适用于等熵流动的交错拉氏Godunov方法

doi:10.19596/j.cnki.1001-246x.8144

计算物理 ›› 2020, Vol. 37 ›› Issue (5): 529-538.DOI: 10.19596/j.cnki.1001-246x.8144

所属专题：第十届全国青年计算物理会议优秀论文

适用于等熵流动的交错拉氏Godunov方法

孙晨¹, 李肖^1,2, 沈智军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:2019-09-18 修回日期:2019-10-22 出版日期:2020-09-25 发布日期:2020-09-25
通讯作者: 沈智军,E-mail:shen_zhijun@iapcm.ac.cn
作者简介:孙晨(1986-),女,安徽,助理研究员,博士,从事计算流体力学方法研究,E-mail:sunchen_iapcm@sina.com
基金资助:
科学挑战专题（JCKY2016212A502）、国家自然科学基金（U1630249，11971071）及计算物理实验室基金资助项目

A Godunov Method with Staggered Lagrangian Discretization Applicable to Isentropic Flows

SUN Chen¹, LI Xiao^1,2, SHEN Zhijun¹

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

Received:2019-09-18 Revised:2019-10-22 Online:2020-09-25 Published:2020-09-25

摘要/Abstract

摘要： 为消除传统单元中心型Godunov方法在求解稀疏波问题时的非物理过热现象，发展一种适用于等熵流动的交错拉氏Godunov方法.主要的特征是采用速度与热力学变量交错分布的形式，避免在单元内进行速度平均，从而消除由于动量平均过程导致的动能耗散.与传统的von Neumann型交错网格方法相比，网格的边界通量由节点处的多维黎曼求解器提供，克服了多维人工粘性选取带来的困难.为减少多维黎曼求解器在求解稀疏波问题时的非物理熵增，给出稀疏波出现的合理判据，从而保证了热力学关系式的满足.数值实验表明：该方法能很好地消除稀疏波的过热现象，同时在求解激波问题时又能保持与传统单元中心型拉氏方法相同的激波捕捉能力.

关键词: 交错网格, 黎曼求解器, 稀疏波, Godunov方法

Abstract: In cell-centered Godunov method,unphysical overheating problem exists in rarefaction flows.We develop a Godunov method with staggered Lagrangian discretization which is applicable to isentropic flows. Velocity and thermodynamic variables are defined in staggered discretization. The velocity averaging process in a cell is avoided,so that the kinetic energy dissipation due to the momentum averaging process is removed. In contrast to the traditional von Neumann staggered grid method, the face flux is provided by a node multidimensional Riemann solver. The difficulty in selecting multidimensional artificial viscosity is overcome. In order to reduce unphysical entropy production of multidimensional Riemann solver in rarefaction problems,we give a reasonable criterion of rarefaction appearance to satisfy the thermodynamic relation. Numerical results show that the method removes overheating problem in rarefaction problems, and retains the property of accurate shock capturing of the original Lagrangian Godunov method as well.

Key words: staggered grid, Riemann solver, rarefaction wave, Godunov method

中图分类号:

O354

孙晨, 李肖, 沈智军. 适用于等熵流动的交错拉氏Godunov方法[J]. 计算物理, 2020, 37(5): 529-538.

SUN Chen, LI Xiao, SHEN Zhijun. A Godunov Method with Staggered Lagrangian Discretization Applicable to Isentropic Flows[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 37(5): 529-538.

参考文献

[1] TORO E F.Riemann solvers and numerical methods for fluid dynamics[M]. 3rd ed. Berlin Heidelberg:Springer-Verlag,2009.
[2] LIOU M S. Open problems in numerical fluxes:Proposed resolutions[C]. 20th AIAA Computational Fluid Dynamics Conference, Hawaii,2011.
[3] LIOU M S. Unresolved problems by shock capturing:Taming the overheating problem[C]. 7th International Conference on Computational Fluid Dynamics,Hawaii,2012.
[4] LIOU M S. Why is the overheating problem diffcult:The role of entropy[C]. 21st AIAA Computational Fluid Dynamics Conference, San Diego,2013.
[5] LIOU M S. The root cause of the overheating problem[C]. 23rd AIAA Computational Fluid Dynamics Conference,Denver,2017.
[6] CHENG J,SHU C W. A high order ENO conservative Lagrangian type scheme for the compressible Euler equations[J]. Journal of Computational Physics,2007,227(2):1567-1596.
[7] LIU W,CHENG J,SHU C W. High order conservative Lagrangian schemes with Lax-Wendroff type time discretization for the compressible Euler equations[J]. Journal of Computational Physics,2009,228(23):8872-8891.
[8] BOSCHERI W,DUMBSER M. A direct arbitrary-Lagrangian-Eulerian ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and nonconservative hyperbolic systems in 3D[J]. Journal of Computational Physics,2014,275(15):484-523.
[9] SHEN Z J,XIE Y W,YAN W. Wall heating and adaptive heat conduction viscosity[J]. Chinese Journal of Computational Physics,2012,29(6):807-814.
[10] HU X Y,KHOO B C. Kinetic energy fix for low internal energy flows[J]. Journal of Computational Physics,2003,193(1):243-259.
[11] XU K,HU J S. Projection dynamics in Godunov-type schemes[J]. Journal of Computational Physics,1998,142(2):412-427.
[12] VON NEUMANN J,RICHTMYER R D. A method for the numerical simulation of hydrodynamics shocks[J]. Journal of Applied Physics,1950,21(3):232-237.
[13] ZHOU H B,XIONG J,LIU W T,et al. An artificial viscosity in Lagrangian hydrodynamics method[J]. Chinese Journal of Computational Physics,2010,27(6):829-832.
[14] CHENG X H,NIE Y F,CAI L,et al. Entropy stable scheme based on moving meshes for hyperbolic conservation laws[J]. Chinese Journal of Computational Physics,2017,34(2):175-182.
[15] 李德元,徐国荣,水鸿寿,等. 二维非定常流体力学数值方法[M]. 北京:科学出版社,1998.
[16] XU X H,NI G X,JIANG S. An entropy fixed cell-centered Lagrangian scheme[J]. International Journal for Numerical Methods in Fluids,2013,72(10):1096-1115.
[17] BRAEUNIG J P. Reducing the entropy production in a collocated Lagrange-Remap scheme[J]. Journal of Computational Physics,2016,314(1):127-144.
[18] COCCHI J P,SAUREL R,LORAUD J C,et al. Some remarks about the resolution of high velocity flows near low densities[J]. Shock Waves,1998,8(2):119-125.
[19] MAIRE P H,LOUBERE R,VACHAL P. Staggered Largrangian discretization based on cell-centered Riemann solver and associated hydrodynamics scheme[J]. Communications in Computational Physics,2011,10(4):940-978.
[20] CARAMANA E J,BURTON D E,SHASHKOV M J,et al. The construction of compatible hydrodynamics algorithms utilizing conservation of total energy[J]. Journal of Computational Physics,1998,146(1):227-262.
[21] DUKOWICZ J K. A general,non-iterative Riemann solver for Godunov's method[J]. Journal of Computational Physics,1985,61(1):119-137.
[22] MAIRE P H,ABGRALL R,BREIL J,et al. A cell-centered Lagrangian scheme for two-dimensional compressible flow problems[J]. Siam Journal on Scientific Computing,2007,29(4):1781-1824.
[23] SEDOV L I. Similarity and dimensional methods in mechanics[M]. New York:Academic Press,1959.

适用于等熵流动的交错拉氏Godunov方法

A Godunov Method with Staggered Lagrangian Discretization Applicable to Isentropic Flows

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