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

  • Lingyan TangEmail author
  • Songhe Song
  • Hong Zhang
Article
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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.

Key words

hyperbolic conservation law maximum-principle-preserving (MPP) positivity-preserving (PP) weighted compact nonlinear scheme (WCNS) finite difference scheme 

Chinese Library Classification

O241 

2010 Mathematics Subject Classification

65N12 76M20 

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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2020

Authors and Affiliations

  1. 1.College of Liberal Arts and SciencesNational University of Defense TechnologyChangshaChina

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