# sandbox/bugs/boundary_2_neumann.c

# MWE: second row of ghost cells is wrong with neumann conditions

`#define BGHOSTS 2`

This minimum working example show that the command lines `s[left] = neumann(a)`

followed by `boundary ({s})`

imposes the same value in the first and second row of ghost cells.

```
int main()
{
init_grid (4);
output_cells (stdout);
scalar s[];
s[left] = neumann(1.);
foreach()
s[] = 0.;
boundary ({s});
foreach()
fprintf (stderr, "%g %g %g\n", x, y, s[]);
foreach_boundary(left)
for (int i = -2; i < 0; i++)
fprintf (stderr, "%g %g %g\n", x + i*Delta, y, s[i]);
}
```

# Outputs

In the second row of cells, the value of `s`

should be 0.5 instead of 0.25. This comes from the definition of the neuman command in common.h:

`@define neumann(x) (Delta*(x) + val(_s,0,0,0))`

which does not distinguish the first and second row of ghost cells and I do not see how to do it. I didn’t find where `boundary()`

is defined and I don’t know how to test if we are in the first or second row of ghost cells.

```
blue="#5082DC"
set terminal @PNG enhanced size 640,640 font ",8"
set output 'boundary.png'
unset key
unset border
unset tics
unset xlabel
unset ylabel
set size ratio -1
plot 'out' w l lc rgb "#7F7F7F", \
'log' u 1:2:3 with labels tc rgb blue
```