Mathc initiation/0050

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	x_stokxy.h

/* ---------------------------------- */
/* save as x_stokxy.h                 */
/* ---------------------------------- */
/*
 *           (curl F).dS
 * 
 * 
    / y1   / x(y) 
   |     |      
   |     |   (curl F).(-f_x, -f_y, 1) dx dy = 
   |     |      
  /  y0  /   x(y) 
 *
 * 
 *  */
 /* ---------------------------------- */
double  curlF_u(

double (*P_M)(double x, double y, double z),
double (*P_N)(double x, double y, double z),
double (*P_P)(double x, double y, double z),

double (*P_f)(double x, double y),

pt2d p
)
{
v3d     u;
v3d  curl;
pt3d  p3d;

     p3d.x = p.x;
     p3d.y = p.y;
     p3d.z = (*P_f)(p.x,p.y);

     u = prod_scal_g_x_g_y((*P_f), p);
  curl =          curl_ijk((*P_M),(*P_N),(*P_P), p3d);

 return( (  curl.i*u.i +
            curl.j*u.j +
            curl.k*u.k )  );
}
/* ---------------------------------- */
/* ---------------------------------- */
double  stokes_dx(
double (*P_M)(double x, double y, double z),
double (*P_N)(double x, double y, double z),
double (*P_P)(double x, double y, double z),

double (*P_f)(double x, double y),

double (*Px0)(double y),
double (*Px1)(double y),
   int   nx,
   
double    y
)
{
pt2d p;

   int i = 0;
double m = 0.;
double M = 0.;


 for(i = 0; i <= nx; i++)
 {
       if(i ==0 || i== nx){m = 1.;}
  else if(fmod(i,2) == 0 ){m = 2.;}
  else                    {m = 4.;}

 p.x =   ((*Px0)(y))+ 
      i*(((*Px1)(y))-((*Px0)(y)))
                    /nx;
 p.y = y;

 M += m * curlF_u(
              (*P_M),(*P_N),(*P_P),
              (*P_f),
                p);
 }

return(((((*Px1)(y))-((*Px0)(y)))*M)
                    / (3*nx) );
}
/* ---------------------------------- */
double stokes_dxdy(

double (*P_M)(double x, double y, double z),
double (*P_N)(double x, double y, double z),
double (*P_P)(double x, double y, double z),

double (*P_f)(double x, double y),

double (*Px0)(double y),
double (*Px1)(double y),
   int   nx,
   
double   y0,
double   y1,
   int   ny
)
{
   int i = 0;
double m = 0.;
double M = 0.;

 for(i = 0; i <= ny; i++)
 {
       if(i ==0 || i== ny){m = 1.;}
  else if(fmod(i,2) == 0 ){m = 2.;}
  else                    {m = 4.;}

 M += m * stokes_dx((*P_M),(*P_N),(*P_P),
                    (*P_f),
                    (*Px0),(*Px1),nx,
                    (y0 + i*(y1-y0)/ny));
 }

  return( ((y1 -y0)*M) / (3*ny) );
}
/* ---------------------------------- */
/* ---------------------------------- */