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Local Characteristic Decomposition Based Central-Upwind Scheme for Compressible Multifluids

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Finite Volumes for Complex Applications X—Volume 2, Hyperbolic and Related Problems (FVCA 2023)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 433))

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Abstract

In this paper, we introduce the local characteristic decomposition based central-upwind (LCD-CU) scheme for compressible multifluids. The scheme is implemented within the hybrid multifluid algorithm from [A. Chertock, S. Chu, and A. Kurganov, J. Sci. Comput, 89(2021), Paper No. 48], according to which we use the level set method to track the position of material interfaces and replace the conservative compressible Euler equations with the pressure-based nonconservative ones in the vicinities of the interfaces. The LCD-CU scheme is used away from the interfaces and this helps to reduce the numerical dissipation in these areas. At the interfaces, we still use the path-conservative central-upwind scheme designed to accurately solve nonconservative hyperbolic systems. This leads to a substantially higher resolution, especially in the two-dimensional case.

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Acknowledgements

The work of A. Kurganov was supported in part by NSFC grant 12171226 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, Southern University of Science and Technology, Shenzhen, 518055, China

    Shaoshuai Chu

  2. 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

Authors
  1. Shaoshuai Chu
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  2. Alexander Kurganov
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Correspondence to Alexander Kurganov .

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Editors and Affiliations

  1. IRMA, Strasbourg, France

    Emmanuel Franck

  2. Weierstrass Institute, Berlin, Germany

    Jürgen Fuhrmann

  3. IRMA, Strasbourg, France

    Victor Michel-Dansac

  4. IRMA, Strasbourg, France

    Laurent Navoret

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Chu, S., Kurganov, A. (2023). Local Characteristic Decomposition Based Central-Upwind Scheme for Compressible Multifluids. In: Franck, E., Fuhrmann, J., Michel-Dansac, V., Navoret, L. (eds) Finite Volumes for Complex Applications X—Volume 2, Hyperbolic and Related Problems. FVCA 2023. Springer Proceedings in Mathematics & Statistics, vol 433. Springer, Cham. https://doi.org/10.1007/978-3-031-40860-1_8

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