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

作     者：Lingyan TANG Songhe SONG Hong ZHANG Lingyan TANG;Songhe SONG;Hong ZHANG

作者机构：College of Liberal Arts and Sciences National University of Defense Technology 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学（英文版）)

年 卷 期：2020年第41卷第1期

页      面：173-192页

核心收录：

学科分类：07[理学] 0805[工学-材料科学与工程（可授工学、理学学位）] 070102[理学-计算数学] 0802[工学-机械工程] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

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

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

摘      要：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.