基于任意拉格朗日—欧拉型移动网格的反应流广义黎曼问题方法

doi:10.19596/j.cnki.1001-246x.8019

计算物理 ›› 2020, Vol. 37 ›› Issue (2): 127-139.DOI: 10.19596/j.cnki.1001-246x.8019

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基于任意拉格朗日—欧拉型移动网格的反应流广义黎曼问题方法

肖敏^1,2, 徐喜华¹, 倪国喜¹

1. 北京应用物理与计算数学研究所, 北京 100088;
2. 中国工程物理研究院研究生院, 北京 100088

收稿日期:2018-12-03 修回日期:2019-03-20 出版日期:2020-03-25 发布日期:2020-03-25
通讯作者: NI Guoxi,E-mail:gxni@iapcm.ac.cn
作者简介:XIAO Min (1992-),female,PhD,major in numerical methods for reactive flows,E-mail:minxiao55@sohu.com
基金资助:
Supported by Science Challenge Project (TZ2016002), National Science Foundation of China (11171154, 11671050, 11771055, 11771053) and 3D numerical simulation platform TB14-1 of China Academy of Engineering Physics

An Arbitrary Lagrangian-Eulerian Type Moving Mesh Generalized Riemann Problem Scheme for Reactive Flows

XIAO Min^1,2, XU Xihua¹, NI Guoxi¹

1. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;
2. Graduate School, China Academy of Engineering Physics, Beijing 100088, China

Received:2018-12-03 Revised:2019-03-20 Online:2020-03-25 Published:2020-03-25
Supported by:
Supported by Science Challenge Project (TZ2016002), National Science Foundation of China (11171154, 11671050, 11771055, 11771053) and 3D numerical simulation platform TB14-1 of China Academy of Engineering Physics

摘要/Abstract

摘要： 提出一种在自由重映移动网格下的广义黎曼问题方法模拟反应流.该方法基于显式的自由重映移动网格广义黎曼问题的解.为保证在时间和空间上的高精度，应用广义黎曼问题方法构造数值通量.为保证反应区的高分辨率，采用变分法生成自适应移动网格.该方法不仅能够保证网格质量，而且能有效地避免任意拉格朗日—欧拉方法中由于显式重映过程而带来的数值误差.包括CJ爆轰及不稳定爆轰的数值实验说明该格式的精确性和鲁棒性，证明这种移动网格下的二阶广义黎曼问题方法可以较好地捕捉反应流的间断与光滑结构.

关键词: 移动网格方法, 任意拉格朗日—欧拉法, 广义黎曼问题方法, 反应流

Abstract: We present a generalized Riemann problem based, remapping free moving mesh scheme to simulate reactive flows. The scheme is based on solution of a generalized Riemann problem on moving meshes and is explicitly remapping free. In construction of numerical fluxes, we use generalized Riemann problem scheme to get high accuracy. A variational approach is applied to generate an adaptive moving mesh to get high resolution in reactive zone. The scheme can not only keep the mesh quality,but also avoid efficiently numerical errors induced by an explicit remapping process in arbitrary Lagrangian-Eulerian methods. Numerical experiments, including Chapmann-Jouguet detonation and unstable detonation, demonstrate accuracy and robustness of the scheme. It shows that the generalized Riemann problem moving mesh method performs well for reactive flows with both discontinuities and smooth structures.

Key words: moving mesh method, ALE, GRP scheme, reactive flow

中图分类号:

肖敏, 徐喜华, 倪国喜. 基于任意拉格朗日—欧拉型移动网格的反应流广义黎曼问题方法[J]. 计算物理, 2020, 37(2): 127-139.

XIAO Min, XU Xihua, NI Guoxi. An Arbitrary Lagrangian-Eulerian Type Moving Mesh Generalized Riemann Problem Scheme for Reactive Flows[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 37(2): 127-139.

参考文献

[1] ZELDOVICH Y B. On the theory of the propagation of detonation in gaseous systems[J]. Technical Report Archive and Image Library(TRAIL), 1950, 10(1261):542-568.
[2] Von NEUMANN J. Theory of detonation waves, John Von Neumann collected works[M]. New York:Macmillan, 1942, 6:1903-1957.
[3] DOERING W. On detonation processes in gases[J]. Ann Phys, 1943, 43:141-172.
[4] FICKETT W, WOOD W. Flow calculations for pulsating one-dimensional detonations[J]. Phys Fluid, 1966, 9 (5):903-916.
[5] BOURLIOUX A, MAJDA A J, ROYTBURD V. Theoretical and numerical structure for unstable one-dimensional detonations[J]. SIAM J Appl Math, 1991, 51 (2):303-343.
[6] COLELLA P, MAJDA A J, ROYTBURD V. Theoretical and numerical structure for reacting shock waves[J]. SIAM J Sci Stat Comput, 1986, 7 (4):1059-1080.
[7] HWANG P, FEDKIW R, MERRIMAN B, et al. Numerical resolution of pulsating detonation waves[J]. Combust Theor Model, 2000, 4 (3):217-240.
[8] PEMBER R B. Numerical methods for hyperbolic conservation laws with stiff relaxation I: Spurious solutions[J]. SIAM J Appl Math, 1993, 53 (5):1293-1330.
[9] QUIRK J. Combustion in high-speed flows[M]. Springer, 1994.
[10] BEN-ARTZI M. The generalized Riemann problem for reactive flows[J]. J Comput Phys, 1989, 81 (1):70-101.
[11] LIU T P. Quasilinear hyerbolic systems[J]. Comm Math Phys, 1979, 68:421-436.
[12] BOURLIOUX A, MAJDA A J. Theoretical and numerical structure of unstable detonations[J]. Phil Trans Roy Soc Lond Series A: Physical and Engineering Sciences, 1995, 350 (1692):29-68.
[13] PAPALEXANDRIS M, LEONARD A, DIMOTAKIS P. Unsplit schemes for hyperbolic conservation laws with source terms in one space dimension[J]. J Comput Phys, 1997, 134 (1):31-61.
[14] BAO W Z, JIN S. The random projection method for hyperbolic conservation laws with stiff reaction terms[J]. J Comput Phys, 2000,163 (1):216-248.
[15] LIU Jingjing, ZENG Xianyang, NI Guoxi. Euler numerical methods for reactive flow with general equation of states in two dimensions[J]. Chinese Journal of Computational Physics, 2018, 35(1): 29-38.
[16] BOURLIOUX A. Numerical study of unstable detonations[D]. New Jersey(United States): Princeton Univ, 1991.
[17] LEVEQUE R, SHYUE K M. One-dimensional front tracking based on high resolution wave propagation methods[J]. SIAM J Sci Comput, 1995, 16 (2):348-377.
[18] AZARENOK B, TANG T. Second-order Godunov-type scheme for reactive flow calculations on moving meshes[J]. J Comput Phys, 2005, 206 (1):48-80.
[19] ZABRODIN A, IVANOV M, KRAIKO A, PROKOPOV G. Numerical solution of multi-dimensional problems in gas dynamics[M]. Moscow:Nauka Press, 1976.
[20] 陈国贤. 自适应移动非结构网格方法及其在流体力学中的应用[D]. 北京:北京大学, 2008.
[21] LI Y, TANG T. Resolving the shock-induced combustion by an adaptive mesh redistribution method[J]. J Comput Phys, 2007, 224(2):587-600.
[22] ZENG Xianyang, NI Guoxi. Moving mesh method for pitching NACA0012 airfoil[J]. Chinese Journal of Computational Physics, 2016, 33(3): 266-272.
[23] JIN C Q, XU K. A unified moving grid gas-kinetic method in Eulerian space for viscous flow computation[J]. J Comput Phys, 2007, 222 (1):155-175.
[24] NI G X, JIANG S, XU K. Remapping-free ALE-type kinetic method for flow computations[J]. J Comput Phys, 2009, 228 (8):3154-3171.
[25] NI G X, JIANG S, XU X H. A moving mesh BGK scheme for multi-material flows[J]. Int J Numer Meth Fluid, 2012, 69 (4):878-896.
[26] XU Xihua, LIU Na, CHEN Yibing. Second-order local-bound-preserving conservative remapping on unstructured polyhedral meshes[J]. Chinese Journal of Computational Physics, 2018, 35(1): 22-28.
[27] HAN E E, LI J Q, TANG H Z. An adaptive GRP scheme for compressible fluid flows[J]. J Comput Phys, 2010, 229 (5):1448-1466.
[28] BEN-ARTZI M, FALCOVITZ J. A second-order Godunov-type scheme for compressible fluid dynamics[J]. J Comput Phys, 1984, 55 (1):1-32.
[29] BEN-ARTZI M, FALCOVITZ J. Generalized Riemann problems in computational fluid dynamics[M]. New York:Cambridge University Press, 2003.
[30] BEN-ARTZI M, LI J Q, WARNECKE G. A direct Eulerian GRP scheme for compressible fluid flows[J]. J Comput Phys, 2006, 218 (1):19-43.
[31] TANG H Z, TANG T. Adaptive mesh methods for one- and two-dimensional hyperbolic conservation laws[J]. SIAM J Numer Anal, 2003, 41 (2):487-515.
[32] COURANT R, FRIEDRICHS K O. Supersonic flow and shock waves[M]. Springer, 1999.
[33] TORO E F. Riemann solvers and numerical methods for fluid dynamics: A practical introduction[M]. Springer, 2009.
[34] LINDSTRÖM D. Numerical computation of viscous detonation waves in two space dimensions[R]. Report No.178, Department of Computing, Uppsala University, 1996.

基于任意拉格朗日—欧拉型移动网格的反应流广义黎曼问题方法

An Arbitrary Lagrangian-Eulerian Type Moving Mesh Generalized Riemann Problem Scheme for Reactive Flows

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