Numerical Simulations of Richtmyer-Meshkov Instability Using Conservative Front-Tracking Method

M. A. Ullah; GAO Wen-bin; MAO De-kang

doi:10.3879/j.issn.1000-0887.2011.01.012

Volume 32 Issue 1

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2011 > 32(1): 113-126

M. A. Ullah, GAO Wen-bin, MAO De-kang. Numerical Simulations of Richtmyer-Meshkov Instability Using Conservative Front-Tracking Method[J]. Applied Mathematics and Mechanics, 2011, 32(1): 113-126. doi: 10.3879/j.issn.1000-0887.2011.01.012

Citation:

PDF( 2406 KB)

Numerical Simulations of Richtmyer-Meshkov Instability Using Conservative Front-Tracking Method

doi: 10.3879/j.issn.1000-0887.2011.01.012

1.
Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China;

Received Date: 2010-08-17
Rev Recd Date: 2010-12-06
Publish Date: 2011-01-15

Abstract

Abstract

Numerical simulations of two Richtmyer-Meshkov(RM)instability experiments were presented using the conservative front tracking method developed in[Mao D.J Comput Phys,2007,226(2): 1550-1588],and compare them with that obtained in[Holmes R L,et al.J Fluid Mech,1995,301: 51-64].The simulations are generally in good agreement with that of Holmes et al.The simulations also captured the nonlinear and compressive phenomena,the self-interactions of the transmitted and reflected wave edges,which was pointed out in Holmes et al's work as the cause of the deceleration of the interfaces.However,the perturbation amplitudes and amplitude growth rates of the interfaces obtained with our conservative front-tracking method are a bit larger than that obtained by Holmes et al.
- Richtmyer-Meshkov instability,
- conservative front-tracking,
- perturbation amplitude,
- amplitude growth rate

FullText(HTML)

References(20)

References

[1]	Richtmyer R D.Taylor instability in shock acceleration of compressible fluids[J].Comm Pure Appl Math, 1960, 13(2): 297-319. doi: 10.1002/cpa.3160130207
[2]	Meshkov E E.Instability of a shock wave accelerated interface between two gases[J].NASA Tech Trans, 1970, F-13: 074.
[3]	Benjamin R, Besnard D, Haas J. Shock and reshock of an unstable interface[R]. LANL Rep Los Alamos National Laboratory, 1993, LA-UR 92-1185.
[4]	Cloutman L D, Wehner M F. Numerical simulation of Richtmyer-Meshkov instabilities[J]. Phys Fluids A, 1992, 4(8): 1821-1830.
[5]	Meyer K A, Blewett P J.Numerical investigation of the stability of a shock-accelerated interface between two fluids[J].Phys Fluids, 1972, 15(5): 753-759. doi: 10.1063/1.1693980
[6]	Holmes R L.A numerical investigation of the Richtmyer-Meshkov instability using front-tracking[D].Ph D Thesis. Stony Broke, USA: State University of New York, 1994.
[7]	Holmes R L, Grove J W, Sharp D H.Numerical investigation of Richtmyer-Meshkov instability using front-tracking[J].J Fluid Mech, 1995, 301: 51-64. doi: 10.1017/S002211209500379X
[8]	Chern I-L, Glimm J, McBryan O, Plohr B, Yaniv S.Front tracking for gas dynamics[J]. J Comput Phys, 1998, 62(1): 83-110.
[9]	Glimm J, Li X L, Liu Y J, Xu Z L, Zhao N. Conservative front-tracking with improved accuracy[J]. SIAM J Numer Anal, 2003, 41(5): 1926-1947. doi: 10.1137/S0036142901388627
[10]	Glimm J, Graham M J, Grove J, Li X L, Smith T M, Tan D, Tangerman F, Zhang Q. Front tracking in two and three dimensions[J]. Comput Math Appl, 1998, 35(7): 1-11.
[11]	Holmes R L, Dimonte G, Fryxell B, Gittings M L, Grove J W, Schneider M, Sharp D H, Velikovich A L,Weaver R P, Zhang Q.Richtmyer-Meshkov instability growth: experiment, simulation and theory[J].J Fluid Mech, 1999, 389: 55-79. doi: 10.1017/S0022112099004838
[12]	Howell B P, Ball G J.Damping of mesh-induced errors in free-Lagrange simulations of Richtmyer-Meshkov instability[J].Shock Waves, 2000, 10(4): 253-264. doi: 10.1007/s001930000055
[13]	Li X L, Zhang Q.A comparative numerical study of the Richtmyer-Meshkov instability with nonlinear anaylsis in two and three dimensions[J].Phys Fluids, 1997, 9(10): 3069-3077. doi: 10.1063/1.869415
[14]	MAO De-kang. Towards front-tracking based on conservation in two space dimensions Ⅱ, tracking discontinuities in capturing fashion[J].J Comput Phys, 2007, 226(2): 1550-1588. doi: 10.1016/j.jcp.2007.06.004
[15]	MAO De-kang. Towards front tracking based on conservation in two space dimensions[J].SIAM J Sci Comput, 2000, 22(1): 113-151. doi: 10.1137/S1064827597310609
[16]	JIANG Guang-shan, SHU Chi-wang. Efficient implementation of weighted ENO schemes[J].J Comput Phys, 1996, 126(1): 202-228. doi: 10.1006/jcph.1996.0130
[17]	LeVeque R J.Finite Volume Methods for Hyperbolic Problems[M].Britain: Press Syndicate of the University of Cambridge, 2002.
[18]	LeVeque R J. Numerical Methods for Conservation Laws[M].Basel, Boston, Berlin: Birkhauser-Verlag, 1990.
[19]	Lax P D, Wendroff B. Systems of conservation laws[J].Comm Pure Appl Math, 1960, 13: 217-237. doi: 10.1002/cpa.3160130205
[20]	Hecht J, Alon U, Shvarts D.Potential flow model of Rayleigh-Taylor and Richtmyer-Meshkov bubble fronts[J].Phys Fluids, 1994, 6(12): 4019-4030. doi: 10.1063/1.868391