A Convergent Nonstaggered Central Scheme for Two-Dimensional Hyperbolic Conservation Laws on Triangles

Abstract

We introduce a nonstaggered central scheme (NCS) for the two-dimensional hyperbolic conservation laws on triangles. The NCS is Riemann-Problem-Solver-Free and is a novel family of central schemes. It has the same simple and clear features as the staggered central scheme. One of the main contributions is that we analyze the convergence property of the NCS on triangular meshes. A dissipation-reducing parameter is constructed to improve the resolution. We introduce a novel method to prove that numerical solutions obtained by the NCS strongly converge to the entropy solution of the two-dimensional scalar conservation law. Several benchmark problems are carried out to verify the convergence and robustness properties. Finally, we show several numerical results of the NCS for the Euler equations on triangles.

Keywords

Nonstaggered central schemes (NCSs) / Entropy measure-valued solutions / Two-dimensional hyperbolic conservation laws / Convergent analysis / A dissipation-reducing parameter / 76M12 / 35L65 / 65L05 / 65M08

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Funding

National Natural Science Foundation of China(12371374, 12271523)

RIGHTS & PERMISSIONS

Shanghai University