Novel Local Characteristic Decomposition Based Path-Conservative Central-Upwind Schemes

TL;DR

This paper presents new path-conservative central-upwind schemes for hyperbolic systems that incorporate local characteristic decomposition and flux globalization to ensure well-balanced solutions for complex fluid models.

Contribution

It introduces a novel combination of local characteristic decomposition with flux globalization and path-conservative techniques for hyperbolic balance laws.

Findings

Schemes effectively handle multifluid systems and shallow water equations.

Achieves well-balanced property through flux globalization.

Demonstrates improved accuracy and stability in numerical tests.

Abstract

We introduce local characteristic decomposition based path-conservative central-upwind schemes for (nonconservative) hyperbolic systems of balance laws. The proposed schemes are made to be well-balanced via a flux globalization approach, in which source terms are incorporated into the fluxes: This helps to enforce the well-balanced property when the resulting quasi-conservative system is solved using the local characteristic decomposition based central-upwind scheme recently introduced in [{\sc A. Chertock, S. Chu, M. Herty, A. Kurganov, and M. Luk\'{a}\v{c}ov\'{a}-Medvi{\softd}ov\'{a}}, J. Comput. Phys., 473 (2023), Paper No. 111718]. Nonconservative product terms are also incorporated into the global fluxes using a path-conservative technique. We illustrate the performance of the developed schemes by applying them to one- and two-dimensional compressible multifluid systems and thermal rotating shallow water equations.