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solver.cpp
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#include "phase_field.h"
const static int max_num_nonzero_stencil=10;
// void phase_field::Phase_field_solver(const int i,const int j,const int k,const real Pfm_dt) {
// Array<int,1> index_grain_nonzero_stencil(max_num_nonzero_stencil,fortranArray);//assume there are at most 10 non-zero phase-fields on all stencil-points,7-stencil pattern is used in 3D.
// index_grain_nonzero_stencil=0;
// Array<int,1> index_phase_nonzero_stencil(max_num_nonzero_stencil,fortranArray);
// index_phase_nonzero_stencil=0;
// int num_nonzero_local=0,num_nonzero_stencil=0;//number of nonzeros in index_grain_nonzero_stencil.
// // int neighbors[7][3]={0};
// // int ii,jj,kk,nn;
// Array<real,2> value_grain_nonzero_stencil(max_num_nonzero_stencil,2,fortranArray);
// value_grain_nonzero_stencil=0.;
// //cout<<"call"<<endl;
// Array<int,2> neighbors(3,6,fortranArray);
// neighbors=
// Get_neighbor(i,ix,-1),j,k,
// Get_neighbor(i,ix,1 ),j,k,
// i,Get_neighbor(j,iy,-1),k,
// i,Get_neighbor(j,iy,1 ),k,
// i,j,Get_neighbor(k,iz,-1),
// i,j,Get_neighbor(k,iz,1 );
//
// for(int ii=1; ii<=max_num_coexist; ii++) {
// if(value_grain1(ii,i,j,k)>cutoff) {
// num_nonzero_local+=1;
// index_grain_nonzero_stencil(ii)=index_grain1(ii,i,j,k);
// index_phase_nonzero_stencil(ii)=Phase_of_grain(index_grain1(ii,i,j,k));
// value_grain_nonzero_stencil(ii,1)=value_grain1(ii,i,j,k);
// }
// }
//
// num_nonzero_stencil=num_nonzero_local;
//
// for(int ii=1; ii<=2*dimensions; ii++) {
// for(int jj=1; jj<=max_num_coexist; jj++) {
// int temp_index=index_grain1(jj,neighbors(1,ii),neighbors(2,ii),neighbors(3,ii));
//
// if(temp_index==0)break;
//
// //cout<<"d";
// real temp_value=value_grain1(jj,neighbors(1,ii),neighbors(2,ii),neighbors(3,ii));
// int kk;
//
// for(kk=1; kk<=max_num_nonzero_stencil; kk++) {
// if(temp_index==index_grain_nonzero_stencil(kk)) {
// value_grain_nonzero_stencil(kk,2)+=temp_value;
// break;
// }
// }
//
// //cout<<kk<<" "<<max_num_nonzero_stencil<<endl;
// if(kk>max_num_nonzero_stencil&&num_nonzero_stencil<max_num_nonzero_stencil) {
// //cout<<"d";
// num_nonzero_stencil+=1;
// index_grain_nonzero_stencil(num_nonzero_stencil)=temp_index;
// index_phase_nonzero_stencil(num_nonzero_stencil)=Phase_of_grain(temp_index);
// value_grain_nonzero_stencil(num_nonzero_stencil,2)+=temp_value;
// }
// }
// }
//
// if(num_nonzero_stencil==1) {
// for(int ii=1; ii<=max_num_coexist; ii++) {
// index_grain2(ii,i,j,k)=index_grain1(ii,i,j,k);
// value_grain2(ii,i,j,k)=value_grain1(ii,i,j,k);
// }
//
// return;
// }
//
// //---------------------------------------------------------------------------------------------
// //=============================================================================================
// /*======now,three arrays to be used for calculation:
// * index_grain_nonzero_stencil,index_phase_nonzero_stencil,value_grain_nonzero_stencil.
// *
// */
// Array<real,1> del_value(max_num_nonzero_stencil,fortranArray);
// del_value=0.;
// real factor1=1./(dx*dx),
// factor2=pi*pi/(2.*eta*eta),
// factor3=pi/eta;
//
// for(int ii=1; ii<=num_nonzero_stencil; ii++) {
// int grainii=index_grain_nonzero_stencil(ii);
// int phaseii=index_phase_nonzero_stencil(ii);
//
// for(int jj=1; (jj<=num_nonzero_stencil); jj++) {
// if (ii==jj)continue;
//
// int grainjj=index_grain_nonzero_stencil(jj);
// int phasejj=index_phase_nonzero_stencil(jj);
//
// // if(grainii<max_num_grains_per_phase&&grainjj<max_num_grains_per_phase)continue;//no interaction between deformed grain.
// if(abs(phaseii-phasejj)==2)continue; //no interaction between pearlite and ferrite.
//
// real del_value_ij=0.;
// del_value_ij=(value_grain_nonzero_stencil(ii,2)*value_grain_nonzero_stencil(jj,1)-
// value_grain_nonzero_stencil(jj,2)*value_grain_nonzero_stencil(ii,1))*factor1;
// del_value_ij+=(value_grain_nonzero_stencil(ii,1)-value_grain_nonzero_stencil(jj,1))*factor2;
// del_value_ij*=intf_energy(phaseii,phasejj);
// //
// del_value_ij+=factor3*sqrt( value_grain_nonzero_stencil(ii,1)*value_grain_nonzero_stencil(jj,1) )*
// Driving_force(grainii,phaseii,grainjj,phasejj,value_conc1(phaseii,i,j,k),value_conc1(phasejj,i,j,k));
// del_value_ij*=mobility(phaseii,phasejj);
// del_value(ii)+=del_value_ij;
// }
//
// del_value(ii)*=Pfm_dt;
// del_value(ii)+=value_grain_nonzero_stencil(ii,1);
//
// if(del_value(ii)>1.0)del_value(ii)=1.0;
//
// else if(del_value(ii)<cutoff)del_value(ii)=0.;
// }
//
// Sort_xyz(del_value,index_grain_nonzero_stencil,max_num_nonzero_stencil);
// real sum_del_value=0.;
//
// for(int ii=1; ii<=max_num_coexist; ii++) {
// int index=Phase_of_grain( index_grain_nonzero_stencil(ii) );
//
// if (del_value(ii)>cutoff) {
// index_grain2(ii,i,j,k)=index_grain_nonzero_stencil(ii);
// value_grain2(ii,i,j,k)=del_value(ii);
// value_phase(index,i,j,k)+=del_value(ii);
// sum_del_value+=del_value(ii);
//
// } else {
// index_grain2(ii,i,j,k)=0;
// value_grain2(ii,i,j,k)=0.;
// value_phase(index,i,j,k)=0.;
// }
// }
//
// for(int ii=1; ii<=max_num_coexist; ii++)
// value_grain2(ii,i,j,k)*=1./sum_del_value;
//
// for(int ii=1; ii<=max_num_phase; ii++)
// value_phase(ii,i,j,k)*=1./sum_del_value;
//
// //Partitioning(total_conc(i,j,k),&value_phase(1,i,j,k),&value_conc1(1,i,j,k));
// Array<double,1> temp_conc(value_conc1(Range::all(),i,j,k));
// Partitioning(total_conc(i,j,k),value_phase(Range::all(),i,j,k),temp_conc);
// return;
// }
void phase_field::Phase_field_solver(const int i,const int j,const int k,const double Pfm_dt) {
const static int max_num_nonzero_stencil=10;
Array<int,1> index_grain_nonzero_stencil(max_num_nonzero_stencil,fortranArray);//assume there are at most 10 non-zero phase-fields on all stencil-points,7-stencil pattern is used in 3D.
index_grain_nonzero_stencil=0;
Array<int,1> index_phase_nonzero_stencil(max_num_nonzero_stencil,fortranArray);
index_phase_nonzero_stencil=0;
int num_nonzero_local=0,num_nonzero_stencil=0;//number of nonzeros in index_grain_nonzero_stencil.
// int neighbors[7][3]={0};
// int ii,jj,kk,nn;
Array<double,2> value_grain_nonzero_stencil(max_num_nonzero_stencil,2,fortranArray);
value_grain_nonzero_stencil=0.;
//cout<<"call"<<endl;
Array<int,2> neighbors(3,6,fortranArray);
neighbors=
Get_neighbor(i,ix,-1),j,k,
Get_neighbor(i,ix,1 ),j,k,
i,Get_neighbor(j,iy,-1),k,
i,Get_neighbor(j,iy,1 ),k,
i,j,Get_neighbor(k,iz,-1),
i,j,Get_neighbor(k,iz,1 );
for(int ii=1; ii<=max_num_coexist; ii++) {
if(value_grain1(ii,i,j,k)>cutoff) {
num_nonzero_local+=1;
index_grain_nonzero_stencil(ii)=index_grain1(ii,i,j,k);
index_phase_nonzero_stencil(ii)=Phase_of_grain(index_grain1(ii,i,j,k));
value_grain_nonzero_stencil(ii,1)=value_grain1(ii,i,j,k);
}
}
num_nonzero_stencil=num_nonzero_local;
for(int ii=1; ii<=2*dimensions; ii++) {
for(int jj=1; jj<=max_num_coexist; jj++) {
int temp_index=index_grain1(jj,neighbors(1,ii),neighbors(2,ii),neighbors(3,ii));
if(temp_index==0)break;
//cout<<"d";
double temp_value=value_grain1(jj,neighbors(1,ii),neighbors(2,ii),neighbors(3,ii));
int kk;
for(kk=1; kk<=max_num_nonzero_stencil; kk++) {
if(temp_index==index_grain_nonzero_stencil(kk)) {
value_grain_nonzero_stencil(kk,2)+=temp_value;
break;
}
}
//cout<<kk<<" "<<max_num_nonzero_stencil<<endl;
if(kk>max_num_nonzero_stencil&&num_nonzero_stencil<max_num_nonzero_stencil) {
//cout<<"d";
num_nonzero_stencil+=1;
index_grain_nonzero_stencil(num_nonzero_stencil)=temp_index;
index_phase_nonzero_stencil(num_nonzero_stencil)=Phase_of_grain(temp_index);
value_grain_nonzero_stencil(num_nonzero_stencil,2)+=temp_value;
}
}
}
if(num_nonzero_stencil==1) {
for(int ii=1; ii<=max_num_coexist; ii++) {
index_grain2(ii,i,j,k)=index_grain1(ii,i,j,k);
value_grain2(ii,i,j,k)=value_grain1(ii,i,j,k);
}
// index_grain2(Range::all(),i,j,k)=index_grain1(Range::all(),i,j,k);
//value_grain2(Range::all(),i,j,k)=value_grain1(Range::all(),i,j,k);
return;
}
//---------------------------------------------------------------------------------------------
//=============================================================================================
/*======now,three arrays to be used for calculation:
* index_grain_nonzero_stencil,index_phase_nonzero_stencil,value_grain_nonzero_stencil.
*
*/
Array<double,1> del_value(max_num_nonzero_stencil,fortranArray);
del_value=0.;
double factor1=1./(dx*dx),
factor2=pi*pi/(2.*eta*eta),
factor3=pi/eta;
Array<double,1> local_conc(max_num_phase,fortranArray);
for(int ii=1; ii<=max_num_phase; ii++)
local_conc(ii)=value_conc1(ii,i,j,k);
//cout<<"num_non "<<num_nonzero_stencil<<endl;
for(int ii=1; ii<=num_nonzero_stencil; ii++) {
int grainii=index_grain_nonzero_stencil(ii);
int phaseii=index_phase_nonzero_stencil(ii);
for(int jj=1; (jj<=num_nonzero_stencil); jj++) {
if (ii==jj)continue;
int grainjj=index_grain_nonzero_stencil(jj);
int phasejj=index_phase_nonzero_stencil(jj);
// if(grainii<max_num_grains_per_phase&&grainjj<max_num_grains_per_phase)continue;//no interaction between deformed grain.
if(abs(phaseii-phasejj)==2)continue; //no interaction between pearlite and ferrite.
double del_value_ij=0.;
del_value_ij=(value_grain_nonzero_stencil(ii,2)*value_grain_nonzero_stencil(jj,1)-
value_grain_nonzero_stencil(jj,2)*value_grain_nonzero_stencil(ii,1))*factor1;
del_value_ij+=(value_grain_nonzero_stencil(ii,1)-value_grain_nonzero_stencil(jj,1))*factor2;
del_value_ij*=intf_energy(phaseii,phasejj);
//
del_value_ij+=factor3*sqrt( value_grain_nonzero_stencil(ii,1)*value_grain_nonzero_stencil(jj,1) )*
Driving_force(grainii,phaseii,grainjj,phasejj,local_conc(phaseii),local_conc(phasejj));
del_value_ij*=mobility(phaseii,phasejj);
del_value(ii)+=del_value_ij;
}
del_value(ii)*=Pfm_dt;
del_value(ii)+=value_grain_nonzero_stencil(ii,1);
if(del_value(ii)>1.0)del_value(ii)=1.0;
else if(del_value(ii)<cutoff)del_value(ii)=0.;
}
//index_grain2(Range::all(),i,j,k)=0;
//value_grain2(Range::all(),i,j,k)=0.;
for(int ii=1; ii<=max_num_phase; ii++)
value_phase(ii,i,j,k)=0.;
Sort_xyz(del_value,index_grain_nonzero_stencil,max_num_nonzero_stencil);
// for(int ii=1;ii<=max_num_nonzero_stencil;ii++)
// index_phase_nonzero_stencil(ii)=Phase_of_grain(index_grain_nonzero_stencil(ii));
double sum_del_value=0.;
for(int ii=1; ii<=max_num_coexist; ii++) {
if (del_value(ii)>cutoff) {
index_grain2(ii,i,j,k)=index_grain_nonzero_stencil(ii);
value_grain2(ii,i,j,k)=del_value(ii);
int index=Phase_of_grain( index_grain_nonzero_stencil(ii) );
value_phase(index,i,j,k)+=del_value(ii);
sum_del_value+=del_value(ii);
} else {
index_grain2(ii,i,j,k)=0;
value_grain2(ii,i,j,k)=0.;
}
}
for(int ii=1; ii<=max_num_coexist; ii++)
value_grain2(ii,i,j,k)*=1./sum_del_value;
for(int ii=1; ii<=max_num_phase; ii++)
value_phase(ii,i,j,k)*=1./sum_del_value;
//Partitioning(total_conc(i,j,k),value_phase(Range::all(),i,j,k),local_conc);
Partitioning(total_conc(i,j,k),&value_phase(1,i,j,k),&value_conc1(1,i,j,k));
//value_conc2(Range::all(),i,j,k)//=local_conc;
// cout<<"run"<<endl;
;
return;
}
/*
void phase_field::Diffusion_solver(const int i,const int j,const int k,const double diff_dt)
{
//Array<int,2> neighbors(3,6,fortranArray);
int neighbors[6][3];
#pragma ivdep
for(int ii=0;ii<6;ii++)
{
neighbors[ii][0]=i;
neighbors[ii][1]=j;
neighbors[ii][2]=k;
}
neighbors[0][0]=Get_neighbor(i,ix,-1);
neighbors[1][0]=Get_neighbor(i,ix,1 );
neighbors[2][1]=Get_neighbor(j,iy,-1);
neighbors[3][1]=Get_neighbor(j,iy,1 );
neighbors[4][2]=Get_neighbor(k,iz,-1);
neighbors[5][2]=Get_neighbor(k,iz,1 );
double del_conc=0.;
for(int ii=0;ii<2*dimensions;ii++)
for(int jj=1;jj<=max_num_phase;jj++)
// del_conc+=sqrt( value_phase(jj,neighbors(1,ii),neighbors(2,ii),neighbors(3,ii))*value_phase(jj,i,j,k) )*
// ( value_conc1(jj,neighbors(1,ii),neighbors(2,ii),neighbors(3,ii))-value_conc1(jj,i,j,k) )*C_diffusivity(jj);
del_conc+=sqrt( value_phase(jj,neighbors[ii][0],neighbors[ii][1],neighbors[ii][2])*value_phase(jj,i,j,k) )*
( value_conc1(jj,neighbors[ii][0],neighbors[ii][1],neighbors[ii][2])-value_conc1(jj,i,j,k) )*C_diffusivity(jj);
del_conc*=(diff_dt/(dx*dx));
total_conc(i,j,k)+=del_conc;
Array<double,1> temp_conc(value_conc2(Range::all(),i,j,k));
Partitioning( total_conc(i,j,k),value_phase(Range::all(),i,j,k),temp_conc );
return;
}*/
void phase_field::Diffusion_solver(const int i,const int j,const int k,const real diff_dt) {
//Array<int,2> neighbors(3,6,fortranArray);
int neighbors[6][3];
for(int ii=0; ii<6; ii++) {
neighbors[ii][0]=i;
neighbors[ii][1]=j;
neighbors[ii][2]=k;
}
neighbors[0][0]=Get_neighbor(i,ix,-1);
neighbors[1][0]=Get_neighbor(i,ix,1 );
neighbors[2][1]=Get_neighbor(j,iy,-1);
neighbors[3][1]=Get_neighbor(j,iy,1 );
neighbors[4][2]=Get_neighbor(k,iz,-1);
neighbors[5][2]=Get_neighbor(k,iz,1 );
real del_conc=0.;
for(int ii=0; ii<2*dimensions; ii++)
for(int jj=1; jj<=max_num_phase; jj++)
del_conc+=sqrt( value_phase(jj,neighbors[ii][0],neighbors[ii][1],neighbors[ii][2])*value_phase(jj,i,j,k) )*
( value_conc1(jj,neighbors[ii][0],neighbors[ii][1],neighbors[ii][2])-value_conc1(jj,i,j,k) )*C_diffusivity(jj);
del_conc*=(diff_dt/(dx*dx));
total_conc(i,j,k)+=del_conc;
Partitioning( total_conc(i,j,k),&value_phase(1,i,j,k),&value_conc2(1,i,j,k) );
//Array<double,1> temp_conc(value_conc2(Range::all(),i,j,k));
//Partitioning(total_conc(i,j,k),value_phase(Range::all(),i,j,k),temp_conc);
return;
}
real phase_field::Driving_force(const int grainii,const int phaseii,const int grainjj,const int phasejj,const real concii,const real concjj) const {
real df=0.;
// if(grainii<max_num_grains_per_phase)
// df-=2e-12;//rex_energy(grainii);
// else if(grainjj<max_num_grains_per_phase)
// df+=2e-12;//rex_energy(grainjj);
if(phaseii!=phasejj)
//int i=max(phaseii,phasejj);
//int j=min(phaseii,phasejj);
df+=thermodynamic.para_entropy(phaseii,phasejj)*(concii-thermodynamic.para_equilibrium_conc(phaseii,phasejj))/thermodynamic.para_equilibrium_dc_dT(phaseii,phasejj);
return df;
}
void phase_field::Partitioning(const real local_conc,const real* phase_array,real* conc_array) {
for(int i=1; i<=max_num_phase; i++) {
real t1=0.,t2=0.;
const real *frac_ptr=phase_array;
for (int j=1; j<=max_num_phase; j++) {
t1+=*frac_ptr*thermodynamic.para_partition_k(i,j);
t2+=*frac_ptr*thermodynamic.para_partition_c(i,j);
frac_ptr++;
}
*conc_array=(local_conc-t2)/t1;
conc_array++;
}
return;
}
// void phase_field::Partitioning(const double local_conc,const Array<double,1>& phase_array,Array<double,1> & conc_array)
// {
// for(int i=1;i<=max_num_phase;i++)
// {
// double t1=0.,t2=0.;
// for (int j=1;j<=max_num_phase;j++)
// {
// t1+=phase_array(j)*thermodynamic.para_partition_k(i,j);
// t2+=phase_array(j)*thermodynamic.para_partition_c(i,j);
// //cout<<t1<<" "<<thermodynamic.para_partition_k(i,j)<<" ";
// }
// conc_array(i)=(local_conc-t2)/t1;
//
// }
// //cout<<endl;
// //cout<<phase_array<<endl;
// //cout<<conc_array<<endl;
// return;
// }
void phase_field::Sort_xyz(Array<real,1>& value,Array<int,1>& grain,const int N) {
for(int i=1; i<=N; i++) {
TinyVector<int,1> max_index=maxIndex(value(Range(i,N)))+(i-1);
std::swap(value(i),value(max_index));
std::swap(grain(i),grain(max_index));
}
}