Generalized Riemann Problem for Gas Dynamic Combustion

LIU Yu-jin; SHENG Wan-cheng

doi:10.3879/j.issn.1000-0887.2011.08.011

Volume 32 Issue 8

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LIU Yu-jin, SHENG Wan-cheng. Generalized Riemann Problem for Gas Dynamic Combustion[J]. Applied Mathematics and Mechanics, 2011, 32(8): 1011-1020. doi: 10.3879/j.issn.1000-0887.2011.08.011

Citation:

LIU Yu-jin, SHENG Wan-cheng. Generalized Riemann Problem for Gas Dynamic Combustion[J]. Applied Mathematics and Mechanics, 2011, 32(8): 1011-1020. doi: 10.3879/j.issn.1000-0887.2011.08.011

Citation:

LIU Yu-jin, SHENG Wan-cheng. Generalized Riemann Problem for Gas Dynamic Combustion[J]. Applied Mathematics and Mechanics, 2011, 32(8): 1011-1020. doi: 10.3879/j.issn.1000-0887.2011.08.011

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Generalized Riemann Problem for Gas Dynamic Combustion

doi: 10.3879/j.issn.1000-0887.2011.08.011

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

Received Date: 2010-11-12
Rev Recd Date: 2011-06-14
Publish Date: 2011-08-15

Abstract

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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References(19)

References

[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