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

TL;DR

This paper introduces second order semi-discrete central schemes for hyperbolic conservation laws on curvilinear grids, extending previous methods to account for geometric effects and applying them to gas dynamics with angular momentum.

Contribution

It generalizes two-dimensional central-upwind schemes to curvilinear grids, including new prescriptions for geometric source terms and applications to gas dynamics with angular momentum.

Findings

Effective handling of geometric effects in flux calculations.

Successful application to Euler equations with angular momentum.

Introduction of a new test problem for angular momentum conservation.

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.