# sandbox/Antoonvh/rc.c

# Enforcing the ratio \frac{R}{\Delta}

Some like to hint at the fidelity of their two-phase simulations in terms of the dimensionless ratio; \frac{R}{\Delta} < \text{Const}, with R a radius of curfavure of the interface and \Delta the grid size. Here we implement a method to enforce this ratio along an interface.

The “challenge” is to make in cooperate with `adapt_wavelet()`

, eventough it is not a wavelet-based criterion.

```
#include "fractions.h"
#include "curvature.h"
#include "view.h"
double DoC = 1./20.; //Use 20 to 40 cells per radius
```

`prolongate_ratio()`

is defined for this purpose only.

```
void prolongate_ratio (Point point, scalar s) {
foreach_child() {
if (s[] != nodata)
s[] += s[]*Delta;
}
}
```

We test the method with a circle of radius R.

```
#define CIRC(R) (sq(x - R + 0.3) + sq(y) - sq(R))
scalar f[], curv[];
int main() {
f.prolongation = f.refine = fraction_refine; //f is the fraction field...
X0 = Y0 = -L0/2;
init_grid (1 << 7);
view (width = 700, height = 700);
//Loop over radii
for (double R = 10; R > 0.1; R /= 1.01) {
fraction (f, CIRC(R)); //Compute drop
boundary ({f}); //is this needed?
curvature (f, curv); //Compute curvature
curv.prolongation = prolongate_ratio; //_then_ overload the prolongation attribute
```

For testing, we do not set an effective maximum level. Note that eventough we have not used proper boundary conditions for `f`

, the resolution remains limited when the interface touches the domains boundaries..

```
adapt_wavelet ({curv}, (double[]){DoC}, maxlevel = 99);
//Make a movie
draw_vof ("f", lc = {1., 0., 1.}, lw = 2);
cells();
save ("plot.mp4");
}
```

It is interesting to compare against the “default” refinement based on the vof field.

```
for (double R = 10; R > 0.1; R /= 1.01) {
fraction (f, CIRC(R));
boundary ({f});
adapt_wavelet ({f}, (double[]){0.01}, maxlevel = 99);
draw_vof ("f", lc = {1., 0., 1.}, lw = 2);
cells();
save ("plot2.mp4");
}
```

Its appears similar, except we do not know how the refinement-citerion value (`0.01`

) compares to \frac{R}{\Delta}. Looking closely, we can see that the curvature-based method uses a more constant grid along the interface, wheareas the fov-based method is more robust in time.

```
}
```