修正压力梯度粒子近似SPH方法计算大密度比界面流动

徐丞君; 徐胜利; 刘庆源

doi:10.21656/1000-0887.390126

修正压力梯度粒子近似SPH方法计算大密度比界面流动

doi: 10.21656/1000-0887.390126

¹中国科学技术大学数学科学学院, 合肥 230026;²清华大学航天航空学院, 北京 100084

详细信息

作者简介:
徐丞君（1991—），男，硕士(E-mail: xucjh@mail.ustc.edu.cn);徐胜利（1965—），男，教授，博士，博士生导师(通讯作者. E-mail: slxu@mail.tsinghua.edu.cn);刘庆源（1990—），男，博士(E-mail: qyliu@ustc.edu.cn).

中图分类号: O242.1
计量
- 文章访问数: 1407
- HTML全文浏览量: 236
- PDF下载量: 530
- 被引次数: 0
出版历程
- 收稿日期: 2018-04-19
- 修回日期: 2018-11-12
- 刊出日期: 2019-01-01

Modified Particle Approximation to Pressure Gradients in the SPH Algorithm for Interfacial Flows With High Density Ratios

¹School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, P.R.China;²School of Aerospace Engineering, Tsinghua University, Beijing 100084, P.R.China

摘要

摘要: 计算了高密度比的多界面流动问题.为保证多相SPH(smoothed-particle hydrodynamics)方法捕捉界面光滑性和消除界面附近压力震荡，修正了动量方程压强梯度项的粒子近似，在界面施加了排斥力.采用Rayleigh-Taylor界面不稳定性、非Boussinesq锁定交换、溃坝和气泡上升等算例验证了该方法的准确性和健壮性，得到不同时刻界面（粒子）分布、压力云图和指定点压力时间分布、界面锋面距离等.所得结果表明：计算结果(如界面形状、光滑性和指定点压力分布等)与实验值或其他文献结果符合较好.修正的压力梯度项粒子近似，改善了多相SPH方法对高密度比、大变形和破碎多相界面的模拟能力和光滑性，同时界面附近未出现明显的压力震荡.
- SPH方法 /
- 多相流 /
- Rayleigh-Taylor界面不稳定 /
- 溃坝 /
- 气泡
Abstract: Interfacial flows with high density ratios ranging from 1 to 1 000 were numerically investigated. Modified particle approximation was proposed for the pressure gradient term in the momentum equation and the repulsive force was imposed for virtual particles outside the interfaces. The Rayleigh-Taylor instability, non-Boussinesq lock exchange, dam-break flow and bubble buoyancy were numerically tested for validation of accuracy and robustness of the new SPH algorithm for multi-fluid flows. The particle distributions, pressure contours and pressure-time distributions at specified points were obtained from the computations. The results are in good agreement with those from references and experimental measurements. The captured interfaces are more smooth in comparison with those from previous literatures and no obvious oscillations are observed in the vicinity of the interfaces.
- smoothed particle hydrodynamics algorithm /
- multi-phase flow /
- Rayleigh-Taylor instability /
- dam-break flow /
- bubble

HTML全文

参考文献(33)

[1]	徐志敏, 宋思远, 辛锋先, 等. 小Reynolds数下粗糙圆管中黏性流场的理论解[J]. 应用数学和力学, 2018,39(2): 123-136.(XU Zhimin, SONG Siyuan, XIN Fengxian, et al. Analytical solution for the viscous flow of small Reynolds numbers in rough pipes[J]. Applied Mathematics and Mechanics,2018,39(2): 123-136.(in Chinese))
[2]	BRACKBILL J, KOTHE D B, ZEMACH C. A continuum method for modeling surface tension[J]. Journal of Computational Physics,1992,100(2): 335-354.
[3]	BALACHANDAR S, EATON J K. Turbulent dispersed multiphase flow[J]. Annual Review of Fluid Mechanics,2010,42: 111-133.
[4]	ZHENG Jun, YU Kaiping, WANG Junfeng,et al. SPH for developing super cavity induced by high speed underwater body[J]. Chinese Journal of Computational Physics,2014,31(1): 27-32.
[5]	上官子柠, 周秀丽, 宋鑫, 等. 典型自由面流动问题的SPH-ALE数值模拟[J].计算物理, 2017,34(6): 641-650.(SHANGGUAN Zining, ZHOU Xiuli, SONG Xin, et al. Numerical simulation of typical free surface flow with SPH-ALE[J]. Chinese Journal of Computational Physics,2017,34(6): 641-650.(in Chinese))
[6]	ESPANOL P, WARREN P. Statistical mechanics of dissipative particle dynamics[J]. Europhysics Letters,1995,30(4): 191-196.
[7]	GINGOLD R A, MONAGHAN J J. Smoothed particle hydrodynamics: theory and application to non-spherical stars[J]. Monthly Notices of the Royal Astronomical Society,1977,181(3): 375-389.
[8]	韩亚伟, 强洪夫. 改进的物理粘性SPH方法及其在溃坝问题中的应用[J]. 计算物理, 2012,29(5): 693-699.(HAN Yawei, QIANG Hongfu. An improved SPH method with physical viscosity and application in dam-break problem[J]. Chinese Journal of Computational Physics,2012,29(5): 693-699.(in Chinese))
[9]	王安文, 徐绯, 张岳青. SPH方法在液固撞击数值模拟中的应用[J]. 计算物理, 2012,29(4): 525-533.(WANG Anwen, XU Fei, ZHANG Yueqing. SPH method in numerical simulation of liquid-solid impact[J]. Chinese Journal of Computational Physics,2012,29(4): 525-533.(in Chinese))
[10]	卞梁, 王肖钧, 章杰, 等. 高速碰撞数值计算中的SPH分区算法[J]. 计算物理, 2011,28(2): 207-212.(BIAN Liang, WANG Xiaojun, ZHANG Jie, et al. Numerical simulation of hypervelocity impact with subdomains in SPH computation[J].Chinese Journal of Computational Physics,2011,28(2): 207-212.(in Chinese))
[11]	COLAGROSSI A, LANDRINI M. Numerical simulation of interfacial flows by smoothed particle hydrodynamics[J].Journal of Computational Physics,2003,191(2): 448-475.
[12]	CHEN Z, ZONG Z, LIU M B, et al. An SPH model for multiphase flows with complex interfaces and large density differences[J]. Journal of Computational Physics,2015,283: 169-188.
[13]	沈雁鸣, 陈坚强. SPH方法对气液两相流自由界面运动的追踪模拟[J]. 空气动力学学报, 2012,30(2): 157-161, 168.(SHEN Yanming, CHEN Jianqiang. Numerical tracking of interface in multiphase flows with smoothed particle hydrodynamics[J]. Acta Aerodynamica Sinica,2012,30(2): 157-161, 168.(in Chinese))
[14]	MONAGHAN J J. SPH without a tensile instability[J]. Journal of Computational Physics,2000,159(2): 290-311.
[15]	HU X Y, ADAMS N A. An incompressible multi-phase SPH method[J]. Journal of Computational Physics,2007,227(1): 264-278.
[16]	COLAGROSSI A. A meshless Lagrangian method for free-surface and interface flows with fragmentation[D]. PhD Thesis. Rome: University of Rome, 2005
[17]	HOOGERBRRUGGE P J, KOELMAN J M V A. Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics[J]. Europhys Letter,1992,19(3): 155-160.
[18]	HU X Y, ADAMS N A. A multi-phase SPH method for macroscopic and mesoscopic flows[J]. Journal of Computational Physics,2006,213(2): 844-861.
[19]	MONAGHAN J J, RAFIEE A. A simple SPH algorithm for multi-fluid flow with high density ratios[J]. International Journal for Numerical Methods in Fluids,2013,71(5): 537-561.
[20]	MONAGHAN J J. Simulating free surface flows with SPH[J]. Journal of Computational Physics,1994,110(2): 399-406.
[21]	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
[22]	EDMOND Y M, SHAO S D. Simulation of near-shore solitary wave mechanics by an incompressible SPH method[J].Applied Ocean Research,2002,24(5): 275-286.
[23]	MONAGHAN J J. Shock simulation by the particle method SPH[J]. Journal of Computational Physics,1983,52(2): 374-389.
[24]	沈雁鸣. 基于SPH方法的物体入水冲击问题数值模拟研究[D]. 博士学位论文. 绵阳: 中国空气动力研究与发展中心研究生部, 2016: 24-26.(SHEN Yanming. A numerical study of water entry problems based on smoothed particle hydrodynamics (SPH) method[D]. PhD Thesis. Mianyang: The Graduate Faculty of China Aerodynamics Research and Development Center, 2016: 24-26.(in Chinese))
[25]	陈臻. SPH算法改进及在晃荡与入水中的应用[D]. 硕士学位论文. 大连: 大连理工大学, 2014.(CHEN Zhen.Improving SPH methodology with its application to sloshing and water entry[D]. Master Thesis. Dalian: Dalian University of Technology, 2014.(in Chinese))
[26]	LIU M B, SHAO J R, CHANG J Z. On the treatment of solid boundary in smoothed particle hydrodynamics[J]. Science China Technological Sciences,2012,55(1): 244-254.
[27]	CUMMINS S J, RUDMAN M. An SPH projection method[J]. Journal of Computational Physics,1999,152(2): 584-607.
[28]	LEE H G, KIM J. Numerical simulation of the three-dimensional Rayleigh-Taylor instability[J]. Computers and Mathematics With Applications,2013,66(8): 1466-1474.
[29]	GRENIER N, ANTUONO M, COLAGROSSI A, et al. An Hamiltonian interface SPH formulation for multi-fluid and free surface flows[J]. Journal of Computational Physics,2009,228(22): 8380-8393.
[30]	DALZIEL S. Toy models for Rayleigh Taylor instability[C]//8th International Workshop on the Physics of Compressible Turbulent Mixing . Lawrence Livermore National Laboratory: UCRL-MI-146350, 2001.
[31]	BIRMAN V K, MARTIN J E, MEIBURG E. The non-Boussinesq lock-exchange problem, part 2: high-resolution simulations[J]. Journal of Fluid Mechanics,2005,537: 125-144.
[32]	LOWE R J, ROTTMAN J W,LINDEN P F. The non-Boussinesq lock-exchange problem, part 1: theory and experiments[J]. Journal of Fluid Mechanics,2005,537: 101-124.
[33]	SUSSMAN M, SMEREKA P, OSHER S. A level set approach for computing solutions to incompressible two-phase flow[J]. Journal of Computational Physics,1994,114(1): 146-159.

施引文献

资源附件(0)

访问统计

点击查看大图

计量

文章访问数: 1407
HTML全文浏览量: 236
PDF下载量: 530
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

修正压力梯度粒子近似SPH方法计算大密度比界面流动

doi: 10.21656/1000-0887.390126

作者简介:
徐丞君（1991—），男，硕士(E-mail: xucjh@mail.ustc.edu.cn);徐胜利（1965—），男，教授，博士，博士生导师(通讯作者. E-mail: slxu@mail.tsinghua.edu.cn);刘庆源（1990—），男，博士(E-mail: qyliu@ustc.edu.cn).

计量

Modified Particle Approximation to Pressure Gradients in the SPH Algorithm for Interfacial Flows With High Density Ratios

计量

目录

留言板

修正压力梯度粒子近似SPH方法计算大密度比界面流动

doi: 10.21656/1000-0887.390126

作者简介: 徐丞君（1991—），男，硕士(E-mail: xucjh@mail.ustc.edu.cn);徐胜利（1965—），男，教授，博士，博士生导师(通讯作者. E-mail: slxu@mail.tsinghua.edu.cn);刘庆源（1990—），男，博士(E-mail: qyliu@ustc.edu.cn).

计量

出版历程

Modified Particle Approximation to Pressure Gradients in the SPH Algorithm for Interfacial Flows With High Density Ratios

计量

出版历程

目录

作者简介:
徐丞君（1991—），男，硕士(E-mail: xucjh@mail.ustc.edu.cn);徐胜利（1965—），男，教授，博士，博士生导师(通讯作者. E-mail: slxu@mail.tsinghua.edu.cn);刘庆源（1990—），男，博士(E-mail: qyliu@ustc.edu.cn).