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arXiv · 2405.01929

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

Shaoshuai Chu·Michael Herty·Alexander Kurganov
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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.

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Shaoshuai Chu, Michael Herty, Alexander Kurganov. 2024-05-03. Novel Local Characteristic Decomposition Based Path-Conservative Central-Upwind Schemes. https://arxiv.org/abs/2405.01929

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