Init_spectral.cpp

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#include <Init_spectral.h>
#include <IJK_Field_vector.h>
#include <string>
 
Implemente_instanciable( Init_spectral, "Init_spectral", Objet_U ) ;
 
Sortie& Init_spectral::printOn( Sortie& os ) const
{
  Objet_U::printOn( os );
  return os;
}
 
Entree& Init_spectral::readOn( Entree& is )
{
  Objet_U::readOn( is );
  return is;
}
 
double randInRange(double min, double max)
{
  return min + ((double)(rand())/(double)(RAND_MAX)) * (max-min);
}
 
void compute_inital_velocity_spectral(IJK_Field_vector3_double& velocity)
{
  Cout << finl;
  Cout << " = Initialisation du champ de vitesse =" << finl;
  Cout << finl;
 
  fftw_plan plan_ux;
  fftw_plan plan_uy;
  fftw_plan plan_uz;
 
  unsigned int seed = 1;
  int kmax = velocity[0].ni();
  // double kpic = 10;
  // double s = 2;
  // DoubleTab coord_velocity_fourier(kmax,2);
  DoubleTab angles(kmax,3); // (theta_1, theta_2 et phi)
 
  // Tirage aleatoire
  srand(seed);
  for(int i=0; i<kmax; i++)
    {
      angles(i,0) = randInRange(0.0, 2.*M_PI);
      angles(i,1) = randInRange(0.0, 2.*M_PI);
      angles(i,2) = randInRange(0.0, 2.*M_PI);
    }
 
  // On définit le tableau des nombres d'ondes de 0 à Kmax/2-1 puis de -Kmax/2 à -1
  DoubleTab kx(kmax, 1);
  for (int i=0 ; i<kmax/2; i++)
    {
      kx[i] = i;
    }
  for (int i=-kmax/2; i<0; i++)
    {
      kx[i+kmax] = i;
    }
  kx[0] = 1; // pour la division par zéro
 
 
  fftw_complex *ux_f = (fftw_complex*) fftw_malloc ( sizeof(fftw_complex) * kmax*kmax*kmax );
  fftw_complex *uy_f = (fftw_complex*) fftw_malloc ( sizeof(fftw_complex) * kmax*kmax*kmax );
  fftw_complex *uz_f = (fftw_complex*) fftw_malloc ( sizeof(fftw_complex) * kmax*kmax*kmax );
  // On va de -16 à 16 (on ne passe pas par zéro)
  // Les données sont stockés de 1 à 16 puis de -16 à -1
  for(int i = 0; i<kmax; i++)
    {
      for(int j = 0; j<kmax; j++)
        {
          // double Sk1k2 = sqrt(kx[i]*kx[i] + kx[j]*kx[j]);
          for(int k = 0; k<kmax; k++)
            {
              // double normK = sqrt(kx[i]*kx[i] + kx[j]*kx[j] + kx[k]*kx[k]);
              // double Ek = 1/kpic * pow(normK/kpic, s) * exp(-s/2. * pow(normK/kpic, 2.));
              // double sqrt_Ek_4piK2 = sqrt(Ek/(4.0*M_PI*normK*normK));
              // const double theta1_k =  angles((int)floor(normK), 0);
              // const double theta2_k =  angles((int)floor(normK), 1);
              // const double phi_k =  angles((int)floor(normK), 2);
              // double cTh1 = cos(theta1_k);
              // double sTh1 = sin(theta1_k);
              // double cTh2 = cos(theta2_k);
              // double sTh2 = sin(theta2_k);
              // double cPhi = cos(phi_k);
              // double sPhi = sin(phi_k);
              // double alphaKr = sqrt_Ek_4piK2 * cTh1 * cPhi;
              // double alphaKi = sqrt_Ek_4piK2 * sTh1 * cPhi;
              // double betaKr = sqrt_Ek_4piK2 * cTh2 * sPhi;
              // double betaKi = sqrt_Ek_4piK2 * sTh2 * sPhi;
              ux_f[(i*kmax+j)*kmax+k][0] = 0; // (alphaKr*normK*j + betaKr*i*k)/(normK*Sk1k2);
              ux_f[(i*kmax+j)*kmax+k][1] = 0; // (alphaKi*normK*j + betaKi*i*k)/(normK*Sk1k2);
              uy_f[(i*kmax+j)*kmax+k][0] = 0; // (betaKr*j*k - alphaKr*normK*i)/(normK*Sk1k2);
              uy_f[(i*kmax+j)*kmax+k][1] = 0; // (betaKi*j*k - alphaKi*normK*i)/(normK*Sk1k2);
              uz_f[(i*kmax+j)*kmax+k][0] = 0; // betaKr*Sk1k2/normK;
              uz_f[(i*kmax+j)*kmax+k][1] = 0; // betaKi*Sk1k2/normK;
            }
        }
    }
  // ux_f[(0*kmax+1)*kmax+0][0] = 1;
  // ux_f[(0*kmax+1)*kmax+0][1] = 1;
  ux_f[((kmax/2+1)*kmax+kmax/2+1)*kmax+kmax/2+1][0] = 1;
  uy_f[((kmax/2+1)*kmax+kmax/2+1)*kmax+kmax/2+1][0] = 1;
 
  // Create output fields in real space
  fftw_complex *ux_r = (fftw_complex*) fftw_malloc ( sizeof(fftw_complex) * kmax*kmax*kmax );
  fftw_complex *uy_r = (fftw_complex*) fftw_malloc ( sizeof(fftw_complex) * kmax*kmax*kmax );
  fftw_complex *uz_r = (fftw_complex*) fftw_malloc ( sizeof(fftw_complex) * kmax*kmax*kmax );
 
  // And fill them with (inverse?) Fourier Transform 3D
  plan_ux = fftw_plan_dft_3d(kmax, kmax, kmax, ux_f, ux_r, FFTW_BACKWARD, FFTW_ESTIMATE);
  plan_uy = fftw_plan_dft_3d(kmax, kmax, kmax, uy_f, uy_r, FFTW_BACKWARD, FFTW_ESTIMATE);
  plan_uz = fftw_plan_dft_3d(kmax, kmax, kmax, uz_f, uz_r, FFTW_BACKWARD, FFTW_ESTIMATE);
 
  // And execute Fourier 3D
  fftw_execute(plan_ux);
  fftw_execute(plan_uy);
  fftw_execute(plan_uz);
 
  //for (int dir = 0; dir < 3; dir++)
  {
    //const IJK_Field_double& v = velocity[dir];
    IJK_Field_double& vx = velocity[0];
    IJK_Field_double& vy = velocity[1];
    IJK_Field_double& vz = velocity[2];
 
    const int ni = vx.ni();
    const int nj = vx.nj();
    const int nk = vx.nk();
    if ((ni != nj) || (nj != nk))
      Process::exit();
 
    for (int k = 0; k < nk; k++)
      {
        for (int j = 0; j < nj; j++)
          {
            for (int i = 0; i < ni; i++)
              {
                // On ne prend que la partie réelle [0]
                vx(i,j,k) =ux_r[(i*kmax +j)*kmax+k][0]/sqrt(2);
                vy(i,j,k) =uy_r[(i*kmax +j)*kmax+k][0]/sqrt(2);
                vz(i,j,k) =uz_r[(i*kmax +j)*kmax+k][0]/sqrt(2);
              }
          }
      }
 
    // Vérification
    // double *Ek_x = new double [kmax];
    // double *Ek_y = new double [kmax];
    // double *Ek_z = new double [kmax];
    // double *nn = new double [kmax];
    // std::fill_n(Ek_x, kmax, static_cast<double>(0));
    // std::fill_n(Ek_y, kmax, static_cast<double>(0));
    // std::fill_n(Ek_z, kmax, static_cast<double>(0));
    // std::fill_n(nk, kmax, static_cast<double>(0));
    // for (int i = 0; i < nk; i++)
    //   {
    //     for (int j = 0; j < nj; j++)
    //       {
    //         for (int k = 0; k < ni; k++)
    //           {
    //             // Test: calcul des spectres
    //             int k2 = (int)(i*i+j*j+k*k);
    //             int indice = (int)(sqrt(k2));
    //             if (indice <= kmax)
    //               {
    //                 Ek_x[indice] += 4.*M_PI*k2*(pow(ux_f[((i*kmax)+j)*kmax+k][0], 2.)+pow(ux_f[((i*kmax)+j)*kmax+k][1], 2.));
    //                 Ek_y[indice] += 4.*M_PI*k2*(pow(uy_f[((i*kmax)+j)*kmax+k][0], 2.)+pow(uy_f[((i*kmax)+j)*kmax+k][1], 2.));
    //                 Ek_z[indice] += 4.*M_PI*k2*(pow(uz_f[((i*kmax)+j)*kmax+k][0], 2.)+pow(uz_f[((i*kmax)+j)*kmax+k][1], 2.));
    //                 nn[indice] += 1;
    //               }
    //           }
    //       }
    //   }
 
    // Écriture vérif (ne marche pas :( )
    // std::string nomfic("spectres.dat");
    // std::ofstream sortie(nomfic.c_str(), ios::out | ios::trunc);
    // for (int i = 0; i < kmax; i++)
    //   {
    //     Ek_x[i] /= nn[i];
    //     Ek_y[i] /= nn[i];
    //     Ek_z[i] /= nn[i];
    //     sortie << i << ", " << Ek_x[i] << ", " << Ek_y[i] << ", " << Ek_z[i] << std::endl;
    //   }
    // sortie.close();
  }
}