SPH方法气-液界面边界条件研究

计算物理 ›› 2017, Vol. 34 ›› Issue (4): 409-416.

SPH方法气-液界面边界条件研究

周杰, 徐胜利

清华大学航天航空学院, 北京 100084

收稿日期:2016-04-06 修回日期:2016-09-18 出版日期:2017-07-25 发布日期:2017-07-25
通讯作者: 徐胜利,E-mail:slxu@mail.tsinghua.edu.cn
作者简介:周杰(1986-),男,博士,助理研究员,研究方向:超声速弹丸入水现象研究,E-mail:Beijihu1986@163.com
基金资助:
博士后基金（2015M581081）、中国运载火箭技术研究院基金（CALT201601）和清华大学自主课题（20161080102）资助项目

On SPH Method with Treatment of Gas-Liquid Interface Boundary Conditions

ZHOU Jie, XU Shengli

School of Aerospace Engineering, Tsinghua University, Beijing 100084, China

Received:2016-04-06 Revised:2016-09-18 Online:2017-07-25 Published:2017-07-25

摘要/Abstract

摘要： 针对界面附近粒子光滑函数截断和非物理穿透问题，提出一种气-液界面边界条件的处理方法.当界面附近支持域出现不同材料粒子，每步计算可在支持域设置虚粒子，按照密度分配方法给虚粒子物理量赋值，并对界面附近粒子引入气-液两相阻力.采用SPH方法和Level-Set方法，计算运动激波对气-液界面作用问题，两者计算结果一致，初步验证了气-液界面边界条件处理的适用性.用SPH方法分别计算超声速气流中的圆截面液柱绕流和下落问题，界面两侧粒子压力和法向速度连续，给出弓形激波、回流区和下游回流区等定性合理结果.表明本文方法可适度避免界面附近流体粒子光滑截断和粒子非物理穿透现象、界面附近流场数值振荡.

关键词: SPH, GFM方法, 激波, 气-液界面

Abstract: To study truncation of an integral function and unphysical penetration of particles near an interface, treatment of boundary conditions at a gas-liquid interface was proposed based on concept of ghost fluid method(GFM). Ghost particles are copied into kernel domain for avoiding truncation of integral function. Parameters are specified near interface for ghost particles according to density distribution method. Drags produced by slip velocity between particles of gas and liquid are included in computation. With comparison of results obtained by methods of SPH and level-set on shock wave interacting with a gas-liquid interface, acceptable numerical precision is shown since results are basically identical for calibration examples. Results are both obtained for cases of streaming around an initially fixed water cylinder and a fall-off of a water cylinder. The phenomena seem physically resasonable based on obtained results. Treatment of gas-liquid interface boundary condition approximately avoids truncation of an integral functions near interface and prevents numerical oscillation, particles penetration for SPH methodology. Pressure and normal velocity are kept continuously on both sides of gas-liquid interface during computation.

Key words: SPH, ghost fluid method, shock wave, gas-liquid interface

中图分类号:

V211.3

周杰, 徐胜利. SPH方法气-液界面边界条件研究[J]. 计算物理, 2017, 34(4): 409-416.

ZHOU Jie, XU Shengli. On SPH Method with Treatment of Gas-Liquid Interface Boundary Conditions[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 34(4): 409-416.

参考文献

[1] LIU G R, LIU M B. Smoothed particle hydrodynamics:A meshfree particle method[M]. German:Springer Berlin/Heidelberg, 2004:1-491.
[2] MONAGHAN J J. On the problem of penetration in particle menthods[J]. Journal of Computer Physics, 1989, 82(1):1-15
[3] LIU M B,LIU G R. Smoothed particle hydrodynamics (SPH):An overview and recent developments[J]. Archives of Computational Methods in Engineering, 2010, 17(1):25-76.
[4] CAPBELL J Q, VIGNJEVIC R, LIBERSKY L D. A contact algorithm for smoothed particle hydrodynamics[J]. Computer Methods in Applied Mechanics and Engineering, 2000, 184(1):49-65.
[5] RANDLES P W, LIBERSKY L D. Smoothed particle hydrodynamics:Some recent improvements and applications[J]. Computer Methods in Applied Mechanics and Engineering, 1996, 139(1):375-408.
[6] BELYTSCKO T, NEAL M. Contact-impact by the pinball algorithm with penalty and Lagrangian methods[J]. International Journal for Numerical Methods in Engineering, 1991, 31(3):547-572.
[7] BELYTSCHKO T, YEH I. The splitting pinball method for contact-impact problems[J]. Computer Methods in Applied Mechanics and Engineering, 1993, 105(3):375-393.
[8] VIGNJEVIC R, VUYST T D, CAMPBELL J C. A frictionless contact algorithm for meshless methods[J]. Computer Modeling in Engineering & Sciences, 2006, 13(1):35-47
[9] VIGNJEVIC R, VUYST T D, CAMPBELL J C. A frictionless contact algorithm for meshless methods[J]. International Conference on Computational & Experimental Engineering and Sciences, 2007, 3(2):107-112
[10] ZIENKIEWICS O. The finite element method[M]. McGraw Hill, London, 1991.
[11] LIU M B, LIU G R, LAM K Y. A new technique to treat material interfaces for smoothed particle hydrodynamics[C]. Proceeding of 1st Asia-Pacific Congress on Computational Mechanics, Sydney, 2001:977-982.
[12] FEDKIW R P, MARQUINA A, MERRIMAN B. An isobaric fix for the overheating problem in multimaterial compressible flows[J]. Journal Computational Physics, 1999, 148:545-578.
[13] XU Shengli, YUE Pengtao, HAN Zhaoyuan. Numerical studies on the mixing of CH₄ and kerosene injected into a supersonic flow with H₂ pilot injection[J]. Applied Mathematics and Mechanics, 2001,22(4):468-477.
[14] LUCY L B. A numerical approach to the testing of the fission hypothesis[J]. The Astronomical Journal, 1977, 82(82):1013-1024
[15] MONAGHAN J J. Particle methods for hydrodynamic[J]. Computer Physics Report,1985, 3(2):71-124.
[16] MONAGHAN J J. Smoothed particle hydrodynamics[J]. Reports on Progress in Physics, 2005, 68(8):1703-1759.
[17] LIBERSKY L D,PETSCHECK A G,CARNEY T C,et al.High strain Lagarangian hydrodynamics a three-dimensional SPH code for dynamic material response[J].Journal of Computational Physics,1993, 109(1):67-75.
[18] ANDREA Colagrossi, MAURIZIO Landrini. Numerical simulation of interfacial flows by smoothed particle hydrodynamics[J]. Journal of Computational Physics, 2003, 191(2):448-475.
[19] VACONDIO R, ROGERS B D, STANSBY P K, et al. SPH modeling of shallow flow with open boundaries for practical flood simulation[J]. Journal of Hydraulic Engineering, 2012,138(6):530-541.
[20] VACONDIO R. Shallow water and Navier-Stokes SPH-like numerical modelling of rapidly varying free-surface flows[D]. Italia:College of engineering, University of Parma, 2010.
[21] LIU T G, KHOO B C, YEO K S. Ghost fluid method for strong shock impacting on material interface[J]. Journal Computational Physics, 2003, 190:651-681.
[22] LIU T G, KHOO B C, WANG C W. The ghost fluid method for compressible gas-water simulation[J]. Journal of Computational Physics, 2005, 204(1):193-221.