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Copy pathImportant_Procedure.cpp
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Important_Procedure.cpp
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// Important_Procedure.cpp
// 2017/5/22 : 2D output is added
// 2017/5/25 : In order to spare stack space, change arguments of function from class type to class referrence type, for example, in 'cal_flux' and 'set_dt' and 'step_on'
// 2017/7/16 : Add iosthermal process when initial energy with pressure and calculating pressure
#include <iostream>
#include <fstream>
#include <iomanip>
#include <cmath>
using namespace std;
#include "Basic_Parameter.h"
#include "Physics_Parameter.h"
#include "Variables_Definition.h"
#include "Procedure.h"
#ifndef min
#define min(a,b) (a<b ? a : b)
#endif
// Clarification of mesh-grid
extern double X[], Y[], Z[], X_interval[], Y_interval[], Z_interval[];
extern int nstep;
double sub_var[8][Grid_Num_x][Grid_Num_y][Grid_Num_z]; //subsidiary_variable
double var_x[8][Grid_Num_x], var_x_plushalfdx[8][Grid_Num_x]; // fx, fxi, used in 2-Lax_Wendroff stepon
// For following procedures
ofstream max_dt_out("max_dt.txt");
ofstream min_dt_out("min_dt.txt");
ofstream pre_out("pressure_is_negative.txt");
void set_mesh()
{
int nx,ny,nz;
int out_Grid_x, out_Grid_y, out_Grid_z;
ofstream out("grid.dat");
X[0]=x_min; Y[0]=y_min; Z[0]=z_min;
nx=Grid_Num_x-1; ny=Grid_Num_y-1; nz=Grid_Num_z-1;
out_Grid_x=(Grid_Num_x-1)/num_out; out_Grid_y=(Grid_Num_y-1)/num_out; out_Grid_z=(Grid_Num_z-1)/num_out;
int i,j,k;
if (uniform_x==True)
{
for (i=0;i<nx;i++)
{
X_interval[i]=(x_max-x_min)/nx;
X[i+1]=X[i]+X_interval[i];
}
}
else
{
for (i=0;i<nx;i++)
{
X_interval[i]=0.01;
X[i+1]=X[i]+X_interval[i];
}
}
X_interval[Grid_Num_x-1]=X_interval[Grid_Num_x-2];
if (uniform_y==True)
{
for (j=0;j<ny;j++)
{
Y_interval[j]=(y_max-y_min)/ny;
Y[j+1]=Y[j]+Y_interval[j];
}
}
else
{
for (j=0;j<ny;j++)
{
Y_interval[j]=0.01;
Y[j+1]=Y[j]+Y_interval[j];
}
}
Y_interval[Grid_Num_y-1]=Y_interval[Grid_Num_y-2];
if (uniform_z==True)
{
for (k=0;k<nz;k++)
{
Z_interval[k]=(z_max-z_min)/nz;
Z[k+1]=Z[k]+Z_interval[k];
}
}
else
{
for (k=0;k<nz;k++)
{
Z_interval[k]=0.01;
Z[k+1]=Z[k]+Z_interval[k];
}
}
Z_interval[Grid_Num_z-1]=Z_interval[Grid_Num_z-2];
out<<setiosflags(ios::fixed)<<setprecision(6);
for (i=0;i<=num_out;i++)
out<<setw(10)<<X[i*out_Grid_x]<<" ";
out<<endl;
if (out_Grid_y !=0)
for (j=0;j<=num_out;j++)
out<<setw(10)<<Y[j*out_Grid_y]<<" ";
out<<endl;
for (k=0;k<=num_out;k++)
out<<setw(10)<<Z[k*out_Grid_z]<<" ";
out<<endl;
out.close();
//cout<<"BASIC_VARIABLE::set_mesh invoked!"<<endl;
// Set mesh-grid
}
/*
Initialising variables and setting mesh-grid, where
pointer points to a variable array, the Main Variables,
and pressure_obj is a referrence to Pressure variable.
This function will initialize the Main Variables pointed by pointer,
and Pressure variable referred by pressure_obj.
*/
void initialize(VARIABLE *pointer, BASIC_VARIABLE &pressure_obj)
{
double rm,rs,bm,bs,v0,betam, pressuremtotal;
double x,y,z, dx,dy,dz, r5;
double rho, Bx, By, Bz, rhoVx, rhoVy, rhoVz;
double B_Energy, V_Energy, pressure;
// Following used are global variables listed in "Basic_Parameter.h"
rm=rho_m_0; rs=rho_s_0;
bm=B_m_0; bs=B_s_0;
v0=v_0;
betam=beta_m;
pressuremtotal=betam*0.5*pow(bm,2)+0.5*pow(bm,2); //betam*0.5*pow(bm,2)=pmsp
VARIABLE *current=new VARIABLE[3];
VARIABLE *sub_mag_field=new VARIABLE[3]; //sub_ for subsidary
int i,j,k,n;
for (i=0;i<Grid_Num_x;i++)
{
for (j=0;j<Grid_Num_y;j++)
for (k=0;k<Grid_Num_z;k++)
{
x=X[i]; dx=X_interval[i];
y=Y[j]; dy=Y_interval[j];
z=Z[k]; dz=Z_interval[k];
rho=0.5*(rm+rs);
r5=pow(x*x+y*y+z*z,5/2); /// attention here 5/2=2
Bx=-bm*3*x*z/r5;
By=-bm*3*y*z/r5;
Bz=-bm*(2*pow(z,2)-pow(x,2)-pow(y,2))/r5;
pointer[0].value[i][j][k]=rho;
pointer[4].value[i][j][k]=Bx;
pointer[5].value[i][j][k]=By;
pointer[6].value[i][j][k]=Bz;
rhoVx=0.;
rhoVy=0.5*v0*By*(1-tanh(x/width_rho))*rho/bs;
rhoVz=0.5*v0*Bz*(1-tanh(x/width_rho))*rho/bs;
pointer[1].value[i][j][k]=rhoVx;
pointer[2].value[i][j][k]=rhoVy;
pointer[3].value[i][j][k]=rhoVz;
B_Energy=0.5*(pow(Bx,2)+pow(By,2)+pow(Bz,2));
V_Energy=0.5*(pow(rhoVx,2)+pow(rhoVy,2)+pow(rhoVz,2))/rho;
pressure=pressuremtotal-B_Energy;
pointer[7].value[i][j][k]=B_Energy+V_Energy+pressure/(phy_gamma - 1);
pressure_obj.value[i][j][k]=pressure;
/*plus half dx: start*/
rho=0.5*(rm+rs);
r5=pow(x*x+y*y+z*z,5/2); /// attention here 5/2=2
Bx=-bm*3*x*z/r5;
By=-bm*3*y*z/r5;
Bz=-bm*(2*pow(z,2)-pow(x,2)-pow(y,2))/r5;
sub_var[0][i][j][k]=rho;
sub_var[4][i][j][k]=Bx;
sub_var[5][i][j][k]=By;
sub_var[6][i][j][k]=Bz;
rhoVx=0.;
rhoVy=0.5*v0*By*(1-tanh((x+dx/2.)/width_rho))*rho/bs;
rhoVz=0.5*v0*Bz*(1-tanh((x+dx/2.)/width_rho))*rho/bs;
sub_var[1][i][j][k]=rhoVx;
sub_var[2][i][j][k]=rhoVy;
sub_var[3][i][j][k]=rhoVz;
B_Energy=0.5*(pow(Bx,2)+pow(By,2)+pow(Bz,2));
V_Energy=0.5*(pow(rhoVx,2)+pow(rhoVy,2)+pow(rhoVz,2))/rho;
pressure=pressuremtotal-B_Energy;
sub_var[7][i][j][k]=B_Energy+V_Energy+pressure/(phy_gamma - 1);
/*plus half dx: end*/
}
}
cal_current(current, pointer);
for (i=0;i<Grid_Num_x;i++)
for (j=0;j<Grid_Num_y;j++)
for (k=0;k<Grid_Num_z;k++)
{
pointer[2].value[i][j][k]=pointer[2].value[i][j][k]+vyi_0*di*current[1].value[i][j][k];
sub_mag_field[0].value[i][j][k]=sub_var[4][i][j][k];
sub_mag_field[1].value[i][j][k]=sub_var[5][i][j][k];
sub_mag_field[2].value[i][j][k]=sub_var[6][i][j][k];
}
cal_current(current,sub_mag_field-4); // -4 is because that sub_mag_field[i]=pointer[i+4];
for (i=0;i<Grid_Num_x;i++)
for (j=0;j<Grid_Num_y;j++)
for (k=0;k<Grid_Num_z;k++)
sub_var[2][i][j][k]=sub_var[2][i][j][k]+vyi_0*di*current[1].value[i][j][k];
for (n=0;n<8;n++)
for (i=0;i<Grid_Num_x;i++)
{
var_x[n][i]=pointer[n].value[i][0][0];
var_x_plushalfdx[n][i]=sub_var[n][i][0][0];
}
for (n=0;n<8;n++)
for (i=0;i<Grid_Num_x;i++)
for (j=0;j<Grid_Num_y;j++)
for (k=0;k<Grid_Num_z;k++)
sub_var[n][i][j][k]=pointer[n].value[i][j][k]-var_x[n][i];
// delete dynamic variable-array
delete []current;
delete []sub_mag_field;
//cout<<"Initialize invoked! But I really don't know the setup written by Teacher Ma! Waiting to be changed to a symmetric Harris Current Sheet!"<<endl;
}
void harris_current_initia(VARIABLE *pointer, BASIC_VARIABLE &pressure_obj)
{
double rhoinfinity, Bal_coeff, norm_lambda;
double x,y,z, dx,dy,dz;
double rho, Bx, By, Bz, rhoVx, rhoVy, rhoVz;
double B_Energy, V_Energy, pressure;
// Following used are global variables listed in "Basic_Parameter.h"
rhoinfinity=rho_infinity;
Bal_coeff=Balance_coefficient;
norm_lambda=normalized_lambda;
VARIABLE *current=new VARIABLE[3];
VARIABLE *sub_mag_field=new VARIABLE[3]; //sub_ for subsidary
int i,j,k,n;
for (i=0;i<Grid_Num_x;i++)
{
for (j=0;j<Grid_Num_y;j++)
for (k=0;k<Grid_Num_z;k++)
{
x=X[i]; dx=X_interval[i];
y=Y[j]; dy=Y_interval[j];
z=Z[k]; dz=Z_interval[k];
rho=pow(1./cosh(x/norm_lambda),2)+rhoinfinity;
Bz=tanh(x/norm_lambda);
By=0;
Bx=0;
pointer[0].value[i][j][k]=rho;
pointer[4].value[i][j][k]=Bx;
pointer[5].value[i][j][k]=By;
pointer[6].value[i][j][k]=Bz;
rhoVx=0.;
rhoVy=0; // rho*Bal_coeff*2./norm_lambda should be present in PIC simulation, not in fluid
// when fluid equation does not take collision into consideration
rhoVz=0;
pointer[1].value[i][j][k]=rhoVx;
pointer[2].value[i][j][k]=rhoVy;
pointer[3].value[i][j][k]=rhoVz;
B_Energy=0.5*(pow(Bx,2)+pow(By,2)+pow(Bz,2));
V_Energy=0.5*(pow(rhoVx,2)+pow(rhoVy,2)+pow(rhoVz,2))/rho;
pressure=Bal_coeff*rho;
if (phy_gamma - 1 < iso_therm_coeff)
pointer[7].value[i][j][k] = B_Energy + V_Energy;
else
pointer[7].value[i][j][k]=B_Energy+V_Energy+pressure/(phy_gamma - 1);
pressure_obj.value[i][j][k]=pressure;
/*plus half dx: start*/
rho=pow(1./cosh((x+dx/2.)/norm_lambda),2)+rhoinfinity;
Bz=tanh((x+dx/2.)/norm_lambda);
By=0;
Bx=0;
sub_var[0][i][j][k]=rho;
sub_var[4][i][j][k]=Bx;
sub_var[5][i][j][k]=By;
sub_var[6][i][j][k]=Bz;
rhoVx=0.;
rhoVy=0; // rho*Bal_coeff*2./norm_lambda should be present in PIC simulation, not in fluid
// when fluid equation does not take collision into consideration
rhoVz=0;
sub_var[1][i][j][k]=rhoVx;
sub_var[2][i][j][k]=rhoVy;
sub_var[3][i][j][k]=rhoVz;
B_Energy=0.5*(pow(Bx,2)+pow(By,2)+pow(Bz,2));
V_Energy=0.5*(pow(rhoVx,2)+pow(rhoVy,2)+pow(rhoVz,2))/rho;
pressure=Bal_coeff*rho;
if (phy_gamma - 1 < iso_therm_coeff)
sub_var[7][i][j][k] = B_Energy + V_Energy;
else
sub_var[7][i][j][k] = B_Energy + V_Energy + pressure / (phy_gamma - 1);
/*plus half dx: end*/
}
}
for (n=0;n<8;n++)
for (i=0;i<Grid_Num_x;i++)
{
var_x[n][i]=pointer[n].value[i][0][0];
var_x_plushalfdx[n][i]=sub_var[n][i][0][0];
}
for (n=0;n<8;n++)
for (i=0;i<Grid_Num_x;i++)
for (j=0;j<Grid_Num_y;j++)
for (k=0;k<Grid_Num_z;k++)
sub_var[n][i][j][k]=pointer[n].value[i][j][k]-var_x[n][i];
// delete dynamic variable-array
delete []current;
delete []sub_mag_field;
//cout<<"Initialize invoked! But I really don't know the setup written by Teacher Ma! Waiting to be changed to a symmetric Harris Current Sheet!"<<endl;
}
void shear_flow_harris_initia(VARIABLE *pointer, BASIC_VARIABLE &pressure_obj)
{
double rhoinfinity, Bal_coeff, norm_lambda;
double x,y,z, dx,dy,dz;
double rho, Bx, By, Bz, rhoVx, rhoVy, rhoVz;
double B_Energy, V_Energy, pressure;
double v_tanh, v_tanh_0, vb, ls, xs;
// Following used are global variables listed in "Physics_Parameter.h"
rhoinfinity=rho_infinity;
Bal_coeff=Balance_coefficient;
norm_lambda=normalized_lambda;
// shear concerned, listed in "Physics_Parameter.h"
vb = velocity_boundary;
ls = shear_length;
xs = shear_location;
v_tanh_0 = 0.5*vb*tanh(-xs/ls);
int i,j,k,n;
for (i=0;i<Grid_Num_x;i++)
{
for (j=0;j<Grid_Num_y;j++)
for (k=0;k<Grid_Num_z;k++)
{
x=X[i]; dx=X_interval[i];
y=Y[j]; dy=Y_interval[j];
z=Z[k]; dz=Z_interval[k];
rho=pow(1./cosh(x/norm_lambda),2)+rhoinfinity;
Bz=tanh(x/norm_lambda);
By=0;
Bx=0;
pointer[0].value[i][j][k]=rho;
pointer[4].value[i][j][k]=Bx;
pointer[5].value[i][j][k]=By;
pointer[6].value[i][j][k]=Bz;
rhoVx=0.;
rhoVy=0; // rho*Bal_coeff*2./norm_lambda should be present in PIC simulation, not in fluid
// when fluid equation does not take collision into consideration
v_tanh = 0.5*vb*tanh( (abs(x)-xs)/ls );
if (x>=0)
rhoVz = rho*(v_tanh-v_tanh_0); // initia shear flow
else
rhoVz = -rho*(v_tanh-v_tanh_0);
pointer[1].value[i][j][k]=rhoVx;
pointer[2].value[i][j][k]=rhoVy;
pointer[3].value[i][j][k]=rhoVz;
B_Energy=0.5*(pow(Bx,2)+pow(By,2)+pow(Bz,2));
V_Energy=0.5*(pow(rhoVx,2)+pow(rhoVy,2)+pow(rhoVz,2))/rho;
pressure=Bal_coeff*rho;
if (phy_gamma - 1 < iso_therm_coeff)
pointer[7].value[i][j][k] = B_Energy + V_Energy;
else
pointer[7].value[i][j][k] = B_Energy + V_Energy + pressure / (phy_gamma - 1);
pressure_obj.value[i][j][k]=pressure;
/*plus half dx: start*/
rho=pow(1./cosh((x+dx/2.)/norm_lambda),2)+rhoinfinity;
Bz=tanh((x+dx/2.)/norm_lambda);
By=0;
Bx=0;
sub_var[0][i][j][k]=rho;
sub_var[4][i][j][k]=Bx;
sub_var[5][i][j][k]=By;
sub_var[6][i][j][k]=Bz;
rhoVx=0.;
rhoVy=0; // rho*Bal_coeff*2./norm_lambda should be present in PIC simulation, not in fluid
// when fluid equation does not take collision into consideration
v_tanh = 0.5*vb*tanh( (abs(x+dx/2.)-xs)/ls );
if (x>=0)
rhoVz = rho*(v_tanh-v_tanh_0); // initia shear flow
else
rhoVz = -rho*(v_tanh-v_tanh_0);
sub_var[1][i][j][k]=rhoVx;
sub_var[2][i][j][k]=rhoVy;
sub_var[3][i][j][k]=rhoVz;
B_Energy=0.5*(pow(Bx,2)+pow(By,2)+pow(Bz,2));
V_Energy=0.5*(pow(rhoVx,2)+pow(rhoVy,2)+pow(rhoVz,2))/rho;
pressure=Bal_coeff*rho;
if (phy_gamma - 1 < iso_therm_coeff)
sub_var[7][i][j][k] = B_Energy + V_Energy;
else
sub_var[7][i][j][k] = B_Energy + V_Energy + pressure / (phy_gamma - 1);
/*plus half dx: end*/
}
}
for (n=0;n<8;n++)
for (i=0;i<Grid_Num_x;i++)
{
var_x[n][i]=pointer[n].value[i][0][0];
var_x_plushalfdx[n][i]=sub_var[n][i][0][0];
}
for (n=0;n<8;n++)
for (i=0;i<Grid_Num_x;i++)
for (j=0;j<Grid_Num_y;j++)
for (k=0;k<Grid_Num_z;k++)
sub_var[n][i][j][k]=pointer[n].value[i][j][k]-var_x[n][i];
//cout<<"shear_flow_harris_initia invoked!"<<endl;
}
void write_out(VARIABLE *pointer, int nstop, double time, double time_interval)
{
int i,j,k, n;
ofstream timeout("temp_step_to_time.dat");
ofstream var_out[8];
ofstream sub_var_out("temp_sub_var.dat"); // This and the following two is very important for calculating
ofstream var_x_out("temp_var_x_out.dat");
ofstream var_x_plushalfdx_out("temp_var_x_plushalfdx.dat");
open_var_files(var_out);
timeout<<setw(6)<<nstop<<setw(6)<<" ";
timeout<<setiosflags(ios::scientific)<<setprecision(16);
timeout<<setw(25)<<time<<setw(25)<<time_interval<<endl;
sub_var_out<<setiosflags(ios::scientific)<<setprecision(16);
var_x_out<<setiosflags(ios::scientific)<<setprecision(16);
var_x_plushalfdx_out<<setiosflags(ios::scientific)<<setprecision(16);
for (n=0;n<8;n++)
{
pointer[n].record(var_out[n]);
for (i=0;i<Grid_Num_x;i++)
{
var_x_out<<setw(25)<<var_x[n][i]<<" ";
var_x_plushalfdx_out<<setw(25)<<var_x_plushalfdx[n][i]<<" ";
for (j=0;j<Grid_Num_y;j++)
{
for (k=0;k<Grid_Num_z;k++)
sub_var_out<<setw(25)<<sub_var[n][i][j][k]<<" ";
sub_var_out<<endl;
}
var_x_out<<endl;
var_x_plushalfdx_out<<endl;
sub_var_out<<endl;
}
var_x_out<<endl;
var_x_plushalfdx_out<<endl;
sub_var_out<<endl;
}
timeout.close();
close_var_files(var_out);
sub_var_out.close();
var_x_out.close();
var_x_plushalfdx_out.close();
}
void read_in(VARIABLE *pointer, int &nstart, double &time, double &time_interval)
{
int i,j,k, n;
ifstream timein("temp_step_to_time.dat");
ifstream var_in[8];
ifstream sub_var_in("temp_sub_var.dat"); // This and the following two is very important for calculating
ifstream var_x_in("temp_var_x_out.dat");
ifstream var_x_plushalfdx_in("temp_var_x_plushalfdx.dat");
open_var_files(var_in);
timein>>nstart>>time>>time_interval;
for (n=0; n<8; n++)
{
pointer[n].fill(var_in[n]);
for (i=0;i<Grid_Num_x;i++)
{
var_x_in>>var_x[n][i];
var_x_plushalfdx_in>>var_x_plushalfdx[n][i];
for (j=0;j<Grid_Num_y;j++)
{
for (k=0;k<Grid_Num_z;k++)
sub_var_in>>sub_var[n][i][j][k];
}
}
}
timein.close();
close_var_files(var_in);
sub_var_in.close();
var_x_in.close();
var_x_plushalfdx_in.close();
}
void cal_current(VARIABLE *current, VARIABLE *pointer, Type T)
{
double Bx_ym, Bx_zm, By_zm, By_xm, Bz_xm, Bz_ym;
double Bx_yp, Bx_zp, By_zp, By_xp, Bz_xp, Bz_yp;
double dx, dy, dz;
int i,j,k, n;
for (i=1;i<Grid_Num_x-1-T;i++)
{
for (j=1;j<Grid_Num_y-1-T;j++)
for (k=1;k<Grid_Num_z-1-T;k++)
{
Bx_ym=pointer[4].value[i][j-1][k]; Bx_yp=pointer[4].value[i][j+1][k];
Bx_zm=pointer[4].value[i][j][k-1]; Bx_zp=pointer[4].value[i][j][k+1];
By_zm=pointer[5].value[i][j][k-1]; By_zp=pointer[5].value[i][j][k+1];
By_xm=pointer[5].value[i-1][j][k]; By_xp=pointer[5].value[i+1][j][k];
Bz_xm=pointer[6].value[i-1][j][k]; Bz_xp=pointer[6].value[i+1][j][k];
Bz_ym=pointer[6].value[i][j-1][k]; Bz_yp=pointer[6].value[i][j+1][k];
dx=X_interval[i-1]+X_interval[i];
dy=Y_interval[j-1]+Y_interval[j];
dz=Z_interval[k-1]+Z_interval[k];
current[0].value[i][j][k]=(Bz_yp-Bz_ym)/dy- \
(By_zp-By_zm)/dz;
current[1].value[i][j][k]=(Bx_zp-Bx_zm)/dz- \
(Bz_xp-Bz_xm)/dx;
current[2].value[i][j][k]=(By_xp-By_xm)/dx- \
(Bx_yp-Bx_ym)/dy;
}
}
// (can write a switch statement to include different extrapolation method
// x-linear extrapolation yz-equivalent
// boundary at i=0,Grid_Num_x-1-T
if(T==Complete) // linear extrapolation
{
// boundary at i=0,Grid_Num_x-1
if (half_x==True)
{
for (j=1;j<Grid_Num_y-1;j++)
for(k=1;k<Grid_Num_z-1;k++)
{
current[0].value[0][j][k]=2*current[0].value[1][j][k]-current[0].value[2][j][k];
current[0].value[Grid_Num_x-1][j][k]=current[0].value[Grid_Num_x-3][Grid_Num_y-1-j][k]; // it's meaning?
current[1].value[0][j][k]=2*current[1].value[1][j][k]-current[1].value[2][j][k];
current[1].value[Grid_Num_x-1][j][k]=current[1].value[Grid_Num_x-3][Grid_Num_y-1-j][k];
current[2].value[0][j][k]=2*current[2].value[1][j][k]-current[2].value[2][j][k];
current[2].value[Grid_Num_x-1][j][k]=-current[2].value[Grid_Num_x-3][Grid_Num_y-1-j][k];
}
}
else
{
for (n=0;n<3;n++)
for (j=1;j<Grid_Num_y-1;j++)
for(k=1;k<Grid_Num_z-1;k++)
{
current[n].value[0][j][k]=2*current[n].value[1][j][k]-current[n].value[2][j][k];
current[n].value[Grid_Num_x-1][j][k]=2*current[n].value[Grid_Num_x-2][j][k]- \
current[n].value[Grid_Num_x-3][j][k];
}
}
// boundary at j=0,Grid_Num_y-1
if (period_y==True)
{
for (n=0;n<3;n++)
for (i=0;i<Grid_Num_x;i++)
for(k=1;k<Grid_Num_z-1;k++)
{
current[n].value[i][0][k]=current[n].value[i][Grid_Num_y-2][k];
current[n].value[i][Grid_Num_y-1][k]=current[n].value[i][1][k];
}
}
else
{
for (n=0;n<3;n++)
for (i=0;i<Grid_Num_x;i++)
for(k=1;k<Grid_Num_z-1;k++)
{
current[n].value[i][0][k]=current[n].value[i][1][k];
current[n].value[i][Grid_Num_y-1][k]=current[n].value[i][Grid_Num_y-2][k];
}
}
// boundary at k=0,Grid_Num_z-1
if (half_z==True)
{
for (i=0;i<Grid_Num_x;i++)
for (j=0;j<Grid_Num_y;j++)
{
current[0].value[i][j][0]=current[0].value[i][j][1];
current[0].value[i][j][Grid_Num_z-1]=current[0].value[i][j][Grid_Num_z-3];
current[1].value[i][j][0]=current[1].value[i][j][1];
current[1].value[i][j][Grid_Num_z-1]=current[1].value[i][j][Grid_Num_z-3];
current[2].value[i][j][0]=current[2].value[i][j][1];
current[2].value[i][j][Grid_Num_z-1]=-current[2].value[i][j][Grid_Num_z-3];
}
}
else
{
if(period_z == True)
{
for (n=0;n<3;n++)
for (i=0;i<Grid_Num_x;i++)
for (j=0;j<Grid_Num_y;j++)
{
current[n].value[i][j][0]=current[n].value[i][j][Grid_Num_z-2];
current[n].value[i][j][Grid_Num_z-1]=current[n].value[i][j][1];
}
}
else
{
for (n=0;n<3;n++)
for (i=0;i<Grid_Num_x;i++)
for (j=0;j<Grid_Num_y;j++)
{
current[n].value[i][j][0]=current[n].value[i][j][1];
current[n].value[i][j][Grid_Num_z-1]=current[n].value[i][j][Grid_Num_z-2];
}
}
}
}
else // T==Incomplete //x-direction equvalent extrapolation
{
// boundary at i=0,Grid_Num_x-1-T
if (half_x==True)
{
for (j=1;j<Grid_Num_y-1-T;j++)
for(k=1;k<Grid_Num_z-1-T;k++)
{
current[0].value[0][j][k]=current[0].value[1][j][k];
current[0].value[Grid_Num_x-1-T][j][k]=current[0].value[Grid_Num_x-2-T][Grid_Num_y-2-j][k];
current[1].value[0][j][k]=current[1].value[1][j][k];
current[1].value[Grid_Num_x-1-T][j][k]=current[1].value[Grid_Num_x-2-T][Grid_Num_y-2-j][k];
current[2].value[0][j][k]=current[2].value[1][j][k];
current[2].value[Grid_Num_x-1-T][j][k]=-current[2].value[Grid_Num_x-2-T][Grid_Num_y-2-j][k];
}
}
else
{
for (n=0;n<3;n++)
for (j=1;j<Grid_Num_y-1-T;j++)
for(k=1;k<Grid_Num_z-1-T;k++)
{
current[n].value[0][j][k]=current[n].value[1][j][k];
current[n].value[Grid_Num_x-1-T][j][k]=current[n].value[Grid_Num_x-2-T][j][k];
}
}
// boundary at j=0,Grid_Num_y-1-T
if (period_y==True)
{
for (n=0;n<3;n++)
for (i=0;i<Grid_Num_x-T;i++)
for(k=1;k<Grid_Num_z-1-T;k++)
{
current[n].value[i][0][k]=current[n].value[i][Grid_Num_y-2-T][k];
current[n].value[i][Grid_Num_y-1-T][k]=current[n].value[i][1][k];
}
}
else
{
for (n=0;n<3;n++)
for (i=0;i<Grid_Num_x-T;i++)
for(k=1;k<Grid_Num_z-1-T;k++)
{
current[n].value[i][0][k]=current[n].value[i][1][k];
current[n].value[i][Grid_Num_y-1-T][k]=current[n].value[i][Grid_Num_y-2-T][k];
}
}
// boundary at k=0,Grid_Num_z-1-T
if (half_z==True)
{
for (i=0;i<Grid_Num_x-T;i++)
for (j=0;j<Grid_Num_y-T;j++)
{
current[0].value[i][j][0]=current[0].value[i][j][1];
current[0].value[i][j][Grid_Num_z-1-T]=current[0].value[i][j][Grid_Num_z-2-T];
current[1].value[i][j][0]=current[1].value[i][j][1];
current[1].value[i][j][Grid_Num_z-1-T]=current[1].value[i][j][Grid_Num_z-2-T];
current[2].value[i][j][0]=current[2].value[i][j][1];
current[2].value[i][j][Grid_Num_z-1-T]=-current[2].value[i][j][Grid_Num_z-2-T];
}
}
else
{
if(period_z == True)
{
for (n=0;n<3;n++)
for (i=0;i<Grid_Num_x-T;i++)
for (j=0;j<Grid_Num_y-T;j++)
{
current[n].value[i][j][0]=current[n].value[i][j][Grid_Num_z-2-T];
current[n].value[i][j][Grid_Num_z-1-T]=current[n].value[i][j][1];
}
}
else
{
for (n=0;n<3;n++)
for (i=0;i<Grid_Num_x-T;i++)
for (j=0;j<Grid_Num_y-T;j++)
{
current[n].value[i][j][0]=current[n].value[i][j][1];
current[n].value[i][j][Grid_Num_z-1-T]=current[n].value[i][j][Grid_Num_z-2-T];
}
}
}
}
//cout<<"Current is calculated form Curl B! It's simple, I know!!!"<<endl;
}
// Homogeneous eta, waiting to be amended.
void set_eta(BASIC_VARIABLE &eta_obj, VARIABLE *pointer, VARIABLE *current, double time, Type T) // Type T is for Complete or Incomplete setting; Type TT is for uniform or non-uniform setting
{
double etam[Grid_Num_y]; // eta_main direction, in another wrod eta along guid field, that is y-directin
double etax, etaz, etal, etab, alpha0=2.0; // etal for eta_localize; etab for eta_background
double ylength=15., xtrig=0.0, ztrig=0.0; // 'ylength' is 'xlen' in Fortran version, which is length of localized region in y-direction; xtrig and ztrig is localized resistivity region's center
double widthx=width_rho, widthz=2*width_rho;
double x,y,z, dx,dy,dz;
int i,j,k;
etab = Lundquist_Number;
etal = localized_Resistivity;
if(T==Complete)
{
for (i=0;i<Grid_Num_x-T;i++)
{
x=X[i];
if(abs(x-xtrig)<=0.5)
etax=1.;
else
etax=1.-pow(tanh((x-xtrig)/widthx),2); // This is ture
for (j=0;j<Grid_Num_y-T;j++)
{
y=Y[j];
if(abs(y)<=ylength) // ylength is the length of localized resitivity region along y-directiont
etam[j]=1; // This is True
else
etam[j]=1.-pow(tanh(abs(y)-ylength),2);
for (k=0;k<Grid_Num_z-T;k++)
{
z=Z[k];
if(abs(abs(z)-ztrig)<=1.)
etaz=1.; // This is True
else
etaz=1.-pow(tanh((abs(z)-ztrig)/widthz),2);
eta_obj.value[i][j][k]=etab+etam[j]*etal*etax*etaz;
}
}
}
}
else
{
for (i=0;i<Grid_Num_x-T;i++)
{
x=X[i]; dx=X_interval[i];
if(abs(x+dx/2.-xtrig)<=0.5)
etax=1.;
else
etax=1.-pow(tanh((x+dx/2.-xtrig)/widthx),2); // This is True
for (j=0;j<Grid_Num_y-T;j++)
{
y=Y[j]; dy=Y_interval[j];
if(abs(y+dy/2.)<=ylength)
etam[j]=1; // This is True
else
etam[j]=1.-pow(tanh(abs(y+dy/2.)-ylength),2);
for (k=0;k<Grid_Num_z-T;k++)
{
z=Z[k]; dz=Z_interval[k];
if(abs(abs(z+dz/2.)-ztrig)<=1.)
etaz=1.; // This is True
else
etaz=1.-pow(tanh(((z+dz/2.)-ztrig)/widthz),2); // ????????? bot tanh((abs(zz(jz)+dz/2.)-ztrig)/aw2)?????
eta_obj.value[i][j][k]=etab+etam[j]*etal*etax*etaz;
}
}
}
}
//cout<<"Set_eta invoked! But for now eta is simply setted to 0.1! And I'm sorry to inform you that you should change it!"<<endl;
}
Logic cal_pressure(BASIC_VARIABLE &pressure_obj, VARIABLE *pointer, Type T)
{
double rho,rhoVx, rhoVy, rhoVz, Bx, By, Bz, Eng, pressure;
double B_Energy, V_Energy;
double positive_value=1e-5;
int i,j,k, times=0;
for (i=0;i<Grid_Num_x-T;i++)
{
for (j=0;j<Grid_Num_y-T;j++)
for (k=0;k<Grid_Num_z-T;k++)
{
rho=pointer[0].value[i][j][k];
rhoVx=pointer[1].value[i][j][k];
rhoVy=pointer[2].value[i][j][k];
rhoVz=pointer[3].value[i][j][k];
Bx=pointer[4].value[i][j][k];
By=pointer[5].value[i][j][k];
Bz=pointer[6].value[i][j][k];
Eng=pointer[7].value[i][j][k];
B_Energy=0.5*(pow(Bx,2)+pow(By,2)+pow(Bz,2));
V_Energy=0.5*(pow(rhoVx,2)+pow(rhoVy,2)+pow(rhoVz,2))/rho;
if (phy_gamma - 1 < iso_therm_coeff) // iso_therm_coeff is a small value
pressure = Balance_coefficient * rho;
else
pressure = (phy_gamma - 1)*(Eng - B_Energy - V_Energy);
pressure_obj.value[i][j][k]=pressure;
if(pressure<0.)
{
if (times==0)
{
pre_out<<endl<<" Oops, pressure is negative, and program can be stopped!!!"<<endl;
pre_out<<"When Type T = "<<T<<" , and time step is nt = "<<nstep<<endl;
pre_out<<"Located in ( xi = "<<setw(3)<<i<<", yj = "<<setw(3)<<j<<", zk = "<<setw(3)<<k<<" ) ";
pre_out<<endl;
pre_out<<setiosflags(ios::scientific)<<setprecision(3);
times+=1;
}
else
{
pre_out<<" ( xi = "<<setw(3)<<i<<", yj = "<<setw(3)<<j<<", zk = "<<setw(3)<<k<<" ) ";
pre_out<<endl;
}
pre_out<<" rho Vx Vy Vz Bx "\
<<" By Bz Eng P"<<endl;
pre_out<<setw(13)<<rho<<setw(12)<<rhoVx/rho<<setw(12)<<rhoVy/rho<<setw(12)<<rhoVz/rho\
<<setw(12)<<Bx<<setw(12)<<By<<setw(12)<<Bz<<setw(13)<<Eng<<setw(11)<<pressure<<endl;
}
if(T==Complete && pressure<positive_value)
pressure_obj.value[i][j][k]=positive_value;
}
}
if (times==0)
return True;
else
return False;
//cout<<"Pressure is calculated from various kinds of energy, and doesn't explicitly step on according to equation!"<<endl;
}
// Extracting electric field from flux of magnetic
void ext_from_var( BASIC_VARIABLE *Electric_field, BASIC_VARIABLE *var, VARIABLE *current, BASIC_VARIABLE &eta_obj)
{
double rho, Vx, Vy, Vz;
double Bx, By, Bz;
double eta;
double current_x, current_y, current_z;
double V_cross_B_x, V_cross_B_y, V_cross_B_z;
// Assignment
int i,j,k;
for (i=0;i<Grid_Num_x;i++)
for (j=0;j<Grid_Num_y;j++)
for (k=0;k<Grid_Num_z;k++)
{
rho=var[0].value[i][j][k];
Vx=var[1].value[i][j][k]/rho;
Vy=var[2].value[i][j][k]/rho;
Vz=var[3].value[i][j][k]/rho;
Bx=var[4].value[i][j][k];
By=var[5].value[i][j][k];
Bz=var[6].value[i][j][k];
current_x=current[0].value[i][j][k];
current_y=current[1].value[i][j][k];
current_z=current[2].value[i][j][k];
eta=eta_obj.value[i][j][k];
//Magnetic Induction Eq.
V_cross_B_x=(Vy-di/rho*current_y)*Bz-(Vz-di/rho*current_z)*By; // don't take di into acount, that is di=0
V_cross_B_y=(Vz-di/rho*current_z)*Bx-(Vx-di/rho*current_x)*Bz;
V_cross_B_z=(Vx-di/rho*current_x)*By-(Vy-di/rho*current_y)*Bx;
Electric_field[2].value[i][j][k]=-V_cross_B_z+eta*current_z;
Electric_field[0].value[i][j][k]=-V_cross_B_x+eta*current_x;
Electric_field[1].value[i][j][k]=-V_cross_B_y+eta*current_y;
}
}
// Setting time-interval
double set_dt(VARIABLE *pointer, BASIC_VARIABLE &eta_obj, VARIABLE *current, BASIC_VARIABLE &pressure_obj, double time, double last_dt)
{
//set_eta(eta_obj, pointer, current, time);
double dt;
double dx,dy,dz,dxyz;
double Temp_dt, dt_min=1000., test_dt=1000.;
double rho, rhoVx, rhoVy, rhoVz, Bx, By, Bz, Eng, pressure;
int max_dt_i, max_dt_j, max_dt_k; // for diagnostic
double max_rho, max_Vx, max_Vy, max_Vz, max_Bx, max_By, max_Bz, max_Eng, max_P; // for diagnostic
int i,j,k, times=0;
for (i=0;i<Grid_Num_x;i++)
{
for (j=0;j<Grid_Num_y;j++)
for (k=0;k<Grid_Num_z;k++)
{
dx=X_interval[i];
dy=Y_interval[j];
dz=Z_interval[k];
dxyz=0.5*dx*dy*dz/ \
sqrt(dx*dx*dy*dy+dy*dy*dz*dz+dz*dz*dx*dx);
rho=pointer[0].value[i][j][k];
rhoVx=pointer[1].value[i][j][k];
rhoVy=pointer[2].value[i][j][k];
rhoVz=pointer[3].value[i][j][k];
Bx=pointer[4].value[i][j][k];
By=pointer[5].value[i][j][k];
Bz=pointer[6].value[i][j][k];
Eng=pointer[7].value[i][j][k];
pressure=pressure_obj.value[i][j][k];
Temp_dt=dxyz/( sqrt( pow(rhoVx,2)+pow(rhoVy,2)+pow(rhoVz,2) )/rho+ \
sqrt( ( Bx*Bx+By*By+Bz*Bz+phy_gamma*pressure )/rho ) );
if (Temp_dt > dt_min)
{
if (times==0)
{
max_dt_out<<endl;
max_dt_out<<" When dt >= "<<int(dt_min)<<" , time step is "<<nstep<<endl\
<<"where location is ( i = "<<setw(3)<<i<<", j = "<<setw(3)<<j<<", k = "<<setw(3)<<k<<" )"<<endl;
max_dt_out<<setiosflags(ios::scientific)<<setprecision(3);
times+=1;
}
else
max_dt_out<<"And ( "<<setw(3)<<i<<", "<<setw(3)<<j<<", "<<setw(3)<<k<<" )"<<endl;
max_dt_out<<" rho Vx Vy Vz Bx "\
<<" By Bz Eng P"<<endl;
max_dt_out<<setw(13)<<rho<<setw(12)<<rhoVx/rho<<setw(12)<<rhoVy/rho<<setw(12)<<rhoVz/rho\
<<setw(12)<<Bx<<setw(12)<<By<<setw(12)<<Bz<<setw(13)<<Eng<<setw(11)<<pressure<<endl;
}
if (Temp_dt < test_dt)
{
test_dt=Temp_dt;
max_dt_i=i; max_dt_j=j; max_dt_k=k;
max_rho=rho; max_Vx=rhoVx/rho; max_Vy=rhoVy/rho; max_Vz=rhoVz/rho;
max_Bx=Bx; max_By=By; max_Bz=Bz; max_Eng=Eng, max_P=pressure;
}
}
}
dt=0.5*min(dt_min,test_dt);
if (time>0 && dt<.5*last_dt)
{
min_dt_out<<setiosflags(ios::scientific)<<setprecision(3);
min_dt_out<<" Noth that dt changes a lot. This dt is calculated on "\
<<"location ( i = "<<setw(3)<<max_dt_i<<", j = "<<setw(3)<<max_dt_j<<", k = "<<setw(3)<<max_dt_k<<" )"<<endl;
min_dt_out<<"And time step is "<<nstep<<" , with variables are:"<<endl;
min_dt_out<<" rho Vx Vy Vz Bx "\
<<" By Bz Eng P"<<endl;
min_dt_out<<setw(13)<<max_rho<<setw(12)<<max_Vx<<setw(12)<<max_Vy<<setw(12)<<max_Vz\
<<setw(12)<<max_Bx<<setw(12)<<max_By<<setw(12)<<max_Bz<<setw(13)<<max_Eng<<setw(11)<<max_P<<endl<<endl;
}
//cout<<"Set_dt invoked! And dt="<<dt<<endl;
return dt;
}
// add fluctuation to B variable
void add_fluc(VARIABLE *var)
{
double norm_lambda;
double x, z, Bkx, Bkz, fluc_B, Vkx, Vkz, fluc_V;
double Bx, Bz, Eng, fluc_Bx, fluc_Bz;
double rho, rhoVx, rhoVz, fluc_rhoVx, fluc_rhoVz;
int i, j, k;
fluc_B=fluctuation_mag;
fluc_V=fluctuation_velocity;
Bkx=fluc_B_kx; Bkz=fluc_B_kz;
Vkx = fluc_V_kx; Vkz = fluc_V_kz;
norm_lambda=normalized_lambda;
// add fluctuation at z=up and down boundary according to <Hurricane, PoP, 1995>, \delta\psi=fluctuation*cos(k_z*z)
if (position_fluc==Boundary)
{
for (j=0;j<Grid_Num_y;j++)
for (k=0; k<Grid_Num_z; k++)
{
z=Z[k];
// at i=0
Bx=var[4].value[0][j][k]; Eng=var[7].value[0][j][k];
fluc_Bx=-Bkz*fluc_B*sin(Bkz*z);
Eng=Eng+1./2*(2*Bx*fluc_Bx+fluc_Bx*fluc_Bx);
rho=var[0].value[0][j][k]; rhoVx=var[1].value[0][j][k];
fluc_rhoVx=rho*(-Vkz*fluc_V*sin(Vkz*z));
Eng=Eng+1./2*(2*rhoVx*fluc_rhoVx+fluc_rhoVx*fluc_rhoVx)/rho;
rhoVx=rhoVx+fluc_rhoVx; var[1].value[0][j][k]=rhoVx;
Bx=Bx+fluc_Bx;
var[4].value[0][j][k]=Bx; var[7].value[0][j][k]=Eng;
// at i=1
Bx=var[4].value[1][j][k]; Eng=var[7].value[1][j][k];
fluc_Bx=-Bkz*fluc_B*sin(Bkz*z);
Eng=Eng+1./2*(2*Bx*fluc_Bx+fluc_Bx*fluc_Bx);
rho=var[0].value[1][j][k]; rhoVx=var[1].value[1][j][k];
fluc_rhoVx=rho*(-Vkz*fluc_V*sin(Vkz*z));
Eng=Eng+1./2*(2*rhoVx*fluc_rhoVx+fluc_rhoVx*fluc_rhoVx)/rho;
rhoVx=rhoVx+fluc_rhoVx; var[1].value[1][j][k]=rhoVx;
Bx=Bx+fluc_Bx;
var[4].value[1][j][k]=Bx; var[7].value[1][j][k]=Eng;
// at i=Grid_Num_x-2
Bx=var[4].value[Grid_Num_x-2][j][k]; Eng=var[7].value[Grid_Num_x-2][j][k];
fluc_Bx=-Bkz*fluc_B*sin(Bkz*z);
Eng=Eng+1./2*(2*Bx*fluc_Bx+fluc_Bx*fluc_Bx);
rho=var[0].value[Grid_Num_x-2][j][k]; rhoVx=var[1].value[Grid_Num_x-2][j][k];
fluc_rhoVx=rho*(-Vkz*fluc_V*sin(Vkz*z));
Eng=Eng+1./2*(2*rhoVx*fluc_rhoVx+fluc_rhoVx*fluc_rhoVx)/rho;
rhoVx=rhoVx+fluc_rhoVx; var[1].value[Grid_Num_x-2][j][k]=rhoVx;