src/test/shock.c

    Shock reflection by a circular cylinder

    The evolution of an initial “step” wave is modelled using the Saint-Venant equations. The wave interacts with a circular cylinder described using embedded solid boundaries. Adaptivity is used to track the wave fronts. This example is discussed in An and Yu, 2012.

    #include "saint-venant.h"
    
    int LEVEL = 9;

    We define a new boundary for the cylinder.

    bid cylinder;
    
    int main() {
      size (5.);
      G = 9.81;
      origin (-L0/2., -L0/2.);
      init_grid (1 << LEVEL);
      run();
    }

    We impose height and velocity on the left boundary.

    #define H0 3.505271526
    #define U0 6.29033769408481
    
    h[left]   = H0;
    eta[left] = H0;
    u.n[left] = U0;
    
    event init (i = 0) {

    The geometry is defined by masking and the initial step function is imposed.

      mask (sq(x + 0.5) + sq(y) < sq(0.5) ? cylinder : none);
      foreach() {
        h[] = (x <= -1 ? H0 : 1.);
        u.x[] = (x <= -1 ? U0 : 0.);
      }
    }
    
    event logfile (i++) {
      stats s = statsf (h);
      fprintf (ferr, "%g %d %g %g %.8f\n", t, i, s.min, s.max, s.sum);
    }

    We generate movies of depth and level of refinement.

    event movie (t += 0.0025; t <= 0.3) {
      output_ppm (h, min = 0.1, max = 6, map = cool_warm, linear = true,
    	      n = 400, file = "depth.mp4");
      scalar l[];
      foreach()
        l[] = level;
      output_ppm (l, map = cool_warm, min = 4, max = LEVEL, n = 400,
    	      file = "level.mp4");
    }

    Animation of the fluid depth

    Animation of the level of refinement

    The mesh is adapted according to the error on the height field.

    event adapt (i++) {
      astats s = adapt_wavelet ({h}, (double[]){1e-2}, LEVEL);
      fprintf (ferr, "# refined %d cells, coarsened %d cells\n", s.nf, s.nc);
    }

    See also