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High-order maximum-principle-preserving and positivity-preserving weighted compact nonlinear schemes for hyperbolic conservation laws

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Abstract

In this paper, the maximum-principle-preserving (MPP) and positivity-preserving (PP) flux limiting technique will be generalized to a class of high-order weighted compact nonlinear schemes (WCNSs) for scalar conservation laws and the compressible Euler systems in both one and two dimensions. The main idea of the present method is to rewrite the scheme in a conservative form, and then define the local limiting parameters via case-by-case discussion. Smooth test problems are presented to demonstrate that the proposed MPP/PP WCNSs incorporating a third-order Runge-Kutta method can attain the desired order of accuracy. Other test problems with strong shocks and high pressure and density ratios are also conducted to testify the performance of the schemes.

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Authors and Affiliations

  1. College of Liberal Arts and Sciences, National University of Defense Technology, Changsha, 410073, China

    Lingyan Tang, Songhe Song & Hong Zhang

Authors
  1. Lingyan Tang
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  2. Songhe Song
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  3. Hong Zhang
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Corresponding author

Correspondence to Lingyan Tang.

Additional information

Project supported by the National Natural Science Foundation of China (No. 11571366) and the Basic Research Foundation of National Numerical Wind Tunnel Project (No. NNW2018-ZT4A08)

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Tang, L., Song, S. & Zhang, H. High-order maximum-principle-preserving and positivity-preserving weighted compact nonlinear schemes for hyperbolic conservation laws. Appl. Math. Mech.-Engl. Ed. 41, 173–192 (2020). https://doi.org/10.1007/s10483-020-2554-8

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  • DOI: https://doi.org/10.1007/s10483-020-2554-8

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

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