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

doi:10.1007/s10483-020-2554-8

Abstract

Abstract: In this paper, the maximum-principle-preserving (MPP) and positivitypreserving (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

2010 MSC Number:

65N12
76M20

Lingyan TANG, Songhe SONG, Hong ZHANG. High-order maximum-principle-preserving and positivity-preserving weighted compact nonlinear schemes for hyperbolic conservation laws. Applied Mathematics and Mechanics (English Edition), 2020, 41(1): 173-192.

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