Local Characteristic Decomposition Based Central-Upwind Scheme

TL;DR

This paper introduces a new class of less diffusive central-upwind schemes for hyperbolic PDEs, utilizing local characteristic decomposition to improve accuracy in capturing complex wave structures.

Contribution

The paper presents a novel local characteristic decomposition approach to enhance central-upwind schemes for nonlinear hyperbolic systems, reducing numerical diffusion.

Findings

The new schemes outperform original central-upwind methods.

Numerical results show improved accuracy in shock and wave capturing.

Applications to Euler equations demonstrate robustness.

Abstract

We propose novel less diffusive schemes for conservative one- and two-dimensional hyperbolic systems of nonlinear partial differential equations (PDEs). The main challenges in the development of accurate and robust numerical methods for the studied systems come from the complicated wave structures, such as shocks, rarefactions and contact discontinuities, arising even for smooth initial conditions. In order to reduce the diffusion in the original central-upwind schemes, we use a local characteristic decomposition procedure to develop a new class of central-upwind schemes. We apply the developed schemes to the one- and two-dimensional Euler equations of gas dynamics to illustrate the performance on a variety of examples. The obtained numerical results clearly demonstrate that the proposed new schemes outperform the original central-upwind schemes.