cout << "Time spent: " << elapsed_seconds.count() << "sec" << '\n';
std::cout << "Speed: " << 1./elapsed_seconds.count() << "fps" << '\n';
}
template <const unsigned int jMax, const unsigned int iMax>
LBM<jMax,iMax>::LBM(Eigen::Array<int,Eigen::Dynamic,Eigen::Dynamic>& grid, Eigen::Array<Eigen::Array3f, Eigen::Dynamic, Eigen::Dynamic> &result):
mObstacle(grid),
mResultGrid(result)
{
assert(grid.cols() == jMax+2 && grid.rows() == iMax+2);
mRescalerU(0)=1;
mRescalerU(1)=0;
mRescalerR(0)=1;
mRescalerR(1)=0;
this->Init();
}
template<const unsigned int jMax,const unsigned int iMax>
void LBM<jMax, iMax>::updateColor()
{
for (unsigned int j = 0; j<jMax; j++)
{
for (unsigned int i = 0; i<iMax; i++)
{
if(i == 0 || j == 0 || mObstacle(i,j) != 0)// || i == iMax-1 || j == jMax-1)
{
mResultGrid(i,j)(0) = mU(i,j)(0);
mResultGrid(i,j)(1) = mU(i,j)(1);
mResultGrid(i,j)(2) = mRho(i,j);
}else if(mObstacle(i,j)!=0)
{
mResultGrid(i,j).setZero();
mResultGrid(i,j)(2) = mRho.mean();
}
}
}
emit colorUpdated();
}
template<const unsigned int jMax, const unsigned int iMax>
void LBM<jMax, iMax>::saveVtk(std::string fileName) const
{
std::ofstream vtkFile;
std::cout << "save " << fileName << '\n';
vtkFile.open(fileName);
vtkFile << "# vtk DataFile Version 2.0" << '\n';
vtkFile << "champ de vitesse" << '\n';
vtkFile << "ASCII" << '\n';
vtkFile << "DATASET RECTILINEAR_GRID" << '\n';
vtkFile << "DIMENSIONS " << iMax+1 << " "<< jMax+1 << " " << 1 << '\n';
vtkFile << "X_COORDINATES " << iMax+1 <<" double" << '\n';
for (unsigned int i = 0; i<iMax+1; i++)
{
vtkFile << X(i) << '\n';
}
vtkFile << "Y_COORDINATES " << jMax+1 <<" double" << '\n';
for (unsigned int j = 0; j<jMax+1; j++)
{
vtkFile << Y(j) << '\n';
}
vtkFile << "Z_COORDINATES " << 1 << " double" << '\n';
vtkFile << 0 << '\n';
vtkFile << "CELL_DATA " << iMax*jMax << '\n';
vtkFile << "SCALARS rho double" << '\n';
vtkFile << "LOOKUP_TABLE default" << '\n';
for (unsigned int j = 0; j<jMax; j++)
{
for (unsigned int i = 0; i<iMax; i++)
{
vtkFile << mRho(i,j) << '\n';
}
}
vtkFile << "VECTORS u double" << '\n';
for (unsigned int j = 0; j<jMax; j++)
{
for (unsigned int i = 0; i<iMax; i++)
{
vtkFile << mU(i,j)(0) << " " << mU(i,j)(1) << " " << 0 << '\n';
}
}
vtkFile.close();
emit endCompute();
}
#endif // LBM_HPP