# sandbox/bugs/stillwater.c

This is just a simple example to demonstrate why I get the error I reported in the forum “Problem with interaction…” (See Case#2 & Case#3). Consider the following stationary case: When I refine the region inside a cylinder at every single timestep using Saint-Venant.h you can see that $h$ is not conserved anymore which is caused by refining the cylinderical region, however $h$ is conserved exactly when I use a uniform mesh. This does not create a big problem when I am using Saint-Venant equations and of course when I just refine at the initial timestep and I have a solitary wave entering the domain. But I think this is the reason for the error I reported before in the forum using Green-Naghdi equations since small errors in the value of $h$ can cause large error in calculating dispersive terms (See. Case 2 and Case 3: Case two I use adaptive mesh with minlevel=6 and maxlevel=10 and I refine the region around the cylinder at $t=0$ and the code stops at the very early timesteps due to the error in h and u caused by refining the cylindrical regin at time step 0 while the code works perfectly when I use $minlevel=maxlevel=10$).

*SP: I can’t see any problem. Either the problem is fixed or you need to make the error clearer i.e. make the code crash or make a graph showing an obvious problem.*

```
#include "saint-venant.h"
int MINLEVEL = 6;
int MAXLEVEL = 9;
int main() {
size (50.);
G = 9.81;
origin (-L0/2., -L0/2.);
init_grid (1 << MINLEVEL);
run();
}
double H0 = 1.0;
event init (i = 0) {
refine (sq(x ) + sq(y)< sq(7) && level < MAXLEVEL);
foreach() {
h[] = H0;
u.x[] = 0.0;
}
conserve_elevation();
}
event logfile (i++) {
stats s = statsf (h);
if (i == 0)
fprintf (stderr, "t i h.min h.max h.sum u.x.rms u.x.max dt\n");
fprintf (stderr, "%g %g %g %g %g\n", t, s.min, s.max, s.sum, dt);
}
event stop (t = 15.) {
return 1;
}
event adapt (i++) {
astats s = adapt_wavelet ({h}, (double[]){1e-4}, MAXLEVEL, MINLEVEL);
refine (sq(x ) + sq(y)< sq(7) && level < MAXLEVEL);
fprintf (ferr, "# refined %d cells, coarsened %d cells\n", s.nf, s.nc);
}
```