欧拉坐标系下具有锐利相界面的可压缩多介质流动数值方法研究

姚成宝; 付梅艳; 韩峰; 闫凯

doi:10.6052/0459-1879-20-054

欧拉坐标系下具有锐利相界面的可压缩多介质流动数值方法研究

doi: 10.6052/0459-1879-20-054

姚成宝^*1), ,,
付梅艳^*†,
韩峰^*,
闫凯^*†

^*西北核技术研究院,西安 710024
^†北京大学数学科学学院,北京 100871

详细信息

通讯作者:
姚成宝

中图分类号: O383
计量
- 文章访问数: 1289
- HTML全文浏览量: 288
- PDF下载量: 98
- 被引次数: 0
出版历程
- 收稿日期: 2020-02-22
- 刊出日期: 2020-08-10

NUMERICAL SCHEME OF MULTI-MATERIAL COMPRESSIBLE FLOW WITH SHARP INTERFACE ON EULERIAN GRIDS

Yao Chengbao^{*1)
, ,},
Fu Meiyan^*†,
Han Feng^*,
Yan Kai^*†

^*Northwest Institute of Nuclear Technology,Xi'an 710024, China
^†School of Mathematical Sciences,Peking University,Beijing 100871,China

摘要

摘要: 可压缩多介质流动问题的数值模拟在国防和工业领域内均具有重要的研究价值,诸如武器设计、爆炸安全防护等,通常具有大变形、高度非线性等特点,是一项极具挑战性的研究课题. 本文提出了一种基于 Euler 坐标系的非结构网格、具有锐利相界面的二维和三维守恒型多介质流动数值方法,可用于模拟可压缩流体和弹塑性固体在极端物理条件下的大变形动力学行为. 利用分片线性的水平集函数重构出单纯形网格内分段线性的相界面,并在混合网格内构建出具有多种介质的相界面几何结构,理论上可以处理全局任意种介质、局部 3 种介质的多介质流动问题. 利用传统的有限体积格式来计算单元边界上同种介质间的数值通量,并通过在相界面法向上求解局部一维多介质 Riemann 问题的精确解来计算不同介质间的数值通量,保证了相界面上的通量守恒. 提出了一种非结构网格上的单元聚合算法,消除了由于网格被相界面分割成较小碎片、违反 CFL 条件,进而可能带来数值不稳定的问题. 针对一维多介质 Riemann 问题、激波与气泡相互作用问题、浅埋爆炸问题、空中强爆炸冲击波和典型坑道内冲击波传播问题开展了数值模拟研究,将计算结果与相关的理论、实验结果进行比对,验证了数值方法的正确性和可靠性.
- 多介质流动 /
- 守恒型方法 /
- 锐利界面 /
- 聚合算法
Abstract: Numerical simulation of multi-material compressible flow problem is of great importance in both the national defense and industry areas, such as weapon design and blast wave defense. Due to the property of large deformation and high nonlinearity, the efficient simulation of multi-material compressible flow becomes a quite challenging problem. A numerical scheme is developed to carry out the simulation of an immiscible multi-material compressible flow with sharp phase interface on two dimensional and three dimensional unstructured Eulerian grids, which can handle the large deformation of compressible fluid and elastoplastic solid under the extreme conditions. We use the level set method to depict the phase interface numerically, and explicitly reconstruct the phase interface in a piecewise linear manifold. The topological structure of the phase interface is constructed explicitly, which can handle any number of media in the whole computational domain and three media in a single cell. The traditional finite volume method is used to calculate the edge numeircal flux between the same material in adjacent cells, while the phase interface flux is calculated by exactly solving a one dimensional multi-material Riemann problem on the normal direction of the phase interface. The above procedures can keep the conservation of the phase interface flux, and the interaction between two media across the phase interface can keep consistent with the real situation. A robust aggregation algorithm is adopted to build cell patches and adjust the conservation variables around the phase interface, which can effectively remove the numerical instability due to the breakdown of the CFL constraint by the cell fragments. Some classical examples and application problems, such as one-dimensional multi-material Riemann problem, gas-bubble interaction problem, intensive airblast problem, sub-surface blast problem, and blast wave propagation in three dimensional sap, which have a good agreement with the corresponding analytical and experimental results, are presented to validate our numerical scheme.
- multi-material flow /
- conservative scheme /
- sharp interface /
- aggregation algorithm

HTML全文

参考文献(1)

[1]	王昭, 严红. 基于气液相界面捕捉的统一气体动理学格式. 力学学报, 2018,50(4):711-721
[1]	( Wang Zhao, Yan Hong. Unified gaskinetic scheme for two phase interface capturing. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(4):711-721 (in Chinese))
[2]	刘文超, 刘曰武. 低渗透煤层气藏中气-水两相不稳定渗流动态分析. 力学学报, 2017,49(4):828-835
[2]	( Liu Wenchao, Liu Yuewu. Dynamic analysis on gas--water two-phase unsteady seepage flow in low-permeable coalbed gas reservoirs. Chinese Journal of Theoretical and Applied Mechanics, 2017,49(4):828-835 (in Chinese))
[3]	Benson D. Computational methods in Lagrangian and Eulerian hydrocodes. Computer Methods in Applied Mechanics and Engineering, 1992,99(2-3):235-394
[4]	贾祖鹏, 张树道, 蔚喜军. 多介质流体动力学计算方法. 北京: 科学出版社, 2014
[4]	( Jia Zupeng, Zhang Shudao, Yu Xijun. Numerical methods of multi-material flow dynamics. Beijing: Science Press, 2014 (in Chinese))
[5]	Hirt C, Amsden A, Cook J. An arbitrary Lagrangian-Eulerian computing method for all flow speeds. Journal of Computational Physics, 1974,14(3):227-253.
[6]	何涛. 基于 ALE 有限元法的流固耦合强耦合数值模拟. 力学学报, 2018,50(2):395-404
[6]	( He Tao. A partitioned strong coupling algorithm for fluid-structure interaction using arbitrary Lagrangian-Eulerian finite element formulation. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(2):395-404 (in Chinese))
[7]	Arienti M. A level set approach to Eulerian--Lagrangian coupling. Journal of Computational Physics, 2003,185(1):213-251
[8]	Hirts C, Nichols B. Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, 1981,39(1):201-225
[9]	张嫚嫚, 孙姣, 陈文义. 一种基于几何重构的 Youngs-VOF 耦合水平集追踪方法. 力学学报, 2019,51(3):775-786
[9]	( Zhang Manman, Sun Jiao, Chen Wenyi. An interface tracking method of coupled Youngs-VOF and level set based on geometric reconstruction. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(3):775-786 (in Chinese))
[10]	Dyadechko V, Shashkov M. Moment-of-fluid interface reconstruction. Los Alamos report A-UR-05-7571, 2005
[11]	Glimm J, Grove J, Li X. Three-dimensional front tracking. SIAM Journal on Scientific Computing, 1998,19(3):1703-727
[12]	Tryggvason G, Bunner B, Esmaeeli A. A front-tracking method for the computations of multiphase flow. Journal of Computational Physics, 2001,169(2):708-759
[13]	Osher S, Sethian J. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton- Jacobi formulations. Journal of Computational Physics, 1988,79(1):12-49
[14]	Sethian J. Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science. Cambridge: Cambridge University Press, 1999
[15]	Fedkiw R. A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method). Journal of Computational Physics, 1999,152(2):457-492
[16]	Liu TG, Khoo BC, Wang CW. The ghost fluid method for compressible gas--water simulation. Journal of Computational Physics, 2005,204(1):193-221
[17]	Liu TG, Khoo BC, Xie WF. Isentropic one-fluid modelling of unsteady cavitating flow. Journal of Computational Physics, 2004,201(1):80-108
[18]	Liu TG, Khoo BC, Yeo K. Ghost fluid method for strong shock impacting on material interface. Journal of Computational Physics, 2003,190(2):651-681
[19]	Liu TG, Khoo BC, Yeo K. Ghost fluid method for strong shock impacting on material interface. Journal of Computational Physics, 2003,190(2):651-681
[20]	Liu TG, Khoo BC, Yeo K. The simulation of compressible multi-medium flow. I. A new methodology with test applications to 1D gas-gas and gas-water cases. Computers & Fluids, 2001,30(3):291-314
[21]	Wang CW, Liu TG, Khoo BC. A real ghost fluid method for the simulation of multimedium compressible flow. SIAM Journal on Scientific Computing, 2006,28(1):278-302
[22]	Gao S, Liu TG, Yao CB. A complete list of exact solutions for one-dimensional elasticperfectly plastic solid Riemann problem without vacuum. Communications in Nonlinear Science and Numerical Simulation, 2018,63:205-227
[23]	Nourgaliev R, Liou M, Theofanous T. Numerical prediction of interfacial instabilities: Sharp interface method (SIM). Journal of Computational Physics, 2008,227(8):3940-3970
[24]	Liu C, Hu C. Adaptive THINC-GFM for compressible multi-medium flows. Journal of Computational Physics, 2017,342:43-65
[25]	白晓. 可压缩多相流问题的数值研究及应用. 合肥:中国科学技术大学, 2016
[25]	( Bai Xiao. Numerical Investigation of compressible multi-phase flows and application. Hefei: University of Science and Technology of China, 2016 (in Chinese))
[26]	Hu XY, Khoo BC, Adams NA, et al. A conservative interface method for compressible flows. Journal of Computational Physics, 2006,219(2):553-578
[27]	Hu XY, Adams NA, Laccarino G. On the HLLC Riemann solver for interface interaction in compressible multi-fluid flow. Journal of Computational Physics, 2009,228(17):6572-6589
[28]	Meyer M, Devesa A, Hickel S, et al. A conservative immersed interface method for large-eddy simulation of incompressible flows. Journal of Computational Physics, 2010,229(18):6300-6317
[29]	Lauer E, Hu XY, Hickel S, et al. Numerical modelling and investigation of symmetric and asymmetric cavitation bubble dynamics. Computers & Fluids, 2012,69(2):1-19
[30]	Tryggvason G, Bunner B, Esmaeeli A. A front-tracking method for the computations of multiphase flow. Journal of Computational Physics, 2001,169(2):708-759
[31]	Di YN, Li R, Tang T. Level set calculations for incompressible two-phase flows on a dynamically adaptive grid. Journal of Scientific Computing, 2007,31(1):75-98
[32]	Eleuteuo FT. Riemann Solvers and Numerical Methods for Fluid Dynamics. USA: Springer, 2009: 102-200
[33]	Guo YH, Li R, Yao CB. A numerical method on Eulerian grids for two-phase compressible flow. Advances in Applied Mathematics and Mechanics, 2016,8(2):187-212
[34]	Shyue K. A fluid-mixture type algorithm for compressible multicomponent flow with Mie-Grüneisen equation of state. Journal of Computational Physics, 2001,171(2):678-707
[35]	Gavrilyuk SL, Favrie N, Saurel R. Modelling wave dynamics of compressible elastic materials. Journal of Computational Physics, 2008,227(5):2941-2969
[36]	Quirk J, Karni S. On the dynamics of a shock-bubble interaction. Journal of Fluid Mechanics, 1996,318:129-163
[37]	Ullah M, Gao W, Mao D. Towards front-tracking based on conservation in two space dimensions III, tracking interfaces. Journal of Computational Physics, 2013,242:268-303
[38]	Haas J, Sturtevant B. Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities. Journal of Fluid Mechanics, 1987,181:41-76
[39]	乔登江. 核爆炸物理概论. 北京: 国防工业出版社, 2003: 51-55
[39]	( Qiao Dengjiang. An Introduction to Nuclear Explosion Physics. Beijing: National Defence Industry Press, 2003: 51-55(in Chinese))
[40]	Glasstone S, Dolan PJ. Effects of nuclear weapons. USA United States Department of Defense and the Energy Research and Development Administration, 1977: 453-501