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

Lingyan TANG, Songhe SONG, Hong ZHANG

doi:10.1007/s10483-020-2554-8

2020 , Vol. 41 >Issue 1: 173 - 192

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

Articles

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

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

Received date: 2019-03-18

Revised date: 2019-06-09

Online published: 2019-12-14

Supported by

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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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

Cite this article

Lingyan TANG, Songhe SONG, Hong ZHANG . High-order maximum-principle-preserving and positivity-preserving weighted compact nonlinear schemes for hyperbolic conservation laws[J]. Applied Mathematics and Mechanics, 2020 , 41(1) : 173 -192 . DOI: 10.1007/s10483-020-2554-8

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