Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Finite difference method for a combustion model


Author: Lung-An Ying
Journal: Math. Comp. 73 (2004), 595-611
MSC (2000): Primary 65M06, 35L65, 76M20, 80A25
DOI: https://doi.org/10.1090/S0025-5718-03-01601-6
Published electronically: October 27, 2003
MathSciNet review: 2031396
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We study a projection and upwind finite difference scheme for a combustion model problem. Convergence to weak solutions is proved under the Courant-Friedrichs-Lewy condition. More assumptions are given on the ignition temperature; then convergence to strong detonation wave solutions or to weak detonation wave solutions is proved.


References [Enhancements On Off] (What's this?)

  • 1. W. Bao and S. Jin, The random projection method for hyperbolic conservation laws with stiff reaction terms, J. Comput. Phys., 163, 216-248, 2000. MR 2001d:76091
  • 2. A. C. Berkenbosch, E. F. Kaasschieter and R. Klein, Detonation capturing for stiff combustion chemistry, Combust. Theory Modelling, 2, 313-348, 1998. MR 2000b:80008
  • 3. R. Courant and K. O. Friedrichs, Supersonic Flow and Shock Waves, Interscience Publishers Inc. New York, 1948. MR 10:637c
  • 4. M. G. Crandall and A. Majda, Monotone difference approximations for scalar conservation laws, Math. Comp., 34, 1-21, 1980. MR 81b:65079
  • 5. P. Colella, A. Majda and V. Roytburd, Theoretical and numerical structure for reacting shock waves, SIAM J. Sci. Stat. Comput., 7, 1059-1080, 1986. MR 87i:76037
  • 6. C. Dafermos, Generalized charateristics and the structure of solutions of hyperbolic conservation laws, Indiana Univ. Math. J., 26, 1097-1119, 1977. MR 56:16151
  • 7. R. J. DiPerna, Convergence of approximate solutions to conservation laws, Arch. Rat. Mech. Anal., 82, 27-70, 1983. MR 84k:35091
  • 8. B. Engquist and B. Sjogreen, Robust Difference Approximations of Stiff Inviscid Detonation Waves, CAM Report 91-03 (UCLA 1991).
  • 9. L. C. Evans, Weak Convergence Methods for Nonlinear Partial Differential Equations, CBMS Regional Conference Series in Mathematics, 74, American Mathematical Society, 1988. MR 91a:35009
  • 10. D. F. Griffiths, A. M. Stuart and H. C. Yee, Numerical wave propagation in an advection equation with a nonlinear source term, SIAM J. Numer. Anal., 29, 1244-1260, 1992. MR 93h:65111
  • 11. R. J. LeVeque and H. C. Yee, A study of numerical methods for hyperbolic conservation laws with stiff source terms, J. Comput. Phys., 86, 187-210, 1990. MR 90k:76009
  • 12. A. Majda, A qualitative model for dynamic combustion, SIAM J. Appl. Math., 41, 70-93, 1981. MR 82j:35096
  • 13. R. B. Pember, Numerical methods for hyperbolic conservation laws with stiff relaxation, I: Spurious solutions, SIAM J. Appl. Math., 53, 1293-1330, 1993. MR 95a:65173
  • 14. L.-a. Ying and Z.-h. Teng, A hyperbolic model of combustion, North Holland Mathematics Studies, 81, North-Holland, Amsterdam, and Kinokuniya, Tokyo, 409-434, 1983. MR 86a:35092

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 65M06, 35L65, 76M20, 80A25

Retrieve articles in all journals with MSC (2000): 65M06, 35L65, 76M20, 80A25


Additional Information

Lung-An Ying
Affiliation: School of Mathematical Sciences, Peking University, People’s Republic of China

DOI: https://doi.org/10.1090/S0025-5718-03-01601-6
Keywords: Combustion, finite difference method, detonation wave, stiff equation
Received by editor(s): November 12, 2001
Received by editor(s) in revised form: October 22, 2002
Published electronically: October 27, 2003
Article copyright: © Copyright 2003 American Mathematical Society

American Mathematical Society