# 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 (stderr, "%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 (stderr, "# refined %d cells, coarsened %d cells\n", s.nf, s.nc);
}