气体动力学燃烧模型的广义Riemann问题

刘玉锦; 盛万成

doi:10.3879/j.issn.1000-0887.2011.08.011

气体动力学燃烧模型的广义Riemann问题

doi: 10.3879/j.issn.1000-0887.2011.08.011

刘玉锦^1,2,
盛万成¹

1.
上海大学数学系,上海 200444;
山东理工大学理学院,山东淄博 255049

基金项目: 国家自然科学基金资助项目(10971130);上海市教委重点学科资助项目(J50101),上海市教委创新基金重点资助项目(11ZZ84)

详细信息

作者简介:
刘玉锦(1979- ),女,山东淄博人,博士生(E-mail:yjliu@shu.edu.cn);盛万成(1963- ),男,新疆人,教授(联系人.Tel:+86-21-66132526;E-mail:mathwcsheng @shu.edu.cn).

中图分类号: O175.27; O175.29; O354.5
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- 被引次数: 0
出版历程
- 收稿日期: 2010-11-12
- 修回日期: 2011-06-14
- 刊出日期: 2011-08-15

Generalized Riemann Problem for Gas Dynamic Combustion

LIU Yu-jin^1,2,
SHENG Wan-cheng¹

1.
Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China;
School of Science, Shandong University of Technology, Zibo, Shandong 255049, P. R. China

摘要

摘要: 考察了在(x,t)平面上原点(t＞0)的邻域内气体动力学燃烧模型的广义Riemann问题．在改进的熵条件下构造了此问题的唯一解．它们是自相似ZND燃烧模型的极限．发现对某些情形,广义Riemann问题的解与相应的Riemann问题的解有本质的不同．特别地,扰动会使得相应Riemann问题的强爆轰波转化为由预压激波点燃的弱爆燃波．在一些情形，尽管相应的Riemann解中不含燃烧波,扰动后燃烧波会出现．这反映了未燃气体的不稳定性．
- 广义Riemann问题 /
- 熵条件 /
- 爆轰波 /
- 爆燃波
Abstract: The generalized Riemann problem for gas dynamic combustion in a neighborhood of the origin(t＞0)in the(x,t)plane was considered.Under the modified entropy conditions, the solutions were constructed uniquely,which were the limits of the selfsimilar ZND combustion model.It was found that,for some cases,there were intrinsical differences between the structures of the perturbed Riemann solutions and the corresponding Riemann solutions.Especially,a strong detonation in the correspo nding Riemann solution may betransformed into a weak deflagration coalescing with pre-compression shock wave after perturbation.And in some cases,although there is no combustion wave of the corresponding Riemann solution,it may occur after perturbation,which shows the instability of unburnt gases.
- generalized Riemann problem /
- entropy conditions /
- detonation wave /
- deflagration wave

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参考文献(19)

[1]	Courant R, Friedrichs K O. Supersonic Flow and Shock Waves[M]. New York: Interscience, 1948.
[2]	Williams F A. Combustion Theory[M]. Menlo Park: Benjamin Commings, 1985.
[3]	Chorin A J. Random choice methods with application to reacting gas flow[J]. J Comp Phys, 1977, 25(3): 253-272. doi: 10.1016/0021-9991(77)90101-2
[4]	Teng Z H, Chorin A J, Liu T P. Riemann problems for reacting gas with application to transition[J]. SIAM J Appl Math, 1982, 42(5): 964-981. doi: 10.1137/0142069
[5]	Zhang T, Zheng Y X. Riemann problem for gasdynamic combustion[J]. J Differential Equations, 1989, 77(2): 203-230. doi: 10.1016/0022-0396(89)90142-3
[6]	Li T T, Yu W C. Boundary Value Problem for Quasilinear Hyperbolic Systems[M]. Duke University Mathematics Series V, 1985.
[7]	Bourgeade A, Le Floch Ph, Raviart P A. Approximate solution of the generalized Riemann problem and application[C]Carasso C, Raviart P A, Serre D.Nonlinear Hyperbolic Problems Proccedings St. Etienne. Lecture Notes in Mathematics 1270, Springer-Verlag, 1986: 1-9.
[8]	Le Floch Ph, Raviart P A. An asymtotic expansion for the solution of the generalized Riemann problem—part 1: general theory[J].Ann Inst H Poincaré, Nonlinear Analysis, 1988, 5(2):179-207.
[9]	Ben-Artzi M. The generalized Riemann problem for reactive flows[J]. Journal of Computational Physics, 1989, 81(1):70-101. doi: 10.1016/0021-9991(89)90065-X
[10]	Bourgeade A, Le Floch Ph, Raviart P A. An asymptotic expansion for the solution of the generalized Riemann problem—part 2: application to the equation of gas dynamics[J]. Ann Inst H Poincaré, Nonlinear Analysis, 1989, 6(6): 437-480.
[11]	Chang T, Hsiao L. The Riemann Problem and Interaction of Waves in Gas Dynamics[M]. Pitman Monographs, No. 41, Longman Scientific and Technical, Essex, 1989.
[12]	Li T T. Global Classical Solutions for Quasilinear Hyperbolic System[M]. New York: John Wiley and Sons, 1994.
[13]	Godlewski E, Raviart P-A. Numerical Approximation of Hyperbolic Systems of Conservation Laws[M]. Appl Math Science 118, New York: Springer, 1996.
[14]	Sheng W C, Sun M N, Zhang T. The generalized Riemann problem for a scalar nonconvex Chapman-Jouguet combustion model[J]. SIAM J Appl Math, 2007, 68(2): 544-561. doi: 10.1137/060672650
[15]	Sun M N, Sheng W C. The generalized Riemann problem for a scalar Chapman-Jouguet combustion model[J]. Z Angew Math Phys, 2009, 60(2): 271-283. doi: 10.1007/s00033-007-6130-y
[16]	Sheng W C, Zhang T. Structural stability of solutions to the Riemann problem for a scalar nonconvex CJ combustion model[J]. Discrete Contin Dyn Syst, 2009, 25(2): 651-667. doi: 10.3934/dcds.2009.25.651
[17]	Bao W, Jin S. The random projection method for hyperbolic conservation laws with stiff reaction terms[J]. J Comput Phys, 2000, 163(1):216-248. doi: 10.1006/jcph.2000.6572
[18]	Tan D C, Zhang T. Riemann problem for the selfsimilar ZND-model in gas dynamical combustion[J]. J Differential Equations, 1992, 95(2): 331-369. doi: 10.1016/0022-0396(92)90035-L
[19]	Hsu C H, Lin S S. Some qualitative properties of the Riemann problem in gas dynamical combustion[J]. J Differential Equations, 1997, 140(1): 10-43. doi: 10.1006/jdeq.1997.3304