void init_KidaVortex(struct Field fldi) {
double a = param.vortex_a;
double b = param.vortex_b;
int i,j,k;
double w0, x, y;
double chi;
chi = b / a;
w0 = 1.0/chi*(chi + 1.0)/(chi-1.0); // According to Kida!
for(i = 0 ; i < NX/NPROC ; i++) {
x = - param.lx / 2 + (param.lx * (i + rank * NX / NPROC)) / NX;
for(j = 0 ; j < NY ; j++) {
y = - param.ly / 2 + (param.ly * j) / NY;
#ifdef WITH_2D
if(x * x / (a * a) + y * y / (b * b) < 1) {
// we are in the vortex
wr1[j + (NY+2) * i] = -w0;
}
else {
wr1[j + (NY+2) * i] = 0.0;
}
#else
for(k = 0 ; k < NZ ; k++) {
if(x * x / (a * a) + y * y / (b * b) < 1) {
// we are in the vortex
wr1[k + j*(NZ+2) + (NZ+2) * NY * i] = -w0;
}
else {
wr1[k + j*(NZ+2) + (NZ+2) * NY * i] = 0.0;
}
}
#endif
}
}
// transform
gfft_r2c(wr1);
for(i = 0 ; i < NTOTAL_COMPLEX ; i++) {
fldi.vx[ i ] += I * ky[i] * w1[i] * ik2t[i];
fldi.vy[ i ] += -I * kxt[i] * w1[i] * ik2t[i];
}
// done
return;
}
void init_Bench(struct Field fldi) {
const double a = 0.3;
const double b = 0.4;
int i,j,k;
double w0, x, y;
double chi;
chi = b / a;
w0 = 1.0/chi*(chi + 1)/(chi-1.0); // According to Kida!
for(i = 0 ; i < NX/NPROC ; i++) {
x = - param.lx / 2. + (param.lx * (i + rank * NX / NPROC)) / NX;
for(j = 0 ; j < NY ; j++) {
y = - param.ly / 2. + (param.ly * j) / NY;
for(k = 0 ; k < NZ ; k++) {
if(x * x / (a * a) + y * y / (b * b) < 1) {
// we are in the vortex
wr1[k + j*(NZ+2) + (NZ+2) * NY * i] = -w0;
}
else {
wr1[k + j*(NZ+2) + (NZ+2) * NY * i] = 0.0;
}
}
}
}
// transform
gfft_r2c(wr1);
for(i = 0 ; i < NTOTAL_COMPLEX ; i++) {
fldi.vx[ i ] += I * ky[i] * w1[i] * ik2t[i];
fldi.vy[ i ] += -I * kxt[i] * w1[i] * ik2t[i];
}
// Brake vertical symmetry
if(rank==0) {
fldi.vx[1] = 1000.0 / NTOTAL;
fldi.vy[1] = 1000.0 / NTOTAL;
#ifdef MHD
fldi.bx[1] = 1000.0 / NTOTAL;
fldi.by[1] = 1000.0 / NTOTAL;
#endif
}
// done
return;
}
void u_iii_forcing(struct Field fldi, double dt) {
double *x, *y, *z;
int i,j,k;
x = (double *) fftw_malloc( sizeof(double complex) * NTOTAL_COMPLEX);
if (x == NULL) ERROR_HANDLER( ERROR_CRITICAL, "No memory for x allocation");
y = (double *) fftw_malloc( sizeof(double complex) * NTOTAL_COMPLEX);
if (y == NULL) ERROR_HANDLER( ERROR_CRITICAL, "No memory for y allocation");
z = (double *) fftw_malloc( sizeof(double complex) * NTOTAL_COMPLEX);
if (z == NULL) ERROR_HANDLER( ERROR_CRITICAL, "No memory for z allocation");
// Initialize the arrays
for(i = 0 ; i < NX/NPROC ; i++) {
for(j = 0 ; j < NY ; j++) {
for(k = 0 ; k < NZ ; k++) {
x[k + (NZ + 2) * j + (NZ + 2) * NY * i] = - param.lx / 2 + (param.lx * (i + rank * NX / NPROC)) / NX;
y[k + (NZ + 2) * j + (NZ + 2) * NY * i] = - param.ly / 2 + (param.ly * j ) / NY;
z[k + (NZ + 2) * j + (NZ + 2) * NY * i] = - param.lz / 2 + (param.lz * k ) / NZ;
}
}
}
// Initialize the extra points (k=NZ and k=NZ+1) to zero to prevent stupid things from happening...
for(i = 0 ; i < NX/NPROC ; i++) {
for(j = 0 ; j < NY ; j++) {
for(k = NZ ; k < NZ + 2 ; k++) {
x[k + (NZ + 2) * j + (NZ + 2) * NY * i] = 0.0;
y[k + (NZ + 2) * j + (NZ + 2) * NY * i] = 0.0;
z[k + (NZ + 2) * j + (NZ + 2) * NY * i] = 0.0;
}
}
}
// Init work array to zero
for(i = 0 ; i < NX/NPROC ; i++) {
for(j = 0 ; j < NY ; j++) {
for(k = 0 ; k < NZ + 2 ; k++) {
wr4[k + (NZ + 2) * j + (NZ + 2) * NY * i] = 0.0;
wr5[k + (NZ + 2) * j + (NZ + 2) * NY * i] = 0.0;
wr6[k + (NZ + 2) * j + (NZ + 2) * NY * i] = 0.0;
}
}
}
/*******************************************************************
** This part can be modified **************************
********************************************************************/
// The velocity field vx,vy,vz is stored in wr1,wr2,wr3
for(i = 0 ; i < 2*NTOTAL_COMPLEX ; i++) {
wr4[i] = param.modified_ABC_flow_D*(
cos(x[i]/param.modified_ABC_flow_m)*(
param.modified_ABC_flow_A*param.modified_ABC_flow_kz*sin(z[i] /(double) param.modified_ABC_flow_kz ) +
param.modified_ABC_flow_C*param.modified_ABC_flow_ky*cos(y[i] /(double) param.modified_ABC_flow_ky)
) +
sin(x[i]/param.modified_ABC_flow_m)/param.modified_ABC_flow_m*(
0
)
);
wr5[i] = param.modified_ABC_flow_D*(
cos(x[i]/param.modified_ABC_flow_m)*(
param.modified_ABC_flow_B*param.modified_ABC_flow_kx*sin(x[i] /(double) param.modified_ABC_flow_kx ) +
param.modified_ABC_flow_A*param.modified_ABC_flow_kz*cos(z[i] /(double) param.modified_ABC_flow_kz)
) +
sin(x[i]/param.modified_ABC_flow_m)/param.modified_ABC_flow_m*(
param.modified_ABC_flow_B*cos(x[i] /(double) param.modified_ABC_flow_kx) +
param.modified_ABC_flow_C*sin(y[i] /(double) param.modified_ABC_flow_ky)
)
);
wr6[i] = param.modified_ABC_flow_D*(
cos(x[i]/param.modified_ABC_flow_m)*(
param.modified_ABC_flow_C*param.modified_ABC_flow_ky*sin(y[i] /(double) param.modified_ABC_flow_ky ) +
param.modified_ABC_flow_B*param.modified_ABC_flow_kx*cos(x[i] /(double) param.modified_ABC_flow_kx)
) +
sin(x[i]/param.modified_ABC_flow_m)/param.modified_ABC_flow_m*(
-param.modified_ABC_flow_A*cos(z[i] /(double) param.modified_ABC_flow_kz) +
-param.modified_ABC_flow_B*sin(x[i] /(double) param.modified_ABC_flow_kx)
)
);
}
gfft_r2c(wr4);
gfft_r2c(wr5);
gfft_r2c(wr6);
for(i = 0 ; i < NTOTAL_COMPLEX ; i++) {
w4[i] = w4[i] * mask[i];
w5[i] = w5[i] * mask[i];
w6[i] = w6[i] * mask[i];
}
for( i = 0; i < NX_COMPLEX/NPROC; i++) {
for( j = 0; j < NY_COMPLEX; j++) {
for( k = 0; k < NZ_COMPLEX; k++) {
fldi.vx[ IDX3D ] += w4[ IDX3D ] * (1 - exp(-nu*k2t[IDX3D]*dt)) ;
fldi.vy[ IDX3D ] += w5[ IDX3D ] * (1 - exp(-nu*k2t[IDX3D]*dt)) ;
fldi.vz[ IDX3D ] += w6[ IDX3D ] * (1 - exp(-nu*k2t[IDX3D]*dt)) ;
}
}
}
#ifdef U_III_FORCING_EXTRA
gfft_c2r_t(w4);
gfft_c2r_t(w5);
gfft_c2r_t(w6);
#ifdef _OPENMP
#pragma omp parallel for private(i) schedule(static)
#endif
for( i = 0 ; i < 2*NTOTAL_COMPLEX ; i++) {
wr10[i] = wr4[i] * wr4[i] / ((double) NTOTAL*NTOTAL);
wr11[i] = wr5[i] * wr5[i] / ((double) NTOTAL*NTOTAL);
#ifndef WITH_2D
wr12[i] = wr6[i] * wr6[i] / ((double) NTOTAL*NTOTAL);
#endif
wr7[i] = wr4[i] * wr5[i] / ((double) NTOTAL*NTOTAL);
wr8[i] = wr4[i] * wr6[i] / ((double) NTOTAL*NTOTAL);
wr9[i] = wr5[i] * wr6[i] / ((double) NTOTAL*NTOTAL);
}
gfft_r2c_t(wr10);
gfft_r2c_t(wr11);
#ifndef WITH_2D
gfft_r2c_t(wr12);
#endif
gfft_r2c_t(wr7);
gfft_r2c_t(wr8);
gfft_r2c_t(wr9);
#ifdef _OPENMP
#pragma omp parallel for private(i) schedule(static)
#endif
for( i = 0 ; i < NTOTAL_COMPLEX ; i++) {
fldi.vx[i] += I * mask[i] / (nu * k2t) * (1 - exp(-nu*k2t[IDX3D]*dt)) * (
kxt[i] * w10[i] + ky[i] * w7[i] + kz[i] * w8[i] );
fldi.vy[i] += I * mask[i] / (nu * k2t) * (1 - exp(-nu*k2t[IDX3D]*dt)) * (
kxt[i] * w7[i] + ky[i] * w11[i] + kz[i] * w9[i] );
fldi.vz[i] += I * mask[i] / (nu * k2t) * (1 - exp(-nu*k2t[IDX3D]*dt)) * (
kxt[i] * w8[i] + ky[i] * w9[i] + kz[i] * w12[i] ); // since kz=0 in 2D, kz*w6 gives 0, even if w6 is some random array
}
#endif
projector(fldi.vx,fldi.vy,fldi.vz);
return;
}
void init_SpatialStructure(struct Field fldi) {
double *x,*y,*z;
int i,j,k;
/*******************************************************************
** This part does not need to be modified **************************
********************************************************************/
// Allocate coordinate arrays
x = (double *) fftw_malloc( sizeof(double complex) * NTOTAL_COMPLEX);
if (x == NULL) ERROR_HANDLER( ERROR_CRITICAL, "No memory for x allocation");
y = (double *) fftw_malloc( sizeof(double complex) * NTOTAL_COMPLEX);
if (y == NULL) ERROR_HANDLER( ERROR_CRITICAL, "No memory for y allocation");
z = (double *) fftw_malloc( sizeof(double complex) * NTOTAL_COMPLEX);
if (z == NULL) ERROR_HANDLER( ERROR_CRITICAL, "No memory for z allocation");
// Initialize the arrays
for(i = 0 ; i < NX/NPROC ; i++) {
for(j = 0 ; j < NY ; j++) {
for(k = 0 ; k < NZ ; k++) {
x[k + (NZ + 2) * j + (NZ + 2) * NY * i] = - param.lx / 2 + (param.lx * (i + rank * NX / NPROC)) / NX;
y[k + (NZ + 2) * j + (NZ + 2) * NY * i] = - param.ly / 2 + (param.ly * j ) / NY;
z[k + (NZ + 2) * j + (NZ + 2) * NY * i] = - param.lz / 2 + (param.lz * k ) / NZ;
}
}
}
// Initialize the extra points (k=NZ and k=NZ+1) to zero to prevent stupid things from happening...
for(i = 0 ; i < NX/NPROC ; i++) {
for(j = 0 ; j < NY ; j++) {
for(k = NZ ; k < NZ + 2 ; k++) {
x[k + (NZ + 2) * j + (NZ + 2) * NY * i] = 0.0;
y[k + (NZ + 2) * j + (NZ + 2) * NY * i] = 0.0;
z[k + (NZ + 2) * j + (NZ + 2) * NY * i] = 0.0;
}
}
}
// Init work array to zero
for(i = 0 ; i < NX/NPROC ; i++) {
for(j = 0 ; j < NY ; j++) {
for(k = 0 ; k < NZ + 2 ; k++) {
wr1[k + (NZ + 2) * j + (NZ + 2) * NY * i] = 0.0;
wr2[k + (NZ + 2) * j + (NZ + 2) * NY * i] = 0.0;
wr3[k + (NZ + 2) * j + (NZ + 2) * NY * i] = 0.0;
wr4[k + (NZ + 2) * j + (NZ + 2) * NY * i] = 0.0;
wr5[k + (NZ + 2) * j + (NZ + 2) * NY * i] = 0.0;
wr6[k + (NZ + 2) * j + (NZ + 2) * NY * i] = 0.0;
}
}
}
/*******************************************************************
** This part can be modified **************************
********************************************************************/
// The velocity field vx,vy,vz is stored in wr1,wr2,wr3
// The magnetic field bx,by,bz is stored in wr4,wr5,wr6 (ignored if MHD is not set)
for(i = 0 ; i < 2*NTOTAL_COMPLEX ; i++) {
// Example: init a flux tube in the x direction+a vertical displacement
// wr4[i] = exp(-(y[i]*y[i]+z[i]*z[i])*20.0);
// wr3[i] = 0.5*cos(x[i] * 2.0 * M_PI);
// Example: twisted flux tube + vertical displacement
wr4[i] = exp(-(y[i]*y[i]+z[i]*z[i])/(0.2*0.2));
wr5[i] = fabs(z[i])*1.0*wr4[i];
wr6[i] = -fabs(y[i])*1.0*wr4[i];
wr3[i] = 0.5*cos(x[i] * 2.0 * M_PI);
if (i==3*NY*(NZ+2)) fprintf(stderr," %d %e",i,x[i]);
}
/*******************************************************************
** This part does not need to be modified **************************
********************************************************************/
// Fourier transform everything
gfft_r2c(wr1);
gfft_r2c(wr2);
gfft_r2c(wr3);
gfft_r2c(wr4);
gfft_r2c(wr5);
gfft_r2c(wr6);
// Transfer data in the relevant array (including dealiasing mask)
for(i = 0 ; i < NTOTAL_COMPLEX ; i++) {
fldi.vx[i] += w1[i] * mask[i];
fldi.vy[i] += w2[i] * mask[i];
fldi.vz[i] += w3[i] * mask[i];
#ifdef MHD
fldi.bx[i] += w4[i] * mask[i];
fldi.by[i] += w5[i] * mask[i];
fldi.bz[i] += w6[i] * mask[i];
#endif
}
// free memory
fftw_free(x);
fftw_free(y);
fftw_free(z);
//done
return;
}