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

arXiv (Cornell University)

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. Lukáčová-Medvi{\softd}ová}, 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.

Authors 3

1. Shaoshuai Chu
2. Michaël Herty Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen

3. Alexander Kurganov