Dealing With Movings and Collisions of Arbitrary Many Discontinuities in a Conservative Front-Tracking Method

LIU Yan; MAO De-kang

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2006 > 27(8): 954-962

LIU Yan, MAO De-kang. Dealing With Movings and Collisions of Arbitrary Many Discontinuities in a Conservative Front-Tracking Method[J]. Applied Mathematics and Mechanics, 2006, 27(8): 954-962.

Citation:

LIU Yan, MAO De-kang. Dealing With Movings and Collisions of Arbitrary Many Discontinuities in a Conservative Front-Tracking Method[J]. Applied Mathematics and Mechanics, 2006, 27(8): 954-962.

Citation:

LIU Yan, MAO De-kang. Dealing With Movings and Collisions of Arbitrary Many Discontinuities in a Conservative Front-Tracking Method[J]. Applied Mathematics and Mechanics, 2006, 27(8): 954-962.

PDF( 381 KB)

Dealing With Movings and Collisions of Arbitrary Many Discontinuities in a Conservative Front-Tracking Method

LIU Yan¹,
MAO De-kang²

1.
Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing 100088, P. R. China;

Received Date: 2005-09-20
Rev Recd Date: 2006-02-20
Publish Date: 2006-08-15

Abstract

Abstract

An approach to deal with movings and collisions of arbitrary many discontinuities in the conservative front tracking method was developed.Using this approach one may develop an "all-purposed and robust" front-tracking algorithm.The algorithm with this approach may have some inconsistency and thus will have O(1) magnitude errors in some grid cells some time.Nevertheless,these errors will be eliminated by the conservation-preserving property of the front-tracking method in the following computation.Numerical examples were presented to illustrate the efficiency of the approach.
- front-tracking,
- conservation-preserving,
- discontinuity cell

FullText(HTML)

References(12)

References

[1]	Colella P,Woodward P R.The numerical simulation of two-dimensional fluid flow with strong shocks[J].J Comput Phys,1984,54(1):115—173. doi: 10.1016/0021-9991(84)90142-6
[2]	Chern I L,Glimm J,McBryan O,et al.Front tracking for gas dynamics[J].J Comput Phys,1986,62(1):83—110. doi: 10.1016/0021-9991(86)90101-4
[3]	Henshaw W D.A scheme for numerical solution of hyperbolic system of conservation laws[J].J Comput Phys,1987,68(1):25—47. doi: 10.1016/0021-9991(87)90042-8
[4]	LeVeque R J,Shyue K M.One dimensional front tracking based on high resolution wave propogation methods[J].SIAM J Sci Comput,1995,16(2):348—377. doi: 10.1137/0916023
[5]	Swartz B K,Wendroff B.A front tracking code based on Godunov's method[J].Appl Numer Math,1986,2(5):385—397. doi: 10.1016/0168-9274(86)90041-3
[6]	MAO De-kang.Towards front tracking based on conservation in two space dimension[J].SIAM J Sci Comput,2000,22(1):113—151. doi: 10.1137/S1064827597310609
[7]	MAO De-kang.A shock tracking technique based on conservation in one space dimension[J].SIAM J Numer Anal,1995,32(5):1677—1703. doi: 10.1137/0732075
[8]	刘妍，茅德康.一种守恒型间断跟踪法中对于间断及其相互作用的处理[J].计算物理，2005,22(6):520—526.
[9]	刘妍，茅德康.一种强健的守恒型间断跟踪法在一维Euler方程组中的实现[J].计算物理，2004,21(3):312—318.
[10]	LeVeque R J.Finite Volume Methods for Hyperbolic Problems[M].the Pitt Building,Trumpington Street,Cambridge, United Kingdom:the Press Syndicate of the University of Cambridge,2002.
[11]	SHU Chi-wang,Osher S.Efficient implementation of essentially non-oscillatory shock-capturing schemes Ⅱ[J].J Comput Phys,1989,83(1):32—78. doi: 10.1016/0021-9991(89)90222-2
[12]	Harten A,Engquist B,Osher S,et al.Uniformly high order accurate essentially non-oscillatory scheme Ⅲ[J].J Comput Phys,1987,71(2):231—303. doi: 10.1016/0021-9991(87)90031-3