int main(int argc, char *argv[])
{
int i;
bool bScale = false;
double fScale = 0.0f;
char * newFName = 0;
DiffSimu smgr( argc, argv );
if (argc < 2) {
printHelp();
exit(-1);
}
i = 1;
while (i<argc) {
if (strcmp("-s", argv[i]) == 0) {
bScale = true;
fScale = atof( argv[++i] );
newFName = argv[++i];
}
i++;
}
if (bScale) {
Grid * g = smgr.getGrid();
if (g != 0) {
scaleGrid(g,fScale);
DpReader dpr;
dpr.SaveToFile(g,newFName);
}
}
return(0);
}
void initTurbulence(ref_ptr<VectorGrid> grid, double Brms, double lMin,
double lMax, double alpha, int seed) {
size_t Nx = grid->getNx();
size_t Ny = grid->getNy();
size_t Nz = grid->getNz();
if ((Nx != Ny) or (Ny != Nz))
throw std::runtime_error("turbulentField: only cubic grid supported");
double spacing = grid->getSpacing();
if (lMin < 2 * spacing)
throw std::runtime_error("turbulentField: lMin < 2 * spacing");
if (lMin >= lMax)
throw std::runtime_error("turbulentField: lMin >= lMax");
if (lMax > Nx * spacing / 2)
throw std::runtime_error("turbulentField: lMax > size / 2");
size_t n = Nx; // size of array
size_t n2 = (size_t) floor(n / 2) + 1; // size array in z-direction in configuration space
// arrays to hold the complex vector components of the B(k)-field
fftwf_complex *Bkx, *Bky, *Bkz;
Bkx = (fftwf_complex*) fftwf_malloc(sizeof(fftwf_complex) * n * n * n2);
Bky = (fftwf_complex*) fftwf_malloc(sizeof(fftwf_complex) * n * n * n2);
Bkz = (fftwf_complex*) fftwf_malloc(sizeof(fftwf_complex) * n * n * n2);
Random random;
if (seed != 0)
random.seed(seed); // use given seed
// calculate the n possible discrete wave numbers
double K[n];
for (int i = 0; i < n; i++)
K[i] = (double) i / n - i / (n / 2);
// construct the field in configuration space
int i;
double k, theta, phase, cosPhase, sinPhase;
double kMin = spacing / lMax;
double kMax = spacing / lMin;
Vector3f b; // real b-field vector
Vector3f ek, e1, e2; // orthogonal base
Vector3f n0(1, 1, 1); // arbitrary vector to construct orthogonal base
for (size_t ix = 0; ix < n; ix++) {
for (size_t iy = 0; iy < n; iy++) {
for (size_t iz = 0; iz < n2; iz++) {
i = ix * n * n2 + iy * n2 + iz;
ek.setXYZ(K[ix], K[iy], K[iz]);
k = ek.getR();
// wave outside of turbulent range -> B(k) = 0
if ((k < kMin) || (k > kMax)) {
Bkx[i][0] = 0;
Bkx[i][1] = 0;
Bky[i][0] = 0;
Bky[i][1] = 0;
Bkz[i][0] = 0;
Bkz[i][1] = 0;
continue;
}
// construct an orthogonal base ek, e1, e2
if (ek.isParallelTo(n0, float(1e-3))) {
// ek parallel to (1,1,1)
e1.setXYZ(-1., 1., 0);
e2.setXYZ(1., 1., -2.);
} else {
// ek not parallel to (1,1,1)
e1 = n0.cross(ek);
e2 = ek.cross(e1);
}
e1 /= e1.getR();
e2 /= e2.getR();
// random orientation perpendicular to k
theta = 2 * M_PI * random.rand();
b = e1 * cos(theta) + e2 * sin(theta);
// normal distributed amplitude with mean = 0 and sigma = k^alpha/2
b *= random.randNorm() * pow(k, alpha / 2);
// uniform random phase
phase = 2 * M_PI * random.rand();
cosPhase = cos(phase); // real part
sinPhase = sin(phase); // imaginary part
Bkx[i][0] = b.x * cosPhase;
Bkx[i][1] = b.x * sinPhase;
Bky[i][0] = b.y * cosPhase;
Bky[i][1] = b.y * sinPhase;
Bkz[i][0] = b.z * cosPhase;
Bkz[i][1] = b.z * sinPhase;
}
}
}
// in-place, complex to real, inverse Fourier transformation on each component
// note that the last elements of B(x) are unused now
float *Bx = (float*) Bkx;
fftwf_plan plan_x = fftwf_plan_dft_c2r_3d(n, n, n, Bkx, Bx, FFTW_ESTIMATE);
fftwf_execute(plan_x);
fftwf_destroy_plan(plan_x);
float *By = (float*) Bky;
fftwf_plan plan_y = fftwf_plan_dft_c2r_3d(n, n, n, Bky, By, FFTW_ESTIMATE);
fftwf_execute(plan_y);
fftwf_destroy_plan(plan_y);
float *Bz = (float*) Bkz;
fftwf_plan plan_z = fftwf_plan_dft_c2r_3d(n, n, n, Bkz, Bz, FFTW_ESTIMATE);
fftwf_execute(plan_z);
fftwf_destroy_plan(plan_z);
// save to grid
for (size_t ix = 0; ix < n; ix++) {
for (size_t iy = 0; iy < n; iy++) {
for (size_t iz = 0; iz < n; iz++) {
i = ix * n * 2 * n2 + iy * 2 * n2 + iz;
Vector3f &b = grid->get(ix, iy, iz);
b.x = Bx[i];
b.y = By[i];
b.z = Bz[i];
}
}
}
fftwf_free(Bkx);
fftwf_free(Bky);
fftwf_free(Bkz);
scaleGrid(grid, Brms / rmsFieldStrength(grid)); // normalize to Brms
}
