Two-dimensional central-upwind schemes for curvilinear grids and application to gas dynamics with angular momentum

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 [A. Kurganov, E. Tadmor, Numer. Methods Partial Differential Equations 18 (2002) 584. [1]]. 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.