虚拟流体方法的设计原则

计算物理 ›› 2016, Vol. 33 ›› Issue (6): 671-680.

虚拟流体方法的设计原则

许亮¹, 冯成亮², 刘铁钢²

1. 中国航天空气动力技术研究院, 北京 100074;
2. 北京航空航天大学数学与系统科学学院数学、信息与行为教育部重点实验室, 北京 100191

收稿日期:2015-08-24 修回日期:2016-02-18 出版日期:2016-11-25 发布日期:2016-11-25
作者简介:许亮(1982-),男,博士,高级工程师,从事计算流体力学研究,E-mail:xul@buaa.edu.cn
基金资助:
国家自然科学基金（11201442）资助项目

Design Principles of Ghost Fluid Method

XU Liang¹, FENG Chengliang², LIU Tiegang²

1. China Academy of Aerospace Aerodynamics, Beijing 100074, China;
2. LMIB & School of Mathematics and Systems Science, Beihang University, Beijing 100191, China

Received:2015-08-24 Revised:2016-02-18 Online:2016-11-25 Published:2016-11-25

摘要/Abstract

摘要： 研究模拟可压缩多介质流的虚拟流体方法，建立一般状态方程下定义虚拟流体状态的基本原则.根据波系结构和使用的自由变量分别推导虚拟流体状态的定义方式.结果表明在这些方式下求解多介质Riemann问题理论上完全精确.进一步总结几种简单有效的虚拟流体方法，这些定义方式不依赖于虚拟流体区域可能产生的波系结构.其中一种类似于反射边界条件，只是界面速度需要首先精确预测出来.数值算例验证了研究结果的合理性.

关键词: 可压缩多介质流, 虚拟流体方法, 多介质Riemann问题, 虚拟流体状态, 一般状态方程

Abstract: By analyzing ghost fluid method for compressible multi-medium flows, fundamentals for defining ghost fluid state with a general equation of state are described. All possible definitions of ghost fluid states are derived according to wave patterns and free variables in ghost fluid region. Following these treatments, it reveals that solution of multi-medium Riemann problem can be obtained exactly in theory. Several simple but effective definitions independent with wave patterns in ghost fluid region, are further summarized. One of these ways is similar to reflective boundary condition. An essential prerequisite is that interfacial velocity must be predicted exactly. Numerical results show that this methodology indeed works reasonably for multi-medium flows.

Key words: compressible multi-medium flows, ghost fluid method, multi-medium Riemann problem, ghost fluid state, general equation of state

中图分类号:

O359

许亮, 冯成亮, 刘铁钢. 虚拟流体方法的设计原则[J]. 计算物理, 2016, 33(6): 671-680.

XU Liang, FENG Chengliang, LIU Tiegang. Design Principles of Ghost Fluid Method[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 33(6): 671-680.

参考文献

[1] LARROUTUROU B. How to preserve the mass fractions positivity when computing compressible multi-component flows[J]. J Comput Phys, 1991, 95(1):59-84.
[2] KARNI S. Hybrid multifluid algorithms[J]. SIAM J Sci Comput, 1996, 17(5):1019-1039.
[3] JENNY P, MULLER B, THOMANN H. Correction of conservative Euler solvers for gas mixtures[J]. J Comput Phys, 1997, 132(1):91-107.
[4] TANG W J,JIANG L, CHENG J B. Algorithm preserving mass fraction maximum principle for multi-component flow[J]. Chinese J Comput Phys, 2014, 31(3):292-306.
[5] COCCHI J P, SAUREL R. A Riemann problem based method for the resolution of compressible multimaterial flows[J]. J Comput Phys, 1997, 137(2):265-298.
[6] LIU T G, KHOO B C, YEO K S. Ghost fluid method for strong shock impacting on material interface[J]. J Comput Phys, 2003, 190(2):651-681.
[7] WANG C W, LIU T G, KHOO B C. A real ghost fluid method for the simulation of multimedium compressible flow[J]. SIAM J Sci Comput, 2006, 28(1):278-302.
[8] FEDKIW R P, ASLAM T, MERRIMAN B, Osher S. A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)[J]. J Comput Phys, 1999, 152(2):457-492.
[9] DING Y, YUAN L, YANG L. An explicit-implicit algorithm for ghost fluid method[J]. Chinese J Comput Phys, 2013, 30(1):27-34.
[10] LIU T G, KHOO B C, WANG C W. The ghost fluid method for compressible gas-water simulation[J]. J Comput Phys, 2005, 204(1):193-221.
[11] SONG P C, WANG C W. Interface treating method for multi-medium flow on triangular meshes[J]. Chinese J Comput Phys, 2012, 29(1):36-42.
[12] LIU T G, XIE W F, KHOO B C. The modified ghost fluid method for coupling of fluid and structure constituted with hydro-elasto-plastic equation of state[J]. SIAM J Sci Comput, 2008, 30(3):1105-1130.
[13] HAAS J F, STURTEVANT B. Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities[J]. J Fluid Mech, 1987, 181(1):41-76.
[14] LIU T G, KHOO B C, YEO K S. The simulation of compressible multi-medium flow Ⅱ:Applications to 2D underwater shock refraction[J]. Comput Fluids, 2001, 30(3):315-337.