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求解带刚性源项标量双曲型守恒律方程的保有界WCNS格式

唐玲艳, 郭嘉, 宋松和   

  1. 国防科技大学文理学院数学系, 长沙 410073
  • 收稿日期:2019-12-11 出版日期:2021-04-15 发布日期:2021-05-13
  • 基金资助:
    “国家数值风洞”工程基础研究课题(NNW2018-ZT4A08)和国家自然科学基金(11571366).

唐玲艳, 郭嘉, 宋松和. 求解带刚性源项标量双曲型守恒律方程的保有界WCNS格式[J]. 计算数学, 2021, 43(2): 241-252.

Tang Lingyan, Guo Jia, Song Songhe. BOUND-PRESERVING WEIGHTED COMPACT NONLINEAR SCHEMES FOR SCALAR CONSERVATION LAWS WITH STIFF SOURCE TERMS[J]. Mathematica Numerica Sinica, 2021, 43(2): 241-252.

BOUND-PRESERVING WEIGHTED COMPACT NONLINEAR SCHEMES FOR SCALAR CONSERVATION LAWS WITH STIFF SOURCE TERMS

Tang Lingyan, Guo Jia, Song Songhe   

  1. Department of Mathematics, College of Liberal Arts and Sciences, National University of Defence Technology, Changsha 410073, China
  • Received:2019-12-11 Online:2021-04-15 Published:2021-05-13
带刚性源项的双曲守恒律方程是很多物理问题,特别是化学反应流的数学模型.本文考虑带刚性源项的标量双曲型守恒律方程,通过时空分离的方式,发展了一类保有界的WCNS格式.对于空间离散,我们将参数化的通量限制器推广到WCNS框架,使得方程对流项离散后满足极值原理.对于时间离散,我们将半离散的WCNS改写成指数形式,采用三阶修正指数型Runge-Kutta格式来控制方程的刚性,保持数值解的界.可以证明,本文格式对带刚性源项的一维标量守恒律方程具有保有界性和弱渐近保持性.数值试验验证了方法的有效性.
Hyperbolic conservation laws with stiff source terms arise in a large number of physical problems, especially the simulation of chemically reactive flows. In this paper, we develop bound-preserving modified exponential Runge-Kutta weighted compact nonlinear schemes (WCNS) to solve scalar conservation laws with stiff source terms. For spatial discretization, we generalize the parameterized flux limiters to WCNS framework, and construct high-order WCNS that preserves the maximum principle for the convection part of equation. For temporal discretization, the semi-discrete WCNS is rewritten in a exponential form and the third order modified exponential Runge-Kutta method is applied to control the stiff part of equation and preserve the bound of the numerical solutions. It can be proved that our scheme has the properties of bound-preserving and weak asymptotic-preserving for one-dimensional scalar conservation laws with stiff source terms. Numerical tests validate the theoretical analysis.

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