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arXiv · 0804.2979

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

Tobias F. Illenseer·Wolfgang J. Duschl
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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.

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Tobias F. Illenseer, Wolfgang J. Duschl. 2008-04-18. Two-Dimensional Central-Upwind Schemes for Curvilinear Grids and Application to Gas Dynamics with Angular Momentum. https://doi.org/10.1016/j.cpc.2009.07.016

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