transform spectral coeff to physical data points

emmanuel germaine, 2010-08-28 10:14

~~DISCUSSION~~ Dear Prof. Gibson,

We can determine the physical values from the spectral coefficients by evaluating the expansion sum (eqn 20 in the user's manual.) I wanted to compared the physical values computed by this sum with the values returned by the method u.makephysical(). This method use the FFTW algorithm and I was expecting no difference. The fact is that, I do not obtained the same results.

I have attached part of the code I am using. Do you think that something is incorrect ?

As the width of the channel is [a,b] = [-1.0,1.0], I haven't normalized the Chebyshev polynomials.

Example of results displayed :

0.00258953      // u from expansion sum
0.00604268      // return of u.makePhysical (FFTW)

Regards, Emmanuel

{
 double pi =3.1415926 ;
 Complex I(0.0,1.0);
 Complex sum_u(0.0,0.0);
 int pause; 
 nx = 5;
 ny = 5; 
 nz = 5;   
//display gridpoint coordinates x,y,z
std::cout << u.x(nx) << ' ' << u.y(ny) << ' ' << u.z(nz) << endl ;

//compute physical value using expansion sum and display
 u.makeSpectral();
 for(int mz=0;mz<u.Mz();++mz)
   for(int my=0;my<u.My();++my)
     for(int mx=0;mx<u.Mx();++mx)
          sum_u += u.cmplx(mx,my,mz,0) *  chebyshev(my,u.y(ny)) * exp(2.0 * pi * I*((u.kx(mx) * u.x(nx) /u.Lx()) + (u.kz(mz) * u.z(nz) / u.Lz()))) ;
        std::cout << 2.0 * sum_u.real()<< endl ;
 
  //display physical value  from makePhysical()   
  u.makePhysical();
  std::cout << u(nx,ny,nz,0)  <<  endl ;

  std::cin >> pause;	
  }