Two-Dimensional Central-Upwind Schemes for Curvilinear Grids and Application to Gas Dynamics with Angular Momentum

Abstract

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.