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Semi-discrete central-upwind Rankine-Hugoniot schemes for hyperbolic systems of conservation laws

Garg, NK and Kurganov, A and Liu, Y (2021) Semi-discrete central-upwind Rankine-Hugoniot schemes for hyperbolic systems of conservation laws. In: Journal of Computational Physics, 428 .

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Official URL: https://dx.doi.org/10.1016/j.jcp.2020.110078


We study semi-discrete central-upwind schemes and develop a new technique that allows one to decrease the amount of numerical dissipation present in these schemes without compromising their robustness. The goal is achieved by obtaining more accurate estimates for the one-sided local speeds of propagation using the discrete Rankine-Hugoniot conditions. In the two-dimensional case, these estimates are further enhanced with the help of the numerical dissipation switch mechanism, which is automatically activated near contact discontinuities and shear layers. The resulting central-upwind Rankine-Hugoniot schemes are tested on a number of numerical examples for both the one- and two-dimensional Euler equations of gas dynamics. The obtained results clearly demonstrate the superiority of the proposed method over the existing semi-discrete central-upwind schemes. © 2020 Elsevier Inc.

Item Type: Journal Article
Publication: Journal of Computational Physics
Publisher: Academic Press Inc.
Additional Information: The copyright of this article belongs to Academic Press Inc.
Keywords: Central-upwind scheme; Contact discontinuities; Hyperbolic systems of conservation laws; Numerical dissipation; Rankine-Hugoniot condition; Shear layer; Switch mechanism; Two-dimensional Euler equations, Gas dynamics
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 01 Feb 2021 11:15
Last Modified: 01 Feb 2021 11:15
URI: http://eprints.iisc.ac.in/id/eprint/67675

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