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anaEul.cpp
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// Created by Abhinav Singh - Copyright (c)
// ANASOL Eulerian case
#define SE_CLASS1
#include "config.h"
#define BOOST_MPL_CFG_NO_PREPROCESSED_HEADERS
#define BOOST_MPL_LIMIT_VECTOR_SIZE 40
#include <iostream>
#include "DCPSE/DCPSE_op/DCPSE_op.hpp"
#include "DCPSE/DCPSE_op/DCPSE_Solver.hpp"
#include "Operators/Vector/vector_dist_operators.hpp"
#include "Vector/vector_dist_subset.hpp"
#include "OdeIntegrators/OdeIntegrators.hpp"
#include <fstream>
void write_mag(std::string filename, double t,double mag){
std::ofstream myFile(filename,std::ios_base::app);
myFile <<t<<","<<mag<< "\n";
myFile.close();
}
constexpr int x = 0;
constexpr int y = 1;
constexpr int z = 2;
double eta=1;
double nu=0;
double gama=1;
double Ks=1;
double Kb=1;
double Kt=1;
double lambda=1;
double zeta=-1; //zeta=-1 corresponds to all previous notations before 2018 paper of Julicher. In our code zeta +ve would mean contractile and negative would mean extensile.
double timeTOL=1e-8;
double max_steady_tol=1e-8;
bool BOTTOMFLOW=0;
//dmu is set later as runtime parameter.
double dmu;
//Stress free.
double mu_t;
double mu_b;
double dt,V_err_eps;
timer tt2;
int wr_f;
int wr_at;
constexpr int Polarization = 0;
constexpr int Velocity = 1;
constexpr int Vorticity = 2;
constexpr int ExtForce = 3;
constexpr int Pressure = 4;
constexpr int Strain_rate = 5;
constexpr int Stress = 6;
constexpr int MolField = 7;
constexpr int VRHS = 8;
constexpr int FE = 9;
constexpr int VT = 10;
constexpr int DV = 11;
constexpr int DPOL = 12;
constexpr int POLD = 13;
constexpr int DIV = 14;
constexpr int DELMU = 15;
constexpr int HPERP = 16;
constexpr int HPARR = 17;
constexpr int POLMAG = 18;
constexpr int TPOLMAG = 19;
void *vectorGlobal,*vectorGlobal_bulk,*vectorGlobal_boundary_up,*vectorGlobal_boundary_down;
const openfpm::vector<std::string> PropNAMES={"00-Polarization","01-Velocity","02-Vorticity","03-ExternalForce","04-Pressure","05-StrainRate","06-Stress","07-MolecularField","08-VelocityRHS","09-FranckEnergyDensity","10-V_t","11-dV","12-dPol","13-P_old","14-div","15-delmu","16-Hperp","17-Hparallel","18-PolMag","19-tPolMag"};
typedef aggregate<double[3], VectorS<3, double>, double[3][3], VectorS<3, double>, double, double[3][3], double[3][3], VectorS<3, double>, VectorS<3, double>, double,VectorS<3, double>,VectorS<3, double>,VectorS<3, double>,VectorS<3, double>,double,double,VectorS<3, double>,double,double,double> ActiveGel3d;
typedef vector_dist_ws<3, double, ActiveGel3d> vector_type;
typedef vector_dist_subset<3, double, ActiveGel3d> vector_type2;
template<typename DX,typename DY,typename DZ,typename DXX,typename DXY,typename DXZ,typename DYY,typename DYZ,typename DZZ>
struct PolarEv
{
DX &Dx;
DY &Dy;
DZ &Dz;
DXX &Dxx;
DXY &Dxy;
DXZ &Dxz;
DYY &Dyy;
DYZ &Dyz;
DZZ &Dzz;
//Constructor
PolarEv(DX &Dx,DY &Dy,DZ &Dz,DXX &Dxx,DXY &Dxy,DXZ &Dxz,DYY &Dyy,DYZ &Dyz,DZZ &Dzz):Dx(Dx),Dy(Dy),Dz(Dz),Dxx(Dxx),Dxy(Dxy),Dxz(Dxz),Dyy(Dyy),Dyz(Dyz),Dzz(Dzz)
{}
void operator()( const state_type_3d_ofp &X , state_type_3d_ofp &dxdt , const double t ) const
{
timer tt;
vector_type &Particles= *(vector_type *) vectorGlobal;
vector_type2 &Particles_bulk= *(vector_type2 *) vectorGlobal_bulk;
vector_type2 &Particles_boundary_up= *(vector_type2 *) vectorGlobal_boundary_up;
vector_type2 &Particles_boundary_down= *(vector_type2 *) vectorGlobal_boundary_down;
auto &v_cl = create_vcluster();
auto Pol = getV<Polarization>(Particles);
auto Pol_bulk = getV<Polarization>(Particles_bulk);
auto V = getV<Velocity>(Particles);
auto W = getV<Vorticity>(Particles);
auto u = getV<Strain_rate>(Particles);
auto h = getV<MolField>(Particles);
auto dPol= getV<DPOL>(Particles);
auto dPol_bulk= getV<DPOL>(Particles_bulk);
auto delmu=getV<DELMU>(Particles);
auto Hperp=getV<HPERP>(Particles);
auto Hpar=getV<HPARR>(Particles);
auto PolMag=getV<POLMAG>(Particles);
auto tPolMag=getV<TPOLMAG>(Particles);
Pol_bulk[x]=X.data.get<0>();
Pol_bulk[y]=X.data.get<1>();
Pol_bulk[z]=X.data.get<2>();
Particles.ghost_get<Polarization>(SKIP_LABELLING);
auto px=Pol[x];
auto py=Pol[y];
auto pz=Pol[z];
auto P_bulk = getV<Pressure>(Particles_bulk);
auto RHS_bulk = getV<VRHS>(Particles_bulk);
auto Dyx = Dxy;
auto Dzy = Dyz;
auto Dzx = Dxz;
auto & bulk = Particles_bulk.getIds();
auto & Boundary_up = Particles_boundary_up.getIds();
auto & Boundary_down = Particles_boundary_down.getIds();
PolMag=Pol[x]*Pol[x]+Pol[y]*Pol[y]+Pol[z]*Pol[z];
for (int j = 0; j < bulk.size(); j++) {
auto p = bulk.get<0>(j);
Particles.getProp<POLMAG>(p) = (Particles.getProp<POLMAG>(p) == 0) ? 1 : Particles.getProp<POLMAG>(p);
}
//Pol[x]=Pol[x]/sqrt(PolMag);
//Pol[y]=Pol[y]/sqrt(PolMag);
//Pol[z]=Pol[z]/sqrt(PolMag);
double pmag=0;
for (int j = 0; j < bulk.size(); j++) {
auto p = bulk.get<0>(j);
if(fabs(1.0-Particles.getProp<POLMAG>(p))>pmag)
{
pmag=fabs(1-Particles.getProp<POLMAG>(p));
}
}
v_cl.max(pmag);
v_cl.execute();
if(v_cl.rank()==0)
{std::cout<<"Max Polarity Magnitude Deviation: "<<pmag<<std::endl;
write_mag("PolMag",t,pmag);
}
auto g = getV<ExtForce>(Particles);
auto P = getV<Pressure>(Particles);
auto sigma = getV<Stress>(Particles);
auto RHS = getV<VRHS>(Particles);
auto FranckEnergyDensity = getV<FE>(Particles);
auto V_t = getV<VT>(Particles);
auto dV = getV<DV>(Particles);
auto div =getV<DIV>(Particles);
auto g_up = getV<ExtForce>(Particles_boundary_up);
auto g_down = getV<ExtForce>(Particles_boundary_down);
auto V_up = getV<Velocity>(Particles_boundary_up);
auto V_down = getV<Velocity>(Particles_boundary_down);
petsc_solver<double> solverPetsc;
solverPetsc.setSolver(KSPGMRES);
solverPetsc.setRestart(5000);
solverPetsc.setPreconditioner(PCNONE);
tt.start();
Particles.ghost_get<Polarization>(SKIP_LABELLING);
texp_v<double> dxpx=Dx(Pol[x]), dxpy=Dx(Pol[y]), dxpz=Dx(Pol[z]), dypx=Dy(Pol[x]), dypy=Dy(Pol[y]), dypz=Dy(Pol[z]),dzpx=Dz(Pol[x]),dzpy=Dz(Pol[y]),dzpz=Dz(Pol[z]),
dxxpx=Dxx(Pol[x]),dxxpy=Dxx(Pol[y]),dxxpz=Dxx(Pol[z]),dyypx=Dyy(Pol[x]), dyypy=Dyy(Pol[y]), dyypz=Dyy(Pol[z]), dzzpx=Dzz(Pol[x]), dzzpy=Dzz(Pol[y]),
dzzpz=Dzz(Pol[z]), dxypx=Dxy(Pol[x]), dxypy=Dxy(Pol[y]), dxypz=Dxy(Pol[z]), dxzpx=Dxz(Pol[x]), dxzpy=Dxz(Pol[y]), dxzpz=Dxz(Pol[z]), dyzpx=Dyz(Pol[x]), dyzpy=Dyz(Pol[y]),
dyzpz=Dyz(Pol[z]),
//Note if mu is changing in space delmu has to go inside the derivative.
dxmuqxx=delmu*Dx((Pol[x]*Pol[x]-1/3.0*(Pol[x]*Pol[x]+Pol[y]*Pol[y]+Pol[z]*Pol[z]))),
dymuqxy=delmu*Dy(Pol[x]*Pol[y]) ,
dzmuqxz=delmu*Dz(Pol[x]*Pol[z]) ,
dxmuqyx=delmu*Dx(Pol[y]*Pol[x]),
dymuqyy=delmu*Dy((Pol[y]*Pol[y]-1/3.0*(Pol[x]*Pol[x]+Pol[y]*Pol[y]+Pol[z]*Pol[z]))),
dzmuqyz=delmu*Dz(Pol[y]*Pol[z]) ,
dxmuqzx=delmu*Dx(Pol[z]*Pol[x]) ,
dymuqzy=delmu*Dy(Pol[z]*Pol[y]),
dzmuqzz=delmu*Dz((Pol[z]*Pol[z]-1/3.0*(Pol[x]*Pol[x]+Pol[y]*Pol[y]+Pol[z]*Pol[z]))),
polmaginv,dPolMag;
FranckEnergyDensity = 0.5*Ks*(dxpx + dypy + dzpz)*(dxpx + dypy + dzpz) +
0.5*Kt*((dypz - dzpy)*px + (-dxpz + dzpx)*py + (dxpy - dypx)*pz)*((dypz - dzpy)*px + (-dxpz + dzpx)*py + (dxpy - dypx)*pz) +
0.5*Kb*((-dxpz*px + dzpx*px - dypz*py + dzpy*py)*
(-dxpz*px + dzpx*px - dypz*py + dzpy*py) +
(dxpy*py - dypx*py + dxpz*pz - dzpx*pz)*
(dxpy*py - dypx*py + dxpz*pz - dzpx*pz) +
(-dxpy*px + dypx*px + dypz*pz - dzpy*pz)*
(-dxpy*px + dypx*px + dypz*pz - dzpy*pz));
h[x]=Ks*(dxxpx + dxypy + dxzpz) +
Kb*((-dxypy - dxzpz + dyypx + dzzpx)*px*px + (-dxypy + dyypx)*py*py + (dypy*dzpx + dxpy*(dypz - 2*dzpy) + dypx*dzpy + dxpz*(-dypy - 2*dzpz) + 2*dzpx*dzpz)*pz + (-dxzpz + dzzpx)*pz*pz +
py*(dypz*dzpx + dxpz*(-2*dypz + dzpy) + dxpy*(-2*dypy - dzpz) + dypx*(2*dypy + dzpz) + (-dxypz - dxzpy + 2*dyzpx)*pz) +
px*(-dxpy*dxpy - dxpz*dxpz + dypx*dypx + dypz*dypz + dzpx*dzpx - 2*dypz*dzpy + dzpy*dzpy + (-dyzpz + dzzpy)*py + (dyypz - dyzpy)*pz)) +
Kt*((-dxzpz + dzzpx)*py*py + (dxpz*dypy - dypy*dzpx + dypx*(2*dypz - dzpy) + dxpy*(-3*dypz + 2*dzpy))*pz + (- dxypy + dyypx)*pz*pz + py*(-dypz*dzpx + dxpz*(2*dypz - 3*dzpy) + 2*dzpx*dzpy + dxpy*dzpz - dypx*dzpz + ( dxypz + dxzpy - 2*dyzpx)*pz) +
px*(-2*dypz*dypz + 4*dypz*dzpy - 2*dzpy*dzpy + ( dyzpz - dzzpy)*py + (- dyypz + dyzpy)*pz));
h[y]= Ks*(dxypx + dyypy + dyzpz) +
Kb*((dxxpy - dxypx)*px*px + (dxxpy - dxypx - dyzpz + dzzpy)*py*py + (dxpz*dypx + dxpy*dzpx - 2*dypx*dzpx + dxpx*(-dypz + dzpy) - 2*dypz*dzpz + 2*dzpy*dzpz)*pz + (-dyzpz + dzzpy)*pz*pz +
py*(dxpy*dxpy + dxpz*dxpz - dypx*dypx - dypz*dypz - 2*dxpz*dzpx + dzpx*dzpx + dzpy*dzpy + (dxxpz - dxzpx)*pz) +
px*(dxpx*(2*dxpy - 2*dypx) + dypz*dzpx + dxpz*(-2*dypz + dzpy) + dxpy*dzpz - dypx*dzpz + (-dxzpz + dzzpx)*py + (-dxypz + 2*dxzpy - dyzpx)*pz)) +
Kt*((-dyzpz + dzzpy)*px*px + (-3*dxpz*dypx + dxpy*(2*dxpz - dzpx) + 2*dypx*dzpx + dxpx*(dypz - dzpy))*pz + (dxxpy - dxypx)*pz*pz + py*(-2*dxpz*dxpz + 4*dxpz*dzpx - 2*dzpx*dzpx + (-dxxpz + dxzpx)*pz) +
px*(-3*dypz*dzpx + dxpz*(2*dypz - dzpy) + 2*dzpx*dzpy - dxpy*dzpz + dypx*dzpz + (dxzpz - dzzpx)*py + (dxypz - 2*dxzpy + dyzpx)*pz));
h[z]=Ks*(dxzpx + dyzpy + dzzpz) +
Kb*((dxxpz - dxzpx)*px*px + (dyypz - dyzpy)*py*py + (dxpy*dxpy + dxpz*dxpz - 2*dxpy*dypx + dypx*dypx + dypz*dypz - dzpx*dzpx - dzpy*dzpy)*pz + (dxxpz - dxzpx + dyypz - dyzpy)*pz*pz +
py*(dxpz*dypx + dxpy*dzpx - 2*dypx*dzpx + dypy*(2*dypz - 2*dzpy) + dxpx*(dypz - dzpy) + (dxxpy - dxypx)*pz) +
px*(dxpz*dypy + dxpx*(2*dxpz - 2*dzpx) - dypy*dzpx + dxpy*(dypz - 2*dzpy) + dypx*dzpy + (2*dxypz - dxzpy - dyzpx)*py + (-dxypy + dyypx)*pz))+
Kt*((dyypz - dyzpy)*px*px + (dxxpz - dxzpx)*py*py + (-2*dxpy*dxpy + 4*dxpy*dypx - 2*dypx*dypx)*pz + py*(-dxpz*dypx + dxpy*(2*dxpz - 3*dzpx) + 2*dypx*dzpx + dxpx*(-dypz + dzpy) + (-dxxpy + dxypx)*pz) +
px*(-dxpz*dypy + dypy*dzpx + dypx*(2*dypz - 3*dzpy) + dxpy*(-dypz + 2*dzpy) + (-2*dxypz + dxzpy + dyzpx)*py + (dxypy - dyypx)*pz));
//defined as p cross h
Hperp[x]=h[z]*Pol[y]-h[y]*Pol[z];
Hperp[y]=h[x]*Pol[z]-h[z]*Pol[x];
Hperp[z]=h[y]*Pol[x]-h[x]*Pol[y];
sigma[x][x] =
-dxpx*(dxpx + dypy + dzpz)*Ks -
dxpy*Kt*pz*(dypz*px - dzpy*px - dxpz*py + dzpx*py + dxpy*pz - dypx*pz) -
dxpz*Kt*py*(-dypz*px + dzpy*px + dxpz*py - dzpx*py - dxpy*pz + dypx*pz) -
0.5*dxpz*Kb*(2*px*(dxpz*px - dzpx*px + (dypz - dzpy)*py) + 2*pz*(dxpy*py - dypx*py + (dxpz - dzpx)*pz)) -
0.5*dxpy*Kb*(2*py*(dxpy*py - dypx*py + (dxpz - dzpx)*pz) + 2*px*(dxpy*px - dypx*px + (-dypz + dzpy)*pz));
sigma[x][y] =
-Ks*dxpy*(dxpx + dypy + dzpz) +
Kt*(-px*dxpz + dxpx*pz)*(dypz*px - dzpy*px - dxpz*py + dzpx*py + dxpy*pz - dypx*pz) +
Kb*(-py*dxpz*(dxpz*px - dzpx*px + (dypz - dzpy)*py) +
dxpx*py*(dxpy*py - dypx*py + (dxpz - dzpx)*pz) -
dxpz*pz*(-px*dxpy + dypx*px + (dypz - dzpy)*pz) +
dxpx*px*(dxpy*px - dypx*px + (dzpy-dypz)*pz));
sigma[x][z] =
-dxpz*(dxpx + dypy + dzpz)*Ks +
dxpy*Kt*px*(dypz*px - dzpy*px - dxpz*py + dzpx*py + dxpy*pz - dypx*pz) +
dxpx*Kt*py*(-dypz*px + dzpy*px + dxpz*py - dzpx*py - dxpy*pz + dypx*pz) -
0.5*dxpx*Kb*(2*px*(-dxpz*px + dzpx*px + (-dypz + dzpy)*py) - 2*pz*(dxpy*py - dypx*py + (dxpz - dzpx)*pz)) -
0.5*dxpy*Kb*(2*py*(-dxpz*px + dzpx*px + (-dypz + dzpy)*py) - 2*pz*(-dxpy*px + dypx*px + (dypz - dzpy)*pz));
sigma[y][x] =
-dypx*(dxpx + dypy + dzpz)*Ks +
dypz*Kt*py*(dypz*px - dzpy*px - dxpz*py + dzpx*py + dxpy*pz - dypx*pz) -
dypy*Kt*pz*(dypz*px - dzpy*px - dxpz*py + dzpx*py + dxpy*pz - dypx*pz) -
0.5*dypz*Kb*(2*px*(dxpz*px - dzpx*px + (dypz - dzpy)*py) + 2*pz*(dxpy*py - dypx*py + (dxpz - dzpx)*pz)) -
0.5*dypy*Kb*(2*py*(dxpy*py - dypx*py + (dxpz - dzpx)*pz) + 2*px*(dxpy*px - dypx*px + (-dypz + dzpy)*pz));
sigma[y][y] =
-dypy*(dxpx + dypy + dzpz)*Ks -
dypz*Kb*py*(dxpz*px - dzpx*px + (dypz - dzpy)*py) -
dypz*Kt*px*(dypz*px - dzpy*px - dxpz*py + dzpx*py + dxpy*pz - dypx*pz) -
dypx*Kt*pz*(-dypz*px + dzpy*px + dxpz*py - dzpx*py -dxpy*pz + dypx*pz) -
dypx*Kb*py*(-dxpy*py + dypx*py + (-dxpz + dzpx)*pz) -
dypx*Kb*px*(-dxpy*px + dypx*px + (dypz - dzpy)*pz) -
dypz*Kb*pz*(-dxpy*px + dypx*px + (dypz - dzpy)*pz);
sigma[y][z] =
-dypz*(dxpx + dypy + dzpz)*Ks +
dypy*Kt*px*(dypz*px - dzpy*px - dxpz*py + dzpx*py + dxpy*pz - dypx*pz) +
dypx*Kt*py*(-dypz*px + dzpy*px + dxpz*py - dzpx*py -dxpy*pz + dypx*pz) -
0.5*dypx*Kb*(2*px*(-dxpz*px + dzpx*px + (-dypz + dzpy)*py) - 2*pz*(dxpy*py - dypx*py + (dxpz - dzpx)*pz)) -
0.5*dypy*Kb*(2*py*(-dxpz*px + dzpx*px + (-dypz + dzpy)*py) - 2*pz*(-dxpy*px + dypx*px + (dypz - dzpy)*pz));
sigma[z][x] =
-dzpx*(dxpx + dypy + dzpz)*Ks -
dzpz*Kt*py*(-dypz*px + dzpy*px + dxpz*py - dzpx*py - dxpy*pz + dypx*pz) +
dzpy*Kt*pz*(-dypz*px + dzpy*px + dxpz*py - dzpx*py - dxpy*pz + dypx*pz) -
0.5*dzpz*Kb*(2*px*(dxpz*px - dzpx*px + (dypz - dzpy)*py) + 2*pz*(dxpy*py - dypx*py + (dxpz - dzpx)*pz)) -
0.5*dzpy*Kb*(2*py*(dxpy*py - dypx*py + (dxpz - dzpx)*pz) + 2*px*(dxpy*px - dypx*px + (-dypz + dzpy)*pz));
sigma[z][y] =
-dzpy*(dxpx + dypy + dzpz)*Ks -
dzpz*Kb*py*(dxpz*px - dzpx*px + (dypz - dzpy)*py) -
dzpz*Kt*px*(dypz*px - dzpy*px - dxpz*py + dzpx*py + dxpy*pz - dypx*pz) +
dzpx*Kt*pz*(dypz*px - dzpy*px - dxpz*py + dzpx*py + dxpy*pz - dypx*pz) -
dzpx*Kb*py*(-dxpy*py + dypx*py + (-dxpz + dzpx)*pz) -
dzpz*Kb*pz*(-dxpy*px + dypx*px + (dypz - dzpy)*pz) +
dzpx*Kb*px*(dxpy*px - dypx*px + (-dypz + dzpy)*pz);
sigma[z][z] =
-dzpz*(dxpx + dypy + dzpz)*Ks -
dzpx*Kt*py*(dypz*px - dzpy*px - dxpz*py + dzpx*py + dxpy*pz - dypx*pz) -
dzpy*Kt*px*(-dypz*px + dzpy*px + dxpz*py - dzpx*py - dxpy*pz + dypx*pz) -
0.5*dzpx*Kb*(2*px*(-dxpz*px + dzpx*px + (-dypz + dzpy)*py) - 2*pz*(dxpy*py - dypx*py + (dxpz - dzpx)*pz)) -
0.5*dzpy*Kb*(2*py*(-dxpz*px + dzpx*px + (-dypz + dzpy)*py) - 2*pz*(-dxpy*px + dypx*px + (dypz - dzpy)*pz));
Particles.ghost_get<Stress,MolField,HPERP>(SKIP_LABELLING);
auto Hp1=Hperp[x];
auto Hp2=Hperp[y];
auto Hp3=Hperp[z];
texp_v<double>
dxHp1=Dx(Hperp[x]),
dxHp2=Dx(Hperp[y]),
dxHp3=Dx(Hperp[z]),
dyHp1=Dy(Hperp[x]),
dyHp2=Dy(Hperp[y]),
dyHp3=Dy(Hperp[z]),
dzHp1=Dz(Hperp[x]),
dzHp2=Dz(Hperp[y]),
dzHp3=Dz(Hperp[z]);
double dxmu=0;
double dymu=0;
double dzmu=0;
dV[x]= -(-0.5*dzpx*Hp2*px + 0.5*dypx*Hp3*px + 0.5*dzpx*Hp1*py + 0.5*dypy*Hp3*py + 0.5*dzpz*Hp3*py -
0.5*px*(-dzpy*Hp1 + dzpx*Hp2 + dzHp2*px - dzHp1*py) - 0.5*dypx*Hp1*pz - 0.5*dypy*Hp2*pz - 0.5*dzpz*Hp2*pz +
0.5*px*(-dypz*Hp1 + dypx*Hp3 + dyHp3*px - dyHp1*pz) + 0.5*py*(-dypz*Hp2 + dypy*Hp3 + dyHp3*py - dyHp2*pz) -
0.5*pz*(dzpz*Hp2 - dzpy*Hp3 - dzHp3*py + dzHp2*pz)
+
0.5*nu*(-(dypz*Hp1*px) + dzpy*Hp1*px + 2*dxpz*Hp2*px - 2*dzpx*Hp2*px - 2*dxpy*Hp3*px + 2*dypx*Hp3*px + dyHp3*px*px - dzHp2*px*px +
dzpx*Hp1*py + dypz*Hp2*py - 2*dxpx*Hp3*py - 2*dypy*Hp3*py - dzpz*Hp3*py - 2*dxHp3*px*py + dzHp1*px*py - dyHp3*py*py -
dypx*Hp1*pz + 2*dxpx*Hp2*pz + dypy*Hp2*pz + 2*dzpz*Hp2*pz - dzpy*Hp3*pz + 2*dxHp2*px*pz - dyHp1*px*pz + dyHp2*py*pz -
dzHp3*py*pz + dzHp2*pz*pz)
+ nu*gama*lambda*(-(dymu*px*py) - dzmu*px*pz + (dxmu*(-2*px*px + py*py + pz*pz))/3. +
((-4*dxpx*px)/3. - dypy*px - dzpz*px + (2*dxpy*py)/3. - dypx*py + (2*dxpz*pz)/3. - dzpx*pz)*delmu)
+ zeta*(dxmuqxx + dymuqxy + dzmuqxz) + Dx(sigma[x][x]) + Dy(sigma[x][y]) + Dz(sigma[x][z])
);
dV[y]= -(-0.5*dzpy*Hp2*px - 0.5*dxpx*Hp3*px - 0.5*dzpz*Hp3*px + 0.5*dzpy*Hp1*py - 0.5*dxpy*Hp3*py +
0.5*py*(dzpy*Hp1 - 1.*dzpx*Hp2 - 1.*dzHp2*px + dzHp1*py) + 0.5*dxpx*Hp1*pz + 0.5*dzpz*Hp1*pz + 0.5*dxpy*Hp2*pz -
0.5*px*(-1.*dxpz*Hp1 + dxpx*Hp3 + dxHp3*px - 1.*dxHp1*pz) - 0.5*py*(-1.*dxpz*Hp2 + dxpy*Hp3 + dxHp3*py - 1.*dxHp2*pz) +
0.5*pz*(dzpz*Hp1 - 1.*dzpx*Hp3 - 1.*dzHp3*px + dzHp1*pz)
+
0.5*nu*(-(dxpz*Hp1*px) - dzpy*Hp2*px + 2*dxpx*Hp3*px + 2*dypy*Hp3*px + dzpz*Hp3*px + dxHp3*px*px - 2*dypz*Hp1*py + 2*dzpy*Hp1*py +
dxpz*Hp2*py - dzpx*Hp2*py - 2*dxpy*Hp3*py + 2*dypx*Hp3*py + 2*dyHp3*px*py - dzHp2*px*py - dxHp3*py*py + dzHp1*py*py -
dxpx*Hp1*pz - 2*dypy*Hp1*pz - 2*dzpz*Hp1*pz + dxpy*Hp2*pz + dzpx*Hp3*pz - dxHp1*px*pz + dzHp3*px*pz + dxHp2*py*pz -
2*dyHp1*py*pz - dzHp1*pz*pz) +
nu*gama*lambda*(-(dxmu*px*py) - dzmu*py*pz + (dymu*(px*px - 2*py*py + pz*pz))/3. + (-(dxpy*px) + (2*dypx*px)/3. - dxpx*py - (4*dypy*py)/3. - dzpz*py + (2*dypz*pz)/3. - dzpy*pz)*delmu)
+zeta*(dxmuqyx + dymuqyy + dzmuqyz) + Dx(sigma[y][x]) + Dy(sigma[y][y]) + Dz(sigma[y][z])
)
;
dV[z]= -(0.5*dxpx*Hp2*px + 0.5*dypy*Hp2*px + 0.5*dypz*Hp3*px - 0.5*dxpx*Hp1*py - 0.5*dypy*Hp1*py - 0.5*dxpz*Hp3*py +
0.5*px*(-1.*dxpy*Hp1 + dxpx*Hp2 + dxHp2*px - 1.*dxHp1*py) - 0.5*py*(dypy*Hp1 - 1.*dypx*Hp2 - 1.*dyHp2*px + dyHp1*py) -
0.5*dypz*Hp1*pz + 0.5*dxpz*Hp2*pz + 0.5*pz*(dxpz*Hp2 - 1.*dxpy*Hp3 - 1.*dxHp3*py + dxHp2*pz) -
0.5*pz*(dypz*Hp1 - 1.*dypx*Hp3 - 1.*dyHp3*px + dyHp1*pz)
+
0.5*nu*(dxpy*Hp1*px - 2*dxpx*Hp2*px - dypy*Hp2*px - 2*dzpz*Hp2*px + dypz*Hp3*px - dxHp2*px*px + dxpx*Hp1*py + 2*dypy*Hp1*py +
2*dzpz*Hp1*py - dypx*Hp2*py - dxpz*Hp3*py + dxHp1*px*py - dyHp2*px*py + dyHp1*py*py - 2*dypz*Hp1*pz + 2*dzpy*Hp1*pz +
2*dxpz*Hp2*pz - 2*dzpx*Hp2*pz - dxpy*Hp3*pz + dypx*Hp3*pz + dyHp3*px*pz - 2*dzHp2*px*pz - dxHp3*py*pz + 2*dzHp1*py*pz +
dxHp2*pz*pz - dyHp1*pz*pz) +
nu*gama*lambda*(-(dxmu*px*pz) - dymu*py*pz + (dzmu*(px*px + py*py - 2*pz*pz))/3. +
(-(dxpz*px) + (2*dzpx*px)/3. - dypz*py + (2*dzpy*py)/3. - dxpx*pz - dypy*pz - (4*dzpz*pz)/3.)*delmu)
+zeta*(dxmuqzx + dymuqzy + dzmuqzz)+Dx(sigma[z][x])+Dy(sigma[z][y])+Dz(sigma[z][z])
);
Particles.ghost_get<DV>(SKIP_LABELLING);
tt.stop();
PolMag=Pol[x]*Pol[x]+Pol[y]*Pol[y]+Pol[z]*Pol[z];
for (int j = 0; j < bulk.size(); j++) {
auto p = bulk.get<0>(j);
Particles.getProp<POLMAG>(p) = (Particles.getProp<POLMAG>(p) == 0) ? 1 : Particles.getProp<POLMAG>(p);
}
Particles.ghost_get<POLMAG>(SKIP_LABELLING);
polmaginv=1.0/PolMag;
auto zdxvx=Dx(V[x]);
auto zdyvx=Dy(V[x]);
auto zdzvx=Dz(V[x]);
auto zdxxvx=Dxx(V[x]);
auto zdxyvx=Dxy(V[x]);
auto zdyxvx=Dxy(V[x]);
auto zdxzvx=Dxz(V[x]);
auto zdzxvx=Dxz(V[x]);
auto zdyyvx=Dyy(V[x]);
auto zdyzvx=Dyz(V[x]);
auto zdzyvx=Dyz(V[x]);
auto zdzzvx=Dzz(V[x]);
auto zdxvy=Dx(V[y]);
auto zdyvy=Dy(V[y]);
auto zdzvy=Dz(V[y]);
auto zdxxvy=Dxx(V[y]);
auto zdxyvy=Dxy(V[y]);
auto zdyxvy=Dxy(V[y]);
auto zdxzvy=Dxz(V[y]);
auto zdzxvy=Dxz(V[y]);
auto zdyyvy=Dyy(V[y]);
auto zdyzvy=Dyz(V[y]);
auto zdzyvy=Dyz(V[y]);
auto zdzzvy=Dzz(V[y]);
auto zdxvz=Dx(V[z]);
auto zdyvz=Dy(V[z]);
auto zdzvz=Dz(V[z]);
auto zdxxvz=Dxx(V[z]);
auto zdxyvz=Dxy(V[z]);
auto zdyxvz=Dxy(V[z]);
auto zdxzvz=Dxz(V[z]);
auto zdzxvz=Dxz(V[z]);
auto zdyyvz=Dyy(V[z]);
auto zdyzvz=Dyz(V[z]);
auto zdzyvz=Dyz(V[z]);
auto zdzzvz=Dzz(V[z]);
auto Stokes1 = eta * (2*Dxx(V[x]) + Dxy(V[y]) + Dyy(V[x]) + Dxz(V[z]) + Dzz(V[x])) +
(nu*nu*gama)*
(
polmaginv*polmaginv*(-2*px*py*(dypx*px + dypy*py + dypz*pz)*(px*px*zdxvx + px*py*(zdxvy + zdyvx) + py*py*zdyvy + px*pz*(zdxvz + zdzvx) +
py*pz*(zdyvz + zdzvy) +pz*pz*zdzvz) -
2*px*pz*(dzpx*px + dzpy*py + dzpz*pz)*(px*px*zdxvx + px*py*(zdxvy + zdyvx) + py*py*zdyvy + px*pz*(zdxvz + zdzvx) +
py*pz*(zdyvz + zdzvy) +pz*pz*zdzvz) +
1/3.0*(2*(dxpx*px + dxpy*py + dxpz*pz)*(-2*px*px + py*py + pz*pz)*
(px*px*zdxvx + px*py*(zdxvy + zdyvx) + py*py*zdyvy + px*pz*(zdxvz + zdzvx) + py*pz*(zdyvz + zdzvy) +
pz*pz*zdzvz))) +
polmaginv*(((4*dxpx*px)/3. + dypy*px + dzpz*px - (2*dxpy*py)/3. + dypx*py - (2*dxpz*pz)/3. + dzpx*pz)*
(px*px*zdxvx + px*py*(zdxvy + zdyvx) + py*py*zdyvy + px*pz*(zdxvz + zdzvx) + py*pz*(zdyvz + zdzvy) +
pz*pz*zdzvz) +
1/3.0*((2*px*px - py*py - pz*pz)*
(2*dxpx*px*zdxvx + px*px*zdxxvx + py*py*zdxxvy +pz*pz*zdxxvz + dxpy*px*(zdxvy + zdyvx) +
dxpx*py*(zdxvy + zdyvx) + 2*dxpy*py*zdyvy + px*py*(zdxxvy + zdyxvx) + dxpz*px*(zdxvz + zdzvx) +
dxpx*pz*(zdxvz + zdzvx) + dxpz*py*(zdyvz + zdzvy) + dxpy*pz*(zdyvz + zdzvy) + 2*dxpz*pz*zdzvz +
px*pz*(zdxxvz + zdzxvx) + py*pz*(zdyxvz + zdzxvy))) +
px*py*(2*dypx*px*zdxvx + px*px*zdxyvx + dypy*px*(zdxvy + zdyvx) + dypx*py*(zdxvy + zdyvx) + 2*dypy*py*zdyvy +
px*py*(zdxyvy + zdyyvx) + py*py*zdyyvy +pz*pz*zdyzvz + dypz*px*(zdxvz + zdzvx) + dypx*pz*(zdxvz + zdzvx) +
dypz*py*(zdyvz + zdzvy) + dypy*pz*(zdyvz + zdzvy) + 2*dypz*pz*zdzvz + px*pz*(zdxyvz + zdzyvx) +
py*pz*(zdyyvz + zdzyvy)) + px*pz*(2*dzpx*px*zdxvx + px*px*zdxzvx + dzpy*px*(zdxvy + zdyvx) +
dzpx*py*(zdxvy + zdyvx) + 2*dzpy*py*zdyvy + px*py*(zdxzvy + zdyzvx) + py*py*zdyzvy +
dzpz*px*(zdxvz + zdzvx) + dzpx*pz*(zdxvz + zdzvx) + dzpz*py*(zdyvz + zdzvy) + dzpy*pz*(zdyvz + zdzvy) +
2*dzpz*pz*zdzvz + px*pz*(zdxzvz + zdzzvx) + py*pz*(zdyzvz + zdzzvy) +pz*pz*zdzzvz))
)
;
auto Stokes2 = eta * (2*Dyy(V[y]) + Dxx(V[y]) + Dxy(V[x]) + Dyz(V[z]) + Dzz(V[y]))+
(gama*nu*nu)*(
polmaginv*polmaginv*(-2*px*py*(dxpx*px + dxpy*py + dxpz*pz)*(px*px*zdxvx + px*py*(zdxvy + zdyvx) + py*py*zdyvy + px*pz*(zdxvz + zdzvx) +
py*pz*(zdyvz + zdzvy) +pz*pz*zdzvz) -
2*py*pz*(dzpx*px + dzpy*py + dzpz*pz)*(px*px*zdxvx + px*py*(zdxvy + zdyvx) + py*py*zdyvy + px*pz*(zdxvz + zdzvx) +
py*pz*(zdyvz + zdzvy) +pz*pz*zdzvz) +
1/3.0*(2*(dypx*px + dypy*py + dypz*pz)*(px*px - 2*py*py + pz*pz)*
(px*px*zdxvx + px*py*(zdxvy + zdyvx) + py*py*zdyvy + px*pz*(zdxvz + zdzvx) + py*pz*(zdyvz + zdzvy) +
pz*pz*zdzvz)))+
polmaginv*((dxpy*px - (2*dypx*px)/3. + dxpx*py + (4*dypy*py)/3. + dzpz*py - (2*dypz*pz)/3. + dzpy*pz)*
(px*px*zdxvx + px*py*(zdxvy + zdyvx) + py*py*zdyvy + px*pz*(zdxvz + zdzvx) + py*pz*(zdyvz + zdzvy) +
pz*pz*zdzvz) + px*py*(2*dxpx*px*zdxvx + px*px*zdxxvx + py*py*zdxxvy +pz*pz*zdxxvz + dxpy*px*(zdxvy + zdyvx) +
dxpx*py*(zdxvy + zdyvx) + 2*dxpy*py*zdyvy + px*py*(zdxxvy + zdyxvx) + dxpz*px*(zdxvz + zdzvx) +
dxpx*pz*(zdxvz + zdzvx) + dxpz*py*(zdyvz + zdzvy) + dxpy*pz*(zdyvz + zdzvy) + 2*dxpz*pz*zdzvz +
px*pz*(zdxxvz + zdzxvx) + py*pz*(zdyxvz + zdzxvy)) +
1/3.0*((-px*px + 2*py*py - pz*pz)*(2*dypx*px*zdxvx + px*px*zdxyvx + dypy*px*(zdxvy + zdyvx) + dypx*py*(zdxvy + zdyvx) +
2*dypy*py*zdyvy + px*py*(zdxyvy + zdyyvx) + py*py*zdyyvy +pz*pz*zdyzvz + dypz*px*(zdxvz + zdzvx) +
dypx*pz*(zdxvz + zdzvx) + dypz*py*(zdyvz + zdzvy) + dypy*pz*(zdyvz + zdzvy) + 2*dypz*pz*zdzvz +
px*pz*(zdxyvz + zdzyvx) + py*pz*(zdyyvz + zdzyvy))) +
py*pz*(2*dzpx*px*zdxvx + px*px*zdxzvx + dzpy*px*(zdxvy + zdyvx) + dzpx*py*(zdxvy + zdyvx) + 2*dzpy*py*zdyvy +
px*py*(zdxzvy + zdyzvx) + py*py*zdyzvy + dzpz*px*(zdxvz + zdzvx) + dzpx*pz*(zdxvz + zdzvx) +
dzpz*py*(zdyvz + zdzvy) + dzpy*pz*(zdyvz + zdzvy) + 2*dzpz*pz*zdzvz + px*pz*(zdxzvz + zdzzvx) +
py*pz*(zdyzvz + zdzzvy) +pz*pz*zdzzvz))
)
;
auto Stokes3 = eta * (2*Dzz(V[z]) + Dxx(V[z]) + Dxz(V[x]) + Dyy(V[z]) + Dyz(V[y]))
+
(gama*nu*nu)*(
polmaginv*polmaginv*(-2*px*pz*(dxpx*px + dxpy*py + dxpz*pz)*(px*px*zdxvx + px*py*(zdxvy + zdyvx) + py*py*zdyvy + px*pz*(zdxvz + zdzvx) +
py*pz*(zdyvz + zdzvy) + pz*pz*zdzvz) -
2*py*pz*(dypx*px + dypy*py + dypz*pz)*(px*px*zdxvx + px*py*(zdxvy + zdyvx) + py*py*zdyvy + px*pz*(zdxvz + zdzvx) +
py*pz*(zdyvz + zdzvy) + pz*pz*zdzvz) +
1/3.0*(2*(dzpx*px + dzpy*py + dzpz*pz)*(px*px + py*py - 2*pz*pz)*
(px*px*zdxvx + px*py*(zdxvy + zdyvx) + py*py*zdyvy + px*pz*(zdxvz + zdzvx) + py*pz*(zdyvz + zdzvy) +
pz*pz*zdzvz))) +
polmaginv*((dxpz*px - (2*dzpx*px)/3. + dypz*py - (2*dzpy*py)/3. + dxpx*pz + dypy*pz + (4*dzpz*pz)/3.)*
(px*px*zdxvx + px*py*(zdxvy + zdyvx) + py*py*zdyvy + px*pz*(zdxvz + zdzvx) + py*pz*(zdyvz + zdzvy) +
pz*pz*zdzvz) + px*pz*(2*dxpx*px*zdxvx + px*px*zdxxvx + py*py*zdxxvy + pz*pz*zdxxvz + dxpy*px*(zdxvy + zdyvx) +
dxpx*py*(zdxvy + zdyvx) + 2*dxpy*py*zdyvy + px*py*(zdxxvy + zdyxvx) + dxpz*px*(zdxvz + zdzvx) +
dxpx*pz*(zdxvz + zdzvx) + dxpz*py*(zdyvz + zdzvy) + dxpy*pz*(zdyvz + zdzvy) + 2*dxpz*pz*zdzvz +
px*pz*(zdxxvz + zdzxvx) + py*pz*(zdyxvz + zdzxvy)) +
py*pz*(2*dypx*px*zdxvx + px*px*zdxyvx + dypy*px*(zdxvy + zdyvx) + dypx*py*(zdxvy + zdyvx) + 2*dypy*py*zdyvy +
px*py*(zdxyvy + zdyyvx) + py*py*zdyyvy + pz*pz*zdyzvz + dypz*px*(zdxvz + zdzvx) + dypx*pz*(zdxvz + zdzvx) +
dypz*py*(zdyvz + zdzvy) + dypy*pz*(zdyvz + zdzvy) + 2*dypz*pz*zdzvz + px*pz*(zdxyvz + zdzyvx) +
py*pz*(zdyyvz + zdzyvy)) +
1/3.0*((-px*px - py*py + 2*pz*pz)*
(2*dzpx*px*zdxvx + px*px*zdxzvx + dzpy*px*(zdxvy + zdyvx) + dzpx*py*(zdxvy + zdyvx) + 2*dzpy*py*zdyvy +
px*py*(zdxzvy + zdyzvx) + py*py*zdyzvy + dzpz*px*(zdxvz + zdzvx) + dzpx*pz*(zdxvz + zdzvx) +
dzpz*py*(zdyvz + zdzvy) + dzpy*pz*(zdyvz + zdzvy) + 2*dzpz*pz*zdzvz + px*pz*(zdxzvz + zdzzvx) +
py*pz*(zdyzvz + zdzzvy) + pz*pz*zdzzvz)))
)
;
auto eq_sigma_xy=eta * (Dx(V[y]) + Dy(V[x])) +
gama*nu*nu*polmaginv*(px*px*px*py*Dx(V[x]) + px*px*py*py*Dx(V[y]) + px*px*py*py*Dy(V[x]) + px*py*py*py*Dy(V[y]) +
px*px*py*pz*Dx(V[z]) + px*px*py*pz*Dz(V[x]) + px*py*py*pz*Dy(V[z]) + px*py*py*pz*Dz(V[y])+ px*py*pz*pz*Dz(V[z]));
//xy rhs
g_up[x]=-(zeta*delmu*px*py + 0.5*Hp3*px*px + 0.5*Hp3*py*py - 0.5*Hp1*px*pz - 0.5*Hp2*py*pz + (0.5*Hp3*px*px - 0.5*Hp3*py*py - 0.5*Hp1*px*pz + 0.5*Hp2*py*pz -
px*py*gama*lambda*delmu)*nu) - sigma[x][y];
Particles.ghost_get<ExtForce>(SKIP_LABELLING);
if(v_cl.rank()==0){
std::cout << "Init of Velocity took " << tt.getwct() << " seconds." << std::endl;
std::cout << "Calculate velocity (step t=" << t << ")" << std::endl;
}
tt.start();
double V_err = 1, V_err_old,sum=0,sum1=0;
int n = 0;
int nmax = 30;
int errctr, Vreset = 0;
V_err = 1;
n = 0;
errctr = 0;
eq_id vx, vy, vz;
vx.setId(0);
vy.setId(1);
vz.setId(2);
P = 0;
V_t = 0;
DCPSE_scheme<equations3d3Pxz, vector_type> Solver(Particles);
Solver.impose(Stokes1, bulk, RHS[0], vx);
Solver.impose(Stokes2, bulk, RHS[1], vy);
Solver.impose(Stokes3, bulk, RHS[2], vz);
Solver.impose(eq_sigma_xy, Boundary_up, g[x], vx);
Solver.impose(V[y], Boundary_up, 0, vy);
Solver.impose(V[z], Boundary_up, 0, vz);
Solver.impose(V[x], Boundary_down, 0, vx);
Solver.impose(V[y], Boundary_down, 0, vy);
Solver.impose(V[z], Boundary_down, 0, vz);
while (V_err >= V_err_eps && n <= nmax) {
Particles.ghost_get<Pressure>(SKIP_LABELLING);
RHS_bulk[x] = dV[x]+Dx(P);
RHS_bulk[y] = dV[y]+Dy(P);
RHS_bulk[z] = dV[z]+Dz(P);
Particles.ghost_get<VRHS>(SKIP_LABELLING);
Solver.reset_b();
Solver.reset_x_ig();
Solver.impose_b(bulk, RHS[0], vx);
Solver.impose_b(bulk, RHS[1], vy);
Solver.impose_b(bulk, RHS[2], vz);
Solver.impose_b(Boundary_up, g[x], vx);
Solver.impose_b(Boundary_up, 0, vy);
Solver.impose_b(Boundary_up, 0, vz);
Solver.impose_b(Boundary_down, 0, vx);
Solver.impose_b(Boundary_down, 0, vy);
Solver.impose_b(Boundary_down, 0, vz);
Solver.impose_x_ig(bulk, V[x], vx);
Solver.impose_x_ig(bulk, V[y], vy);
Solver.impose_x_ig(bulk, V[z], vz);
Solver.impose_x_ig(Boundary_up, V[x], vx);
Solver.impose_x_ig(Boundary_up, V[y], vy);
Solver.impose_x_ig(Boundary_up, V[z], vz);
Solver.impose_x_ig(Boundary_down, V[x], vx);
Solver.impose_x_ig(Boundary_down, V[y], vy);
Solver.impose_x_ig(Boundary_down, V[z], vz);
Solver.solve_with_solver_ig(solverPetsc, V[x], V[y], V[z]);
V_up[y]=0.0;
V_down[y]=0.0;
Particles.ghost_get<Velocity>(SKIP_LABELLING);
div = -(Dx(V[x]) + Dy(V[y])+Dz(V[z]));
P = P + div;
sum = 0;
sum1 = 0;
for (int j = 0; j < bulk.size(); j++) {
auto p = bulk.get<0>(j);
sum += (Particles.getProp<VT>(p)[0] - Particles.getProp<Velocity>(p)[0]) *
(Particles.getProp<VT>(p)[0] - Particles.getProp<Velocity>(p)[0]) +
(Particles.getProp<VT>(p)[1] - Particles.getProp<Velocity>(p)[1]) *
(Particles.getProp<VT>(p)[1] - Particles.getProp<Velocity>(p)[1]) +
(Particles.getProp<VT>(p)[2] - Particles.getProp<Velocity>(p)[2]) *
(Particles.getProp<VT>(p)[2] - Particles.getProp<Velocity>(p)[2]);
sum1 += Particles.getProp<Velocity>(p)[0] * Particles.getProp<Velocity>(p)[0] +
Particles.getProp<Velocity>(p)[1] * Particles.getProp<Velocity>(p)[1]+
Particles.getProp<Velocity>(p)[2] * Particles.getProp<Velocity>(p)[2];
}
v_cl.sum(sum);
v_cl.sum(sum1);
v_cl.execute();
sum = sqrt(sum);
sum1 = sqrt(sum1);
V_err_old = V_err;
V_err = sum/sum1;
if (V_err > V_err_old || abs(V_err_old - V_err) < 1e-8) {
errctr++;
} else {
errctr = 0;
}
if (n > 5) {
if (errctr > 3) {
if(v_cl.rank()==0){
std::cout << "CONVERGENCE LOOP BROKEN DUE TO INCREASE/VERY SLOW DECREASE IN ERROR : " <<V_err<< std::endl;
}
Vreset = 1;
break;
} else {
Vreset = 0;
}
}
V_t = V;
n++;
if (v_cl.rank() == 0) {
std::cout << "Rel l2 cgs err in V: " << V_err << std::endl;
}
}
tt.stop();
Particles.ghost_get<Velocity>(SKIP_LABELLING);
u[x][x] = Dx(V[x]);
u[x][y] = 0.5 * (Dx(V[y]) + Dy(V[x]));
u[x][z] = 0.5 * (Dx(V[z]) + Dz(V[x]));
u[y][x] = 0.5 * (Dy(V[x]) + Dx(V[y]));
u[y][y] = Dy(V[y]);
u[y][z] = 0.5 * (Dy(V[z]) + Dz(V[y]));
u[z][x] = 0.5 * (Dz(V[x]) + Dx(V[z]));
u[z][y] = 0.5 * (Dz(V[y]) + Dy(V[z]));
u[z][z] = Dz(V[z]);
if (v_cl.rank() == 0) {
std::cout << "Rel l2 cgs err in V = " << V_err << " and took " << tt.getwct() << " seconds with " << n
<< " iterations."
<< std::endl;
}
//t_old=t;
W[x][x] = 0;
W[x][y] = 0.5 * (Dy(V[x]) - Dx(V[y]));
W[x][z] = 0.5 * (Dz(V[x]) - Dx(V[z]));
W[y][x] = 0.5 * (Dx(V[y]) - Dy(V[x]));
W[y][y] = 0;
W[y][z] = 0.5 * (Dz(V[y]) - Dy(V[z]));
W[z][x] = 0.5 * (Dx(V[z]) - Dz(V[x]));
W[z][y] = 0.5 * (Dy(V[z]) - Dz(V[y]));
W[z][z] = 0;
tPolMag=Pol[x]*Pol[x]+Pol[y]*Pol[y]+Pol[z]*Pol[z];
auto it = Particles.getDomainIterator();
while (it.isNext()) {
auto p = it.get();
Particles.getProp<TPOLMAG>(p) = (Particles.getProp<TPOLMAG>(p) == 0) ? 1 : Particles.getProp<TPOLMAG>(p);
++it;
}
Particles.ghost_get<TPOLMAG>(SKIP_LABELLING);
polmaginv=1.0/tPolMag;
Hpar=-gama*(lambda*delmu-nu*polmaginv*(Pol[x]*Pol[x]*u[x][x] + 2*Pol[x]*Pol[y]*u[x][y] + 2*Pol[x]*Pol[z]*u[x][z] + Pol[y]*Pol[y]*u[y][y] + 2*Pol[y]*Pol[z]*u[y][z] + Pol[z]*Pol[z]*u[z][z]));
dPol_bulk[x] = (Hpar*Pol[x] - Hperp[z]*Pol[y] + Hperp[y]*Pol[z])/gama-nu*(Pol[x]*u[x][x]+Pol[y]*u[x][y]+Pol[z]*u[x][z]) + lambda*Pol[x]*delmu + (W[x][x]*Pol[x]+W[x][y]*Pol[y]+W[x][z]*Pol[z])-Pol[x]*div-(V[x]*dxpx+V[y]*dypx+V[z]*dzpx);
dPol_bulk[y] = (Hpar*Pol[y] - Hperp[x]*Pol[z] + Hperp[z]*Pol[x])/gama-nu*(Pol[x]*u[y][x]+Pol[y]*u[y][y]+Pol[z]*u[y][z]) + lambda*Pol[y]*delmu + (W[y][x]*Pol[x]+W[y][y]*Pol[y]+W[y][z]*Pol[z])-Pol[y]*div-(V[x]*dxpy+V[y]*dypy+V[z]*dzpy);
dPol_bulk[z] = (Hpar*Pol[z] - Hperp[y]*Pol[x] + Hperp[x]*Pol[y])/gama-nu*(Pol[x]*u[z][x]+Pol[y]*u[z][y]+Pol[z]*u[z][z]) + lambda*Pol[z]*delmu + (W[z][x]*Pol[x]+W[z][y]*Pol[y]+W[z][z]*Pol[z])-Pol[z]*div-(V[x]*dxpz+V[y]*dypz+V[z]*dzpz);
dPol=dPol/sqrt(PolMag);
dxdt.data.get<0>()=dPol[x];
dxdt.data.get<1>()=dPol[y];
dxdt.data.get<2>()=dPol[z];
}
};
template<typename DX,typename DY,typename DZ,typename DXX,typename DXY,typename DXZ,typename DYY,typename DYZ,typename DZZ>
struct CalcVelocity
{
DX &Dx;
DY &Dy;
DZ &Dz;
DXX &Dxx;
DXY &Dxy;
DXZ &Dxz;
DYY &Dyy;
DYZ &Dyz;
DZZ &Dzz;
//Constructor
int ctr;
double t_old;
//Constructor
CalcVelocity(DX &Dx,DY &Dy,DZ &Dz,DXX &Dxx,DXY &Dxy,DXZ &Dxz,DYY &Dyy,DYZ &Dyz,DZZ &Dzz):Dx(Dx),Dy(Dy),Dz(Dz),Dxx(Dxx),Dxy(Dxy),Dxz(Dxz),Dyy(Dyy),Dyz(Dyz),Dzz(Dzz)
{
ctr = 0;
t_old = -dt;
}
void operator() (state_type_3d_ofp &state, double t)
{
timer tt;
vector_type &Particles= *(vector_type *) vectorGlobal;
vector_type2 &Particles_bulk= *(vector_type2 *) vectorGlobal_bulk;
vector_type2 &Particles_boundary_up= *(vector_type2 *) vectorGlobal_boundary_up;
vector_type2 &Particles_boundary_down= *(vector_type2 *) vectorGlobal_boundary_down;
auto &v_cl = create_vcluster();
auto &bulk=Particles_bulk.getIds();
auto Pol = getV<Polarization>(Particles);
auto Pol_bulk = getV<Polarization>(Particles_bulk);
auto Pol_old = getV<POLD>(Particles);
auto dPol = getV<DPOL>(Particles);
auto tPolMag=getV<TPOLMAG>(Particles);
if (t != 0) {
Pol_bulk[x]=state.data.get<0>();
Pol_bulk[y]=state.data.get<1>();
Pol_bulk[z]=state.data.get<2>();
tPolMag=Pol[x]*Pol[x]+Pol[y]*Pol[y]+Pol[z]*Pol[z];
Pol[x]=Pol[x]/sqrt(tPolMag);
Pol[y]=Pol[y]/sqrt(tPolMag);
Pol[z]=Pol[z]/sqrt(tPolMag);
if (v_cl.rank() == 0) {
std::cout << "Time step " << ctr << " : " << t << " over." <<"dt is set to: "<<(t-t_old)<< std::endl;
std::cout << "----------------------------------------------------------" << std::endl;
}
ctr++;
}
if(ctr%wr_at==0 || ctr==wr_f){
Particles.deleteGhost();
Particles.write_frame("Polar3d", ctr,t,BINARY);
Particles.ghost_get<0>();
}
dPol[x]=Pol[x]-Pol_old[x];
dPol[y]=Pol[y]-Pol_old[y];
dPol[z]=Pol[z]-Pol_old[z];
double MaxRateOfChange=0;
for (int j = 0; j < bulk.size(); j++) {
auto p = bulk.get<0>(j);
for (int i=0;i<3;i++){
if(fabs((Particles.getProp<DPOL>(p)[i]))>MaxRateOfChange)
{
MaxRateOfChange=fabs(Particles.getProp<DPOL>(p)[i]);
}
}
}
v_cl.max(MaxRateOfChange);
v_cl.execute();
if(v_cl.rank()==0)
{std::cout<<"MaxRateOfChange: "<<MaxRateOfChange<<std::endl;
}
if(MaxRateOfChange<max_steady_tol && ctr>5)
{
tt2.stop();
if(v_cl.rank()==0)
{std::cout<<"Steady State Reached."<<std::endl;
std::cout << "The simulation took " << tt2.getcputime() << "(CPU) ------ " << tt2.getwct()
<< "(Wall) Seconds.";}
openfpm_finalize();
exit(0);
}
Pol_old = Pol;
dPol=0;
t_old=t;
state.data.get<0>()=Pol[x];
state.data.get<1>()=Pol[y];
state.data.get<2>()=Pol[z];
}
};
int main(int argc, char* argv[])
{
{ openfpm_init(&argc,&argv);
auto &v_cl = create_vcluster();
tt2.start();
//size_t grd_sz = int(std::atof(argv[1]));
size_t grd_sz_z = 5;//int(std::atof(argv[2]));
double tf = std::atof(argv[1]);
dt = tf/std::atof(argv[2]);
wr_f=int(std::atof(argv[2]));
wr_at=int(std::atof(argv[3]));
V_err_eps = double(std::atof(argv[4]));
//size_t grd_sz=int(sqrt(8.0*std::atof(argv[2])/125.0)+1);
size_t grd_sz=int(sqrt(0.64*std::atof(argv[2]))+1);
double boxsize = 10.0;
const size_t sz[3] = {grd_sz, grd_sz+1, grd_sz_z};
double spacing_p = 10.0 / (sz[0]);
double spacing_np = 10.0 / (sz[1] - 1);
Box<3, double> box({0, 0, 0}, {boxsize, boxsize, (grd_sz_z)*spacing_p});
size_t bc[3] = {PERIODIC, NON_PERIODIC, PERIODIC};
double Lx = box.getHigh(0);
double Ly = box.getHigh(1);
double Lz = box.getHigh(2);
double rCut = 3.9 * spacing_p;
double rCut2 = 3.9 * spacing_p;
int ord = 2;
int ord2 = 2;
double sampling_factor = 3.1;
double sampling_factor2 = 1.9;
Ghost<3, double> ghost(rCut2+spacing_np/8.0);
vector_dist_ws<3, double, ActiveGel3d> Particles(0,box,bc,ghost);
Particles.setPropNames(PropNAMES);
double x0, y0, z0, x1, y1, z1;
x0 = box.getLow(0);
y0 = box.getLow(1);
z0 = box.getLow(2);
x1 = boxsize;
y1 = boxsize;
z1 = boxsize;
if (v_cl.rank() == 0) {
std::cout<<"GridSize:"<<sz[0]<<"x"<<sz[1]<<"x"<<sz[2]<<std::endl;
std::cout<<"Spacing Periodic:"<<spacing_p<<", Spacing Np:"<<spacing_np<<std::endl;
}
auto it = Particles.getGridIterator(sz);
while (it.isNext()) {
Particles.add();
auto key = it.get();
double x = key.get(0) * spacing_p;
Particles.getLastPos()[0] = x;
double y = key.get(1) * spacing_np;
if (key.get(1)==grd_sz)
{
Particles.getLastPos()[1] = 10.0-1e-6;
}
else if (key.get(1)==0)
{
Particles.getLastPos()[1] = 0.0+1e-6;
}
else
{
Particles.getLastPos()[1] = y;
}
double z = key.get(2) * spacing_p;
Particles.getLastPos()[2] = z;
if (y>10.0-spacing_np/8.0)
{
Particles.getLastSubset(1);
}
else if (y<spacing_np/8.0)
{
Particles.getLastSubset(2);
}
else
{
Particles.getLastSubset(0);
}
++it;
}
Particles.map();
Particles.ghost_get<Polarization,DPOL,DELMU,ExtForce>();
auto Pol = getV<Polarization>(Particles);
auto dPol= getV<DPOL>(Particles);
auto Pol_old = getV<POLD>(Particles);
auto g = getV<ExtForce>(Particles);
auto V = getV<Velocity>(Particles);
auto P = getV<Pressure>(Particles);
auto delmu=getV<DELMU>(Particles);
auto PolMag=getV<POLMAG>(Particles);
g = 0;
delmu = dmu;
P = 0;
V = 0;
Pol_old=0;
Particles.ghost_get<ExtForce>(SKIP_LABELLING);
double theta0,IPx=0,IPy=0;
auto it2 = Particles.getDomainIterator();
while (it2.isNext()) {
auto p = it2.get();
Point<3, double> xp = Particles.getPos(p);
Particles.getProp<0>(p)[x] = cos(M_PI * xp[y] / (2.0 * Ly));
Particles.getProp<0>(p)[y] = sin(M_PI * xp[y] / (2.0 * Ly));
Particles.getProp<0>(p)[z] = 0;
if (xp[1]==y1)
{
Particles.getProp<0>(p)[x] = 0;
Particles.getProp<0>(p)[y] = 1.0;
Particles.getProp<0>(p)[z] = 0;
}
++it2;
}
vector_dist_subset<3, double, ActiveGel3d> Particles_bulk(Particles,0);
vector_dist_subset<3, double, ActiveGel3d> Particles_boundary_up(Particles,1);
vector_dist_subset<3, double, ActiveGel3d> Particles_boundary_dw(Particles,2);
auto Pol_bulk = getV<Polarization>(Particles_bulk);
auto & bulk = Particles_bulk.getIds();
auto & Boundary_up = Particles_boundary_up.getIds();
auto & Boundary_down = Particles_boundary_dw.getIds();
Derivative_x Dx(Particles, ord, rCut, sampling_factor, support_options::RADIUS);
Derivative_y Dy(Particles, ord, rCut, sampling_factor, support_options::RADIUS);
Derivative_z Dz(Particles, ord, rCut, sampling_factor, support_options::RADIUS);
Derivative_xy Dxy(Particles, ord, rCut2, sampling_factor2, support_options::RADIUS);
Derivative_yz Dyz(Particles, ord, rCut2, sampling_factor2, support_options::RADIUS);
Derivative_xz Dxz(Particles, ord, rCut2, sampling_factor2, support_options::RADIUS);
auto Dyx = Dxy;
auto Dzy = Dyz;
auto Dzx = Dxz;
Derivative_xx Dxx(Particles, ord, rCut2, sampling_factor2,
support_options::RADIUS);
Derivative_yy Dyy(Particles, ord, rCut2, sampling_factor2,
support_options::RADIUS);
Derivative_zz Dzz(Particles, ord, rCut2, sampling_factor2,
support_options::RADIUS);
Particles.write("Init");
vectorGlobal=(void *) &Particles;
vectorGlobal_bulk=(void *) &Particles_bulk;
vectorGlobal_boundary_up=(void *) &Particles_boundary_up;
vectorGlobal_boundary_down=(void *) &Particles_boundary_dw;
PolarEv<Derivative_x,Derivative_y,Derivative_z,Derivative_xx,Derivative_xy,Derivative_xz,Derivative_yy,Derivative_yz,Derivative_zz> System(Dx,Dy,Dz,Dxx,Dxy,Dxz,Dyy,Dyz,Dzz);
CalcVelocity<Derivative_x,Derivative_y,Derivative_z,Derivative_xx,Derivative_xy,Derivative_xz,Derivative_yy,Derivative_yz,Derivative_zz> CalcVelocityObserver(Dx,Dy,Dz,Dxx,Dxy,Dxz,Dyy,Dyz,Dzz);
state_type_3d_ofp tPol;
tPol.data.get<0>()=Pol[x];
tPol.data.get<1>()=Pol[y];
tPol.data.get<2>()=Pol[z];
dPol=0.0;
//V_t = V;
PolMag=Pol[x]*Pol[x]+Pol[y]*Pol[y]+Pol[z]*Pol[z];
Particles.ghost_get<Polarization>(SKIP_LABELLING);
double tim = 0;
std::vector<double> inter_times;
std::ofstream myFile("PolMag");
myFile <<argv[1]<<","<<argv[2]<<","<<argv[3]<<","<<argv[4]<<","<< "\n";
myFile.close();
boost::numeric::odeint::adams_bashforth_moulton<2,state_type_3d_ofp,double,state_type_3d_ofp,double,boost::numeric::odeint::vector_space_algebra_ofp> abm;
size_t steps;
steps = boost::numeric::odeint::integrate_const(abm , System , tPol , tim , tf , dt, CalcVelocityObserver);
std::cout << "Time steps: " << steps << std::endl;
Pol_bulk[x]=tPol.data.get<0>();
Pol_bulk[y]=tPol.data.get<1>();
Pol_bulk[z]=tPol.data.get<2>();
Particles.deleteGhost();
Particles.write_frame("anaEul", wr_f,tf,BINARY);
Particles.save("EulEND");
Dx.deallocate(Particles);
Dy.deallocate(Particles);
Dz.deallocate(Particles);
Dxy.deallocate(Particles);
Dxz.deallocate(Particles);
Dyz.deallocate(Particles);
Dxx.deallocate(Particles);
Dyy.deallocate(Particles);
Dzz.deallocate(Particles);
Particles.deleteGhost();
tt2.stop();
if (v_cl.rank() == 0) {
std::cout << "The simulation took " << tt2.getcputime() << "(CPU) ------ " << tt2.getwct()
<< "(Wall) Seconds.";
}
}
openfpm_finalize();
}