  In this work we present new second order semi-discrete central schemes for
systems of hyperbolic conservation laws on curvilinear grids. Our methods
generalise the two-dimensional central-upwind schemes developed by Kurganov and
Tadmor. In these schemes we account for area and volume changes in the
numerical flux functions due to the non-cartesian geometries. In case of
vectorial conservation laws we introduce a general prescription of the
geometrical source terms valid for various orthogonal curvilinear coordinate
systems. The methods are applied to the two-dimensional Euler equations of
inviscid gas dynamics with and without angular momentum transport. In the
latter case we introduce a new test problem to examine the detailed
conservation of specific angular momentum.
