一维含化学反应流体力学方程组的ALE间断有限元方法

doi:10.19596/j.cnki.1001-246x.8005

计算物理 ›› 2020, Vol. 37 ›› Issue (1): 1-9.DOI: 10.19596/j.cnki.1001-246x.8005

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一维含化学反应流体力学方程组的ALE间断有限元方法

戢美璇^1,2, 蔚喜军¹, 宋明阳^1,2

1. 北京应用物理与计算数学研究所计算物理重点实验室, 北京 100088;
2. 东北师范大学数学与统计学院, 吉林长春 130024

收稿日期:2018-11-14 修回日期:2019-01-24 出版日期:2020-01-25 发布日期:2020-01-25
作者简介:戢美璇(1993-),女,硕士,主要从事多相反应流数值方法研究,E-mail:695294702@qq.com
基金资助:
国家自然科学基金（11571002，11772067，11702028）资助项目

ALE Discontinuous Finite Element Method for One-dimensional Fluid Dynamics Equations with Chemical Reactions

JI Meixuan^1,2, YU Xijun¹, SONG Mingyang^1,2

1. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;
2. School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, China

Received:2018-11-14 Revised:2019-01-24 Online:2020-01-25 Published:2020-01-25

摘要/Abstract

摘要： 研究一维含化学反应流体力学方程组的数值模拟方法.结合理想气体状态方程并利用HLLC解法器在各个单元边界处的数值通量，给出ALE间断有限元方法.高阶计算时，使用TVD斜率限制器对数值解可能产生的非物理振荡进行抑制.结果表明：该算法能够保持物理量的守恒性和高精度，并能够清晰地捕捉爆轰波的结构特征.

关键词: 多相反应流, HLLC解法器, ALE方法

Abstract: A numerical simulation method for one-dimensional chemical reaction fluid mechanics equations is studied. Combining ideal gas state equation and using numerical flux of HLLC solution at boundary of each element, we present an ALE discontinuous finite element method. In high-order calculations, TVD slope limiter is used to suppress non-physical oscillation that may result from numerical solutions. Numerical results show that the algorithm maintains conservation and high precision of physical quantity. It captures clearly structural characteristics of detonation waves.

Key words: multiphase reaction flow, HLLC solver, ALE method

中图分类号:

戢美璇, 蔚喜军, 宋明阳. 一维含化学反应流体力学方程组的ALE间断有限元方法[J]. 计算物理, 2020, 37(1): 1-9.

JI Meixuan, YU Xijun, SONG Mingyang. ALE Discontinuous Finite Element Method for One-dimensional Fluid Dynamics Equations with Chemical Reactions[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 37(1): 1-9.

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一维含化学反应流体力学方程组的ALE间断有限元方法

ALE Discontinuous Finite Element Method for One-dimensional Fluid Dynamics Equations with Chemical Reactions

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