  We investigate the applicability of curvilinear grids in the context of
astrophysical simulations and WENO schemes. With the non-smooth mapping
functions from Calhoun et al. (2008), we can tackle many astrophysical problems
which were out of scope with the standard grids in numerical astrophysics. We
describe the difficulties occurring when implementing curvilinear coordinates
into our WENO code, and how we overcome them. We illustrate the theoretical
results with numerical data. The WENO finite difference scheme works only for
high Mach number flows and smooth mapping functions whereas the finite volume
scheme gives accurate results even for low Mach number flows and on non-smooth
grids.
