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New Low-Dissipation Central-Upwind Schemes

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Abstract

In this paper, we develop new second-order low-dissipation central-upwind (LDCU) schemes for hyperbolic systems of conservation laws. Like all of the Godunov-type schemes, the proposed LDCU schemes are developed in three steps: reconstruction, evolution, and projection. A major novelty of our approach is in the projection step, which is based on a subcell resolution and designed to sharper approximate contact waves while ensuring a non-oscillatory property of the projected solution. In order to achieve this goal, we take into account properties of the contact waves. We design the LDCU schemes for both the one- and two-dimensional Euler equations of gas dynamics. The new schemes are tested on a variety of numerical examples. The obtained results clearly demonstrate that the proposed LDCU schemes contain substantially smaller amount of numerical dissipation and achieve higher resolution compared with their existing counterparts.

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Data and Software Availability

The data that support the findings of this study and FORTRAN codes developed by the authors and used to obtain all of the presented numerical results are available from the corresponding author upon reasonable request.

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Funding

The work of A. Kurganov was supported in part by NSFC Grants 12171226 and 12111530004, and by the fund of the Guangdong Provincial Key Laboratory of Computational Science and Material Design (No. 2019B030301001).

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Authors and Affiliations

  1. Department of Mathematics, Shenzhen International Center for Mathematics and Guangdong Provincial Key Laboratory of Computational Science and Material Design, Southern University of Science and Technology, Shenzhen, 518055, China

    Alexander Kurganov & Ruixiao Xin

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  1. Alexander Kurganov
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  2. Ruixiao Xin
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Correspondence to Alexander Kurganov.

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Kurganov, A., Xin, R. New Low-Dissipation Central-Upwind Schemes. J Sci Comput 96, 56 (2023). https://doi.org/10.1007/s10915-023-02281-8

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  • DOI: https://doi.org/10.1007/s10915-023-02281-8

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