GfsInitVorticity

From Gerris

GfsInitVorticity uses the given vorticity distribution to compute a two-dimensional stream-function and the corresponding velocity field. Due to limitations in the type of boundary conditions for the stream-function–vorticity equation, the vorticity field given as argument must vanish before reaching the boundaries of the domain.

The syntax in parameter files is:

 [ GfsGenericInit ] [ GfsFunction ]

Examples

• Coalescence of a pair of Gaussian vortices (Gerris logo)

    InitVorticity {} {
        /* We use nested functions for simplicity (this will not work on MACOSX) */
        double vortex (double xc, double yc, double r) {
            double r2 = (x - xc)*(x - xc) + (y - yc)*(y - yc);
            return 2.*M_PI*exp (- 2.*r2/(r*r));
        }
        double r = 0.01, theta = 30.*M_PI/180.;
        return vortex (-r*sin(theta), r*cos(theta), 0.01) + 
               vortex (r*sin(theta), -r*cos(theta), 0.01);
    }

• Convergence for the three-way vortex merging problem

  InitVorticity {} {
    double vortex (double xo, double yo, double s) {
      double r = sqrt ((x - xo)*(x - xo) + (y - yo)*(y - yo));
      return s*(1. + tanh (100.*(0.03 - r)))/2.;
    }
    return vortex (0., 0., -150.) + 
           vortex (0.09, 0., 50.) + 
           vortex (-0.045, 0.0779422863406, 50.) +
           vortex (-0.045, -0.0779422863406, 50.);
  }