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3dmhdphsic.h
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#ifndef _3DMHD_PHISIC_H_
#define _3DMHD_PHISIC_H_
#include "3dmhddata.h"
#include "3dmhdparam.h"
#include "3dmhdset.h"
#include "3dmhdutils.h"
#include <cstring>
#include <fstream>
#include <math.h>
#include <mpi.h>
#include <vector>
#define ICOORD_ERROR "mkGrid: Invalid ICOORD number"
#define NGRID_ERROR "mkGrid: Invalid nGrid number"
void trapzd(double (*func)(double), double a, double b, double& s, int n);
void polint(double xa[], double ya[], int n, double x, double& y, double& dy);
void mmid(std::vector<double>& Y, const std::vector<double>& DYDX, int NVAR, double XS, double HTOT, int NSTP, double* YOUT);
void rzextr(int IEST, double XEST, double* YEST, double* YZ, std::vector<std::vector<double>>& d, double* DY, int NV, int NUSE);
void derivs(double ZZ, double* Y, int NV, double* DYDX);
void ODEINT(double* YSTART, double X1, double X2);
void RKQC(double* Y, double* DYDX, int N, double& X, double HTRY, double EPS, double* YSCAL, double& HDID, double& HNEXT);
void RK4(double* Y, double* DYDX, int N, double X, double H, double* YOUT);
void tube();
defineDimSwitch(const double&, uMax, xMax, yMax, zMax);
defineDimSwitch(const double&, uu1, XX1, YY1, ZZ1);
defineDimSwitch(const double&, uu2, XX2, YY2, ZZ2);
defineDimSwitch(const double&, ua, XA, YA, ZA);
defineDimSwitch(const double&, ub, XB, YB, ZB);
defineDimSwitch(const double&, uc, XC, YC, ZC);
defineDimSwitch(const double&, ud, XD, YD, ZD);
template <DIM dim> void mkGrid(double sCode, double& sPhys, double& dssds, double& d2ssds2) {
#if nGrid == 0
double sMax = uMax<dim>();
sPhys = sCode * sMax;
dssds = 1.0f / sMax;
d2ssds2 = 0.0f;
#elif nGrid == 1
double sMax = uMax<dim>();
double s1 = uu1<dim>(), s2 = uu2<dim>();
double a1 = (s2 - s1) / sMax;
double a = atan(s1);
double a2 = atan(s2) - a3;
if (sCode == 0.0) {
sPhys = 0.0f;
} else if (sCode == 1.0) {
sPhys = sMax;
} else {
sPhys = (tan(a2 * sCode + a3) - s1) / a1;
}
double denominator = 1.0f + (s1 + a1 * sPhys) * (s1 + a1 * sPhys);
dssds = a1 / a2 / denominator;
d2ssds2 = -2.0f * a1 * a1 * (s1 + a1 * sPhys) / (a2 * denominator * denominator);
#elif nGrid == 2
double a = ua<dim>(), b = ub<dim>(), c = uc<dim>(), d = ud<dim>();
if (c <= 1.0E-09) {
sPhys = sCode * sMax;
dssds = 1.0f / sMax;
d2ssds2 = 0.0f;
} else {
double sH = (1.0f - d) * PI / (d * atan((a - b) * c) + 2.0f * atan(b * c) - d * atan((a + b) * c));
double sK = 2.0f * c * PI * sMax / (2.0f * c * PI + sH * (2.0f * c * (atan((a - b) * c) * (a - b) - atan((a + b) * c) * (a + b) + atan((a - b - 1.0f) * c) + atan((a + b - 1.0f) * c) * (a + b - 1.0f) + atan((1.0f - a + b) * c) * (a - b)) - log(1.0f + (a - b) * (a - b) * c * c) + log(1.0f + (a + b) * (a + b) * c * c) - log(1.0f + (a + b - 1.0f) * (a + b - 1.0f) * c * c) + log(1.0f + (1.0f - a + b) * (1.0f - a + b) * c * c)));
dssds = 1.0f / (sK * (1.0f + sH / PI * (atan(c * (sCode - a - b)) + atan(c * (a - sCode - b)))));
d2ssds2 = -dssds * dssds * dssds * c * sH * sK / PI * (1.0f / (1.0f + c * c * (a + b - sCode) * (a + b - sCode)) - 1.0f / (1.0f + c * c * (a - b - sCode) * (a - b - sCode)));
sPhys = sK / (2.0f * c * PI) * (2.0f * c * PI * sCode + sH * (2.0f * c * (atan((a - b) * c) * (a - b) - atan((a + b) * c) * (a + b) + atan((a - b - sCode) * c) * sCode + atan((a + b - sCode) * c) * (a + b - sCode) + atan((sCode - a + b) * c) * (a - b)) - log(1.0f + (a - b) * (a - b) * c * c) + log(1.0f + (a + b) * (a + b) * c * c) - log(1.0f + (a + b - sCode) * (a + b - sCode) * c * c) + log(1.0f + (sCode - a + b) * (sCode - a + b) * c * c)));
}
if (sCode == 0.0) sPhys = 0.0f;
if (sCode == 1.0f) sPhys = sMax;
break;
#else
exit_err(NGRID_ERROR);
#endif
}
void xJacobi() {
// Returns the x coordinate Jacobian transformation elements.
const double ORX = 1.0f / float(nx - ix - 1);
for (int i = 0; i < nx - ix; ++i) EXX[i + 1] = float(i) * ORX;
for (int i = 1; i < nx - ix + 1; ++i) {
double sPhys, dssds, d2ssds2;
mkGrid<DIM::X>(EXX[i], sPhys, dssds, d2ssds2);
EXX[i] = sPhys;
dxxdx[i] = dssds;
d2xxdx2[i] = d2ssds2;
DDX[i] = ORX * (1.0f / dssds);
}
}
void yJacobi() {
// Full computational grid with evenly spaced y values between zero and one
const double ORY = 1.0f / float(nPy - 1);
static double YY[nPy];
for (int j = 0; j < nPy; ++j) YY[j] = float(j) * ORY;
double sPhys, dssds, d2ssds2;
if (myPEy == 0) {
for (int j = 0; j < iy / 2; ++j) {
mkGrid<DIM::Y>(0.0f, sPhys, dssds, d2ssds2);
WYY[j] = sPhys, dyydy[j] = dssds, d2yydy2[j] = d2ssds2;
}
for (int j = iy / 2; j < nRy + iy; ++j) {
mkGrid<DIM::Y>(YY[j - iy / 2], sPhys, dssds, d2ssds2);
WYY[j] = sPhys, dyydy[j] = dssds, d2yydy2[j] = d2ssds2;
}
} else if (myPEy == nPEy - 1) {
for (int j = 0; j < nRy + iy / 2; ++j) {
mkGrid<DIM::Y>(YY[j + nPy - nRy - iy / 2], sPhys, dssds, d2ssds2);
WYY[j] = sPhys, dyydy[j] = dssds, d2yydy2[j] = d2ssds2;
}
for (int j = nRy + iy / 2; j < nRy + iy; ++j) {
mkGrid<DIM::Y>(1.0f, sPhys, dssds, d2ssds2);
WYY[j] = sPhys, dyydy[j] = dssds, d2yydy2[j] = d2ssds2;
}
} else {
for (int j = 0; j < ny; ++j) {
mkGrid<DIM::Y>(YY[j + myPEy * nRy - iy / 2], sPhys, dssds, d2ssds2);
WYY[j] = sPhys, dyydy[j] = dssds, d2yydy2[j] = d2ssds2;
}
}
for (int j = 0; j < ny; ++j) DDY[j] = ORY * (1.0f / dyydy[j]);
}
void zJacobi() {
const double ORZ = 1.0f / float(nPz - 1);
static double ZZ[nPz];
for (int k = 0; k < nPz; ++k) ZZ[k] = float(k) * ORZ;
double sPhys, dssds, d2ssds2;
if (myPEz == 0) {
for (int k = 0; k < iz / 2; ++k) {
mkGrid<DIM::Z>(0.0f, sPhys, dssds, d2ssds2);
ZEE[k] = sPhys, dzzdz[k] = dssds, d2zzdz2[k] = d2ssds2;
}
for (int k = iz / 2; k < nRz + iz; ++k) {
mkGrid<DIM::Z>(ZZ[k - iz / 2], sPhys, dssds, d2ssds2);
ZEE[k] = sPhys, dzzdz[k] = dssds, d2zzdz2[k] = d2ssds2;
}
} else if (myPEz == nPEz - 1) {
for (int k = 0; k < nRz + iz / 2; ++k) {
mkGrid<DIM::Z>(ZZ[k + nPz - nRz - iz / 2], sPhys, dssds, d2ssds2);
ZEE[k] = sPhys, dzzdz[k] = dssds, d2zzdz2[k] = d2ssds2;
}
for (int k = nRz + iz / 2; k < nRz + iz; ++k) {
mkGrid<DIM::Z>(1.0f, sPhys, dssds, d2ssds2);
ZEE[k] = sPhys, dzzdz[k] = dssds, d2zzdz2[k] = d2ssds2;
}
} else {
for (int k = 0; k < nz; ++k) {
mkGrid<DIM::Z>(ZZ[k + myPEz * nRz - iz / 2], sPhys, dssds, d2ssds2);
ZEE[k] = sPhys, dzzdz[k] = dssds, d2zzdz2[k] = d2ssds2;
}
}
for (int k = 0; k < nz; ++k) DDZ[k] = ORZ * (1.0f / dzzdz[k]);
}
double FF(double x) {
return A * A * (x * x * x * x * x) * square(std::exp(-x * x) - C) /
square(A * (x * x * x) + 1.0f);
}
void qromb(double (*func)(double), double a, double b, double& ss) {
const int JMAX = 20;
const int JMAXP = JMAX + 1;
const int k = 5;
const int KM = k - 1;
const double EPS = 1.0e-9f;
static double h[JMAXP], s[JMAXP];
h[0] = 1.0f;
for (int j = 0; j < JMAX; j++) {
trapzd(func, a, b, s[j], j);
if (j >= KM) {
double dss;
polint(&h[j - KM], &s[j - KM], k, 0.0f, ss, dss);
if (fabs(dss) <= EPS * fabs(ss)) return;
}
s[j + 1] = s[j];
h[j + 1] = 0.25f * h[j];
}
exit_err("Too many steps in qromb");
}
void polint(double xa[], double ya[], int n, double x, double& y, double& dy) {
const int NMAX = 10;
int ns = 0;
double dif, dift;
static double c[NMAX], d[NMAX];
dif = std::abs(x - xa[0]);
for (int i = 0; i < n; i++) {
double dift = std::abs(x - xa[i]);
if (dift < dif) ns = i, dif = dift;
c[i] = d[i] = ya[i];
}
y = ya[ns--];
for (int m = 0; m < n; m++) {
for (int i = 0; i < n - m; i++) {
double ho = xa[i] - x;
double hp = xa[i + m] - x;
double w = c[i + 1] - d[i];
double den = ho - hp;
if (den == 0.0) exit_err("Failure in polint");
den = w / den;
d[i] = hp * den;
c[i] = ho * den;
}
y += (dy = (2 * ns < (n - m) ? c[ns + 1] : d[ns--]));
}
}
void trapzd(double (*func)(double), double a, double b, double& s, int n) {
if (n == 0) {
s = 0.5f * (b - a) * (func(a) + func(b));
} else {
int it = std::pow(2, n - 1);
double tnm = float(it);
double del = (b - a) / tnm;
double x = a + 0.5f * del;
double sum = 0.0f;
for (int j = 0; j < it; j++) {
sum += func(x);
x += del;
}
s = 0.5f * (s + (b - a) * sum / tnm);
}
}
// CHECKED
void bsstep(double* Y, double* DYDX, int NV, double& X, double HTRY, double EPS, double& HDID, double& HNEXT) {
const int NMAX = 10;
const int IMAX = 11;
const int NUSE = 7;
const double ONE = 1.0f;
const double SHRINK = 0.95f;
const double GROW = 1.2f;
double H = HTRY;
double XSAV = X;
static double YERR[NMAX], YSeq[NMAX];
std::vector<double> YSAV(NMAX), DYSAV(NMAX);
std::vector<int> NSeq{2, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96};
std::vector<std::vector<double>> D(NMAX, std::vector<double>(NUSE));
for (int i = 0; i < NV; ++i) YSAV[i] = Y[i], DYSAV[i] = DYDX[i];
while (1) {
for (int i = 0; i < IMAX; ++i) {
mmid(YSAV, DYSAV, NV, XSAV, H, NSeq[i], YSeq);
double XEST = square(H / NSeq[i]);
rzextr(i, XEST, YSeq, Y, D, YERR, NV, NUSE);
double ERRMAX = 0.0f;
for (int j = 0; j < NV; ++j) {
ERRMAX = std::max(ERRMAX, std::abs(YERR[j] / Y[j]));
}
ERRMAX /= EPS;
if (ERRMAX < 1) {
X = X + H;
HDID = H;
if (i == NUSE) {
HNEXT = H * SHRINK;
} else if (i == NUSE - 1) {
HNEXT = H * GROW;
} else {
HNEXT = (H * NSeq[NUSE - 1]) / NSeq[i];
}
return;
}
}
H = 0.25f * H / std::pow(2.0f, (IMAX - NUSE) / 2);
if (X + H == X) exit_err("BSSTEP: Step size underflow");
}
}
// CHECKED
void mmid(std::vector<double>& Y, const std::vector<double>& DYDX, int NVAR, double XS, double HTOT, int NSTP, double* YOUT) {
const int NMAX = 10;
static double YM[NMAX], YN[NMAX];
double H = HTOT / NSTP, X = XS + H;
for (int i = 0; i < NVAR; ++i) YM[i] = Y[i], YN[i] = Y[i] + H * DYDX[i];
// 假设 derivs 函数是外部定义的函数，根据你的实际情况调用它
derivs(X, YN, NVAR, YOUT);
double H2 = 2.0f * H;
for (int N = 2; N <= NSTP; ++N) {
for (int i = 0; i < NVAR; ++i) {
double SWAP = YM[i] + H2 * YOUT[i];
YM[i] = YN[i];
YN[i] = SWAP;
}
X = X + H;
derivs(X, YN, NVAR, YOUT);
}
for (int i = 0; i < NVAR; ++i) YOUT[i] = 0.5f * (YM[i] + YN[i] + H * YOUT[i]);
}
// CHECKED
void rzextr(int IEST, double XEST, double* YEST, double* YZ, std::vector<std::vector<double>>& D, double* DY, int NV, int NUSE) {
const int IMAX = 11;
const int NMAX = 10;
const int NCOL = 7;
// X 需要在多次调用中保存值 fortran : save x
static double X[IMAX], FX[NCOL];
X[IEST] = XEST;
if (IEST == 0) {
for (int j = 0; j < NV; ++j) YZ[j] = D[j][0] = DY[j] = YEST[j];
} else {
int M1 = std::min(IEST + 1, NUSE);
for (int k = 1; k < M1; ++k) {
FX[k] = X[IEST - k] / XEST;
}
for (int j = 0; j < NV; ++j) {
double YY = YEST[j];
double V = D[j][0];
double C = YY;
double DDY;
D[j][0] = YY;
for (int k = 1; k < M1; ++k) {
double B1 = FX[k] * V;
double B = B1 - C;
if (B != 0.0) {
B = (C - V) / B;
DDY = C * B;
C = B1 * B;
} else {
DDY = V;
}
V = D[j][k];
D[j][k] = DDY;
YY = YY + DDY;
}
DY[j] = DDY;
YZ[j] = YY;
}
}
}
// CHECKED
void derivs(double zz, double* Y, int NV, double* DYDX) {
double z, dzzdz, d2zzdz2;
mkGrid<DIM::Z>(zz, z, dzzdz, d2zzdz2);
double RKAP = 1.0f;
if (PZP != 0.0) RKAP += (RKAPST - 1.0f) / 2.0f * (1.0f + tanh((zz - PZP) / SIGMA));
// if(myPE==0) printf("RKAP=%.20lf\n",RKAP);
DYDX[0] = THETA / RKAP / dzzdz;
DYDX[1] = GRAV / (1.0f + Y[0]) / dzzdz;
}
void getbackground(double x, double& t, double& rho) {
static double YSTART[2];
YSTART[0] = YSTART[1] = 1;
ODEINT(YSTART, 2.0f, x);
t = YSTART[0], rho = YSTART[1] / YSTART[0];
}
/**
* this function is defined in 3dmhdset.f, original version:
*
c========================================================================
c Specification of radiative conductivity (M. Rempel).
c========================================================================
subroutine kappa(z,rho,t,krad)
implicit none
real*8 z,rho,t,alpha,beta,krad
c beta=0.0
c krad=t**6*sqrt(t)/rho**2
c krad=(beta+krad)/(beta+1.0f)
c krad=krad+(1.25-krad)*exp(-(z/0.25)**2)
krad=rho
c krad=(0.9**10+krad**10)**0.1
krad=krad+(1.25-krad)*exp(-5.0*z)
return
end
c========================================================================
*
*/
double kappa(double z, double rho, double t) {
return rho + (1.25f - rho) * exp(-5.0f * z);
}
void derivs1(double x, double yt[2], double dyt[2]) {
const double nad = 0.41f;
const double os = 1.0f;
double krad = kappa(x, yt[1] / yt[0], yt[0]);
double nrad = 0.4f / krad;
if (nrad <= os * nad) {
dyt[0] = nrad;
dyt[1] = yt[1] / yt[0];
} else {
dyt[0] = nad;
dyt[1] = yt[1] / yt[0];
}
}
// void (*derivs1)(double, double[], double[])
// void (*RKQC)(double[], double[], int, double&, double&, double, double[], double&, double&)
void ODEINT(double* YSTART, double X1, double X2) {
const int NVAR = 2, NMAX = 2, MAXSTP = 1000;
const int KMAX = 1;
const double TINY = 1.0e-30f;
const double DXSAV = 1e-4; // literal as double
const double EPS = 1e-8; // literal as double
const double H1 = 1e-4; // literal as double
const double HMIN = 1e-50; // literal as double
int nok = 0, nbad = 0, KOUNT = 0;
static double YSCAL[NMAX], Y[NMAX], DYDX[NMAX], XP[100], YP[NVAR][100];
double X = X1, H = (X2 > X1) ? H1 : -H1;
for (int i = 0; i < NVAR; ++i) Y[i] = YSTART[i];
double XSAV = X - DXSAV * 2.0f;
for (int NSTP = 1; NSTP <= MAXSTP; ++NSTP) {
derivs1(X, Y, DYDX);
for (int i = 0; i < NVAR; ++i) {
YSCAL[i] = std::abs(Y[i]) + std::abs(H * DYDX[i]) + TINY;
}
if (KOUNT < KMAX - 1 && std::abs(X - XSAV) > std::abs(DXSAV)) {
XSAV = X;
XP[KOUNT] = X;
for (int i = 0; i < NVAR; ++i) YP[i][KOUNT] = Y[i];
KOUNT++;
}
if ((X + H - X2) * (X + H - X1) > 0) H = X2 - X;
double HDID, HNEXT;
RKQC(Y, DYDX, NVAR, X, H, EPS, YSCAL, HDID, HNEXT);
if (HDID == H) {
nok++;
} else {
nbad++;
}
if ((X - X2) * (X2 - X1) >= 0) {
// for (int i = 0; i < NVAR; ++i) YSTART[i] = Y[i];
if (KMAX != 0) {
XP[KOUNT] = X;
for (int i = 0; i < NVAR; ++i) YP[i][KOUNT] = Y[i];
KOUNT++;
}
// 将需要用到的数据返回 getbackground
for (int i = 0; i < NVAR; ++i) YSTART[i] = YP[i][KOUNT - 1];
return;
}
if (std::abs(HNEXT) < HMIN) exit_err("Stepsize smaller than minimum.");
H = HNEXT;
}
exit_err("Too many steps.");
}
void RKQC(double* Y, double* DYDX, int N, double& X, double HTRY, double EPS, double* YSCAL, double& HDID, double& HNEXT) {
const int MAXN = 10;
const double FCOR = 1.0f / 15.0f;
const double ONE = 1.0f;
const double SAFETY = 0.9f;
const double ERRCON = 6.0e-4f;
static double YTEMP[MAXN], YSAV[MAXN], DYSAV[MAXN];
const double PGROW = -0.20f;
const double PSHRNK = -0.25f;
double XSAV = X;
for (int i = 0; i < N; i++) YSAV[i] = Y[i], DYSAV[i] = DYDX[i];
double H = HTRY;
while (true) {
double HH = 0.5f * H;
RK4(YSAV, DYSAV, N, XSAV, HH, YTEMP);
X = XSAV + HH;
derivs1(X, YTEMP, DYDX);
RK4(YTEMP, DYDX, N, X, HH, Y);
X = XSAV + H;
if (X == XSAV) {
exit_err("Stepsize not significant in RKQC.");
break;
}
RK4(YSAV, DYSAV, N, XSAV, H, YTEMP);
double ERRMAX = 0.0f;
for (int i = 0; i < N; i++) {
YTEMP[i] = Y[i] - YTEMP[i];
ERRMAX = std::max(ERRMAX, fabs(YTEMP[i] / YSCAL[i]));
}
ERRMAX = ERRMAX / EPS;
if (ERRMAX > 1.0) {
H = SAFETY * H * pow(ERRMAX, PSHRNK);
} else {
HDID = H;
if (ERRMAX > ERRCON) {
HNEXT = SAFETY * H * pow(ERRMAX, PGROW);
} else {
HNEXT = 4.0f * H;
}
break;
}
}
for (int i = 0; i < N; i++) Y[i] += YTEMP[i] * FCOR;
}
void RK4(double* Y, double* DYDX, int N, double X, double H, double* YOUT) {
const int NMAX = 10;
static double YT[NMAX], DYT[NMAX], DYM[NMAX];
double HH = H * 0.5f, H6 = H / 6.0f, XH = X + HH;
for (int i = 0; i < N; i++) YT[i] = Y[i] + HH * DYDX[i];
derivs1(XH, YT, DYT);
for (int i = 0; i < N; i++) YT[i] = Y[i] + HH * DYT[i];
derivs1(XH, YT, DYM);
for (int i = 0; i < N; i++) YT[i] = Y[i] + H * DYM[i], DYM[i] = DYT[i] + DYM[i];
derivs1(X + H, YT, DYT);
for (int i = 0; i < N; i++) YOUT[i] = Y[i] + H6 * (DYDX[i] + DYT[i] + 2.0f * DYM[i]);
}
double RAN2(int& IDUM) {
const int M = 714025, IA = 1366, IC = 150889;
const double RM = 1.0f / M;
static int IIY = 0;
static int IIR[97];
if (IDUM < 0) {
IDUM = fmod(IC - IDUM, M);
for (int j = 0; j < 97; ++j) {
IDUM = fmod(IA * IDUM + IC, M);
IIR[j] = IDUM;
}
IDUM = fmod(IA * IDUM + IC, M);
IIY = IDUM;
}
int j = (97 * IIY) / M;
if (j >= 97 || j < 0) exit_err("RAN2: Error.");
IIY = IIR[j];
double randomValue = float(IIY) * RM;
IDUM = (IA * IDUM + IC) % M;
IIR[j] = IDUM;
return randomValue;
}
void Static() {
const int NV = 2;
const double EPS = 1.0E-12f;
const double RPI = 2.0f * asin(1.0f);
static double Y[NV], DYDX[NV];
static double RND[ny][nx], T[nPz], R[nPz], RK[nPz], DRK[nPz];
static double IIR[97];
std::string FNAME;
double DZZ = 1.0f / float(nPz - 1);
fill(&RU[0][0][0], 0.0f, nx * ny * nz);
fill(&RV[0][0][0], 0.0f, nx * ny * nz);
fill(&RW[0][0][0], 0.0f, nx * ny * nz);
double SZ, SDZZDZ, SD2ZZDZ2;
#if !lShr
#if lRem
for (int k = 0; k < nPz; k++) {
mkGrid<DIM::Z>(static_cast<float>(k) / static_cast<float>(nPz - 1), SZ, SDZZDZ, SD2ZZDZ2);
getbackground(SZ, T[k], R[k]);
RK[k] = kappa(SZ, R[k], T[k]);
RK[k] *= 8.07f * THETA * REPR;
}
mkGrid<DIM::Z>(0, SZ, SDZZDZ, SD2ZZDZ2);
DRK[0] = (-3.0f * RK[0] + 4.0f * RK[1] - RK[2]) * hz * SDZZDZ;
for (int k = 1; k < nPz - 1; ++k) {
mkGrid<DIM::Z>(static_cast<float>(k) / static_cast<float>(nPz - 1), SZ, SDZZDZ, SD2ZZDZ2);
DRK[k] = (RK[k + 1] - RK[k - 1]) * hz * SDZZDZ;
}
mkGrid<DIM::Z>(1, SZ, SDZZDZ, SD2ZZDZ2);
DRK[nPz - 1] = (3.0f * RK[nPz - 1] - 4.0f * RK[nPz - 2] + RK[nPz - 3]) * hz * SDZZDZ;
if (myPE == 0) {
int pos = fOut.find(" ") - 1;
std::string FNAME = fOut.substr(0, pos) + ".strat";
std::ofstream outFile(FNAME.c_str());
for (int k = 0; k < nPz; ++k) {
outFile << T[k] << " " << R[k] << " " << RK[k] / REPR << " " << DRK[k] / REPR << std::endl;
}
outFile.close();
}
TU = T[0];
DZTB = T[nPz - 1] - 4.0f / 3.0f * T[nPz - 2] + 1.0f / 3.0f * T[nPz - 3];
DZTU = T[0] - 4.0f / 3.0f * T[1] + 1.0f / 3.0f * T[2];
#else
T[0] = 1.0f, R[0] = 1.0f;
Y[0] = 0.0f, Y[1] = 0.0f;
double ZZ = 0.0f;
for (int k = 1; k < nPz; ++k) {
double HTRY = DZZ;
derivs(ZZ, Y, NV, DYDX);
double HDID, HNEXT;
bsstep(Y, DYDX, NV, ZZ, HTRY, EPS, HDID, HNEXT);
if (HDID != HTRY) exit_err("Static: Static structure error.");
T[k] = 1.0f + Y[0];
R[k] = exp(Y[1]) / (1.0f + Y[0]);
}
#endif
#else
for (int k = 0; k < nPz; k++) {
T[k] = 1.0f, R[k] = 1.0f;
}
#endif
// Divide among processors.
if (myPEz == 0) {
for (int z = 0; z < iz / 2; z++) {
for (int x = 1; x < nx - ix + 1; x++) {
for (int y = 1; y < ny - iy + 1; y++) {
TT[z][y][x] = T[0];
RO[z][y][x] = R[0];
}
}
#if lRem
RKAPA[z] = RK[0];
DKAPA[z] = DRK[0];
#endif
}
for (int z = iz / 2; z < nz; z++) {
for (int x = 1; x < nx - ix + 1; x++) {
for (int y = 1; y < ny - iy + 1; y++) {
TT[z][y][x] = T[z - iz / 2];
RO[z][y][x] = R[z - iz / 2];
}
}
#if lRem
RKAPA[z] = RK[z - iz / 2];
DKAPA[z] = DRK[z - iz / 2];
#endif
}
} else if (myPEz == nPEz - 1) {
for (int z = 0; z < nRz + iz / 2; z++) {
for (int y = 1; y < ny - iy + 1; y++) {
for (int x = 1; x < nx - ix + 1; x++) {
TT[z][y][x] = T[nPz - nRz - iz / 2 + z];
RO[z][y][x] = R[nPz - nRz - iz / 2 + z];
}
}
#if lRem
RKAPA[z] = RK[nPz - nRz - iz / 2 + z];
DKAPA[z] = DRK[nPz - nRz - iz / 2 + z];
#endif
}
for (int z = nRz + iz / 2; z < nRz + iz; z++) {
for (int y = 1; y < ny - iy + 1; y++) {
for (int x = 1; x < nx - ix + 1; x++) {
TT[z][y][x] = T[nPz - 1];
RO[z][y][x] = R[nPz - 1];
}
}
#if lRem
RKAPA[z] = RK[nPz - 1];
DKAPA[z] = DRK[nPz - 1];
#endif
}
} else {
int Start = myPEz * nRz - iz / 2;
for (int z = 0; z < nz; z++) {
for (int y = 1; y < ny - iy + 1; y++) {
for (int x = 1; x < nx - ix + 1; x++) {
TT[z][y][x] = T[Start + z];
RO[z][y][x] = R[Start + z];
}
}
}
#if lRem
std::memcpy(RKAPA, RK + Start, sizeof(double) * nz);
std::memcpy(DKAPA, DRK + Start, sizeof(double) * nz);
#endif
}
#if lMag
if (AMPB != 0.0) {
double CLN = -4.0f * log(2.0f) / (BFH * BFH);
for (int z = iz / 2 + 1; z <= nz - iz / 2; z++) {
for (int y = 0; y < ny; y++) {
for (int x = 0; x < nx; x++) {
BX[z][y][x] = AMPB * exp(CLN * square(ZEE[z] - BZP));
}
}
}
fill(&BY[0][0][0], 0.0f, nx * ny * nz);
fill(&BZ[0][0][0], 0.0f, nx * ny * nz);
for (int z = iz / 2 + 1; z <= nz - iz / 2; z++) {
for (int y = 1; y < ny - iy + 1; y++) {
for (int x = 1; x < nx - ix + 1; x++) {
RO[z][y][x] -= (BX[z][y][x] * BX[z][y][x] / TT[z][y][x]) * OBETA;
}
}
}
} else {
tube();
}
#endif
if (AMPT != 0.0) {
#define ISW 1
#if ISW == 1
int IDUM = -62659;
for (int nnz = 0; nnz < nPEz; nnz++) {
for (int k = iz / 2; k < nz - iz / 2; k++) {
int iTag = k;
for (int nny = 0; nny < nPEy; nny++) {
if (myPE == 0) {
for (int y = iy / 2; y < ny - iy / 2; y++) {
for (int x = ix / 2; x < nx - ix / 2; x++) {
RND[y][x] = 1.0f + AMPT * (RAN2(IDUM) - 0.5E00);
}
}
if ((nny + nPEy * nnz) != 0) {
MPI_Send(RND, nx * ny, MPI_DOUBLE, nny + nPEy * nnz, iTag, MPI_COMM_WORLD);
} else {
std::memcpy(&WW1[k][0][0], RND, sizeof(double) * nx * ny);
}
} else {
if (myPE == (nny + nPEy * nnz)) {
MPI_Status status;
MPI_Recv(&WW1[k][0][0], nx * ny, MPI_DOUBLE, 0, iTag, MPI_COMM_WORLD, &status);
}
}
}
}
}
for (int z = iz / 2; z < nz - iz / 2; z++) {
for (int y = iy / 2; y < ny - iy / 2; y++) {
for (int x = ix / 2; x < nx - ix / 2; x++) {
#if !lShr
TT[z][y][x] = TT[z][y][x] * WW1[z][y][x];
#else
RV[z][y][x] = RV[z][y][x] + WW1[z][y][x] - 1.0f;
#endif
}
}
}
#else
double RPI = 2.0f * asin(1.0f);
for (int z = iz / 2; z < nz - iz / 2; ++z) {
for (int y = 1; y < ny - iy + 1; ++y) {
for (int x = 1; x < nx - ix + 1; ++x) {
double RKY = WYY[y] / yMax * float(nPy) / (float(nPy) + 1.0f) * 2.0f * RPI * 8.0f;
double RKZ = ZEE[z] / zMax * 2.0f * RPI;
#if !lShr
TT[z][y][x] = TT[z][y][x] + AMPT * sin(RKY) * sin(RKZ) / RO[z][y][x];
#else
RV[z][y][x] = RV[z][y][x] + AMPT * sin(RKY) * sin(RKZ) / RO[z][y][x];
#endif
}
}
}
#endif
#undef ISW
}
}
void tube() {
#if lMag
fill(&BX[0][0][0], 0.0f, nx * ny * nz);
fill(&BY[0][0][0], 0.0f, nx * ny * nz);
fill(&BZ[0][0][0], 0.0f, nx * ny * nz);
#endif
double OGAMMA = 1.0f / GAMMA;
setup(ipar, par);
static double XN[nTubes], ZN[nTubes], RRN[nTubes], expI[nTubes], HN[nTubes], QN[nTubes], BYN[nTubes], AN[nTubes];
double XCENT, ZCENT, R_MAX, C_MT, LAMBDA, VZ0;
int JCUT, xl, xr, yl, yr, zl, zr;
#if nTube == 0
#if lMag
fill(&BX[0][0][0], 0.0f, nx * ny * nz);
fill(&BY[0][0][0], 0.0f, nx * ny * nz);
fill(&BZ[0][0][0], 0.0f, nx * ny * nz);
#endif
fill(&RU[0][0][0], 0.0f, nx * ny * nz);
fill(&RV[0][0][0], 0.0f, nx * ny * nz);
fill(&RW[0][0][0], 0.0f, nx * ny * nz);
#elif nTube == 1
XCENT = par[34];
ZCENT = par[35];
R_MAX = par[36];
C_MT = par[37];
A = par[38];
C = exp(-R_MAX * R_MAX);
double ROGAPR = pow(RO[2][1][2], GAMMA) / (RO[2][1][2] * TT[2][1][2]);
JCUT = iy / 2 + 1;
xl = 1, xr = nx - ix + 1;
yl = 1, yr = ny - iy + 1;
zl = iz / 2, zr = nz - iz / 2;
for (int z = zl; z < zr; ++z) {
for (int x = xl; x < xr; ++x) {
double XNEW = EXX[x] - XCENT;
double ZNEW = ZEE[z] - ZCENT;
double RNEW = sqrt(XNEW * XNEW + ZNEW * ZNEW);
if (RNEW < R_MAX) {
BY[z][JCUT][x] = (exp(-RNEW * RNEW) - C) / (1.0f - C);
double BPHI = BY[z][JCUT][x] * C_MT * A * pow(RNEW, 3) / (A * pow(RNEW, 3) + 1.0f);
if (RNEW != 0.0) {
BX[z][JCUT][x] = BPHI * ZNEW / RNEW;
BZ[z][JCUT][x] = -BPHI * XNEW / RNEW;
}
double DPR_TOT;
qromb(FF, RNEW, R_MAX, DPR_TOT);
double DPR = OBETA / square(1.0f - C) * DPR_TOT - (square(BX[z][JCUT][x]) + square(BY[z][JCUT][x]) + square(BZ[z][JCUT][x])) * OBETA / 2.0f;
double PRE = RO[z][JCUT][x] * TT[z][JCUT][x] + DPR;
RO[z][JCUT][x] = pow(ROGAPR * PRE, OGAMMA);
TT[z][JCUT][x] = PRE / RO[z][JCUT][x];
}
}
}
for (int z = zl; z < zr; ++z) {
for (int y = yl; y < yr; ++y) {
for (int x = xl; x < xr; ++x) {
RO[z][y][x] = RO[z][JCUT][x];
TT[z][y][x] = TT[z][JCUT][x];
BX[z][y][x] = BX[z][JCUT][x];
BY[z][y][x] = BY[z][JCUT][x];
BZ[z][y][x] = BZ[z][JCUT][x];
}
}
}
fill(&RU[0][0][0], 0.0f, nx * ny * nz);
fill(&RV[0][0][0], 0.0f, nx * ny * nz);
fill(&RW[0][0][0], 0.0f, nx * ny * nz);
#elif nTube == 2
XCENT = par[34];
ZCENT = par[35];
R_MAX = par[36];
C_MT = par[37];
A = par[38];
C = exp(-R_MAX * R_MAX);
double LAMBDA = par[51];
double VZ0 = par[52];
fill(&RW[0][0][0], 0.0f, nx * ny * nz);
JCUT = iy / 2 + 1;
xl = 1, xr = nx - ix + 1;
yl = 1, yr = ny - iy + 1;
zl = iz / 2, zr = nz - iz / 2;
for (int z = zl; z < zr; ++z) {
for (int x = xl; x < xr; ++x) {
double XNEW = EXX[x] - XCENT;
double ZNEW = ZEE[z] - ZCENT;
double RNEW = sqrt(XNEW * XNEW + ZNEW * ZNEW);
if (RNEW < R_MAX) {
BY[z][JCUT][x] = (exp(-RNEW * RNEW) - C) / (1.0f - C);
double BPHI = BY[z][JCUT][x] * C_MT * A * pow(RNEW, 3) / (A * pow(RNEW, 3) + 1.0f);
if (RNEW != 0.0) {
BX[z][JCUT][x] = BPHI * ZNEW / RNEW;
BZ[z][JCUT][x] = -BPHI * XNEW / RNEW;
}
double DPR_TOT;
qromb(FF, RNEW, R_MAX, DPR_TOT);
double DPR = OBETA / square(1.0f - C) * DPR_TOT - (square(BX[z][JCUT][x]) + square(BY[z][JCUT][x]) + square(BZ[z][JCUT][x])) * OBETA / 2.0f;
double PRE = RO[z][JCUT][x] * TT[z][JCUT][x] + DPR;
TT[z][JCUT][x] = PRE / RO[z][JCUT][x];
}
}
}
for (int z = zl; z < zr; ++z) {
for (int y = yl; y < yr; ++y) {
for (int x = xl; x < xr; ++x) {
TT[z][y][x] = TT[z][JCUT][x];
BX[z][y][x] = BX[z][JCUT][x];
BY[z][y][x] = BY[z][JCUT][x];
BZ[z][y][x] = BZ[z][JCUT][x];
RW[z][y][x] = RW[z][JCUT][x];
}
}
}
std::fill(&RU[0][0][0], &RU[0][0][0] + nx * ny * nz, 0.0f);
std::fill(&RV[0][0][0], &RV[0][0][0] + nx * ny * nz, 0.0f);
for (int z = zl; z < zr; ++z) {
for (int y = yl; y < yr; ++y) {
for (int x = xl; x < xr; ++x) {
RW[z][y][x] *= sin(2 * PI * WYY[y] / LAMBDA - PI / 2);
}
}
}
#elif nTube == 3
XCENT = par[34];
ZCENT = par[35];
R_MAX = par[36];
C_MT = par[37];
A = par[38];
C = exp(-R_MAX * R_MAX);
LAMBDA = par[51];
VZ0 = par[52];
fill(&RW[0][0][0], 0.0f, nx * ny * nz);
JCUT = iy / 2 + 1;
xl = 1, xr = nx - ix + 1;
yl = 1, yr = ny - iy + 1;
zl = iz / 2, zr = nz - iz / 2;
for (int z = zl; z < zr; ++z) {
for (int x = xl; x < xr; ++x) {
double XNEW = EXX[x] - XCENT;
double ZNEW = ZEE[z] - ZCENT;
double RNEW = sqrt(XNEW * XNEW + ZNEW * ZNEW);
if (RNEW < R_MAX) {
BY[z][JCUT][x] = (exp(-RNEW * RNEW) - C) / (1.0f - C);
double BPHI = BY[z][JCUT][x] * C_MT * A * pow(RNEW, 3) / (A * pow(RNEW, 3) + 1.0f);
if (RNEW != 0.0) {
BX[z][JCUT][x] = BPHI * ZNEW / RNEW;
BZ[z][JCUT][x] = -BPHI * XNEW / RNEW;
}
double DPR_TOT;
qromb(FF, RNEW, R_MAX, DPR_TOT);
double DPR = OBETA / square(1.0f - C) * DPR_TOT - (square(BX[z][JCUT][x]) + square(BY[z][JCUT][x]) + square(BZ[z][JCUT][x])) * OBETA / 2.0f;
double PRE = RO[z][JCUT][x] * TT[z][JCUT][x] + DPR;
TT[z][JCUT][x] = PRE / RO[z][JCUT][x];
}
}
}
for (int z = zl; z < zr; ++z) {
for (int y = yl; y < yr; ++y) {
for (int x = xl; x < xr; ++x) {
TT[z][y][x] = TT[z][JCUT][x];
BX[z][y][x] = BX[z][JCUT][x];
BY[z][y][x] = BY[z][JCUT][x];
BZ[z][y][x] = BZ[z][JCUT][x];
RW[z][y][x] = RW[z][JCUT][x];
}
}
}
std::fill(&RU[0][0][0], &RU[0][0][0] + nx * ny * nz, 0.0f);
std::fill(&RV[0][0][0], &RV[0][0][0] + nx * ny * nz, 0.0f);
std::fill(&RW[0][0][0], &RW[0][0][0] + nx * ny * nz, 0.0f);
#elif nTube == 4
ZCENT = par[35];
R_MAX = par[36];
C_MT = par[37];
A = par[38];
int JCUT = iy / 2 + 1;
int xl = 1, xr = nx - ix + 1;
int yl = 1, yr = ny - iy + 1;
int zl = iz / 2, zr = nz - iz / 2;
for (int z = zl; z < zr; ++z) {
for (int x = xl; x < xr; ++x) {
double ZNEW = ZEE[z] - ZCENT;
double RNEW = sqrt(ZNEW * ZNEW);
BY[z][JCUT][x] = (1.0f - tanh((RNEW - R_MAX) / A)) / 2;
double PRE = RO[z][JCUT][x] * TT[z][JCUT][x] - BY[z][JCUT][x] * BY[z][JCUT][x] * OBETA / 2.0f;
RO[z][JCUT][x] = PRE / TT[z][JCUT][x];
}
}
for (int z = zl; z < zr; ++z) {
for (int y = yl; y < yr; ++y) {
for (int x = xl; x < xr; ++x) {
BY[z][y][x] = BY[z][JCUT][x];
RO[z][y][x] = RO[z][JCUT][x];
}
}
}
std::fill(&RU[0][0][0], &RU[0][0][0] + nx * ny * nz, 0.0f);
std::fill(&RV[0][0][0], &RV[0][0][0] + nx * ny * nz, 0.0f);
#elif nTube == 5
ZCENT = par[35];
R_MAX = par[36];
C_MT = par[37];
A = par[38];
double HH = par[55];
bool ISTAG = 1;
int N = 0;
double DCOL = xMax / float(NCOL);
double DROW = 2.0f * R_MAX / float(nRow);
for (int k = 1; k <= nRow; k++) {
for (int i = 1; i <= NCOL; i++) {
if (ISTAG == 0) {
XN[N - 1] = float(i) * DCOL - DCOL / 2.0f;
} else {
XN[N - 1] = float(i) * DCOL - float(k) * DCOL / 2.0f;
if (XN[N - 1] < 0.0) {
XN[N - 1] = xMax + XN[N - 1];
}
}
ZN[N - 1] = ZCENT - R_MAX - DROW / 2.0f + float(k) * DROW;
N++;
}
}