Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations part IV. Stability vs. methods of discretizing nonlinear source terms in reaction-convection equations

International Journal of Computational Fluid Dynamics

Volumn 6, Issue 2, 1996, Pages 89-123

  Lafon, A ^a   Yee, H C ^b  

^a DRET/SDR   (France)

^b NASA AMES RESEARCH CENTER   (United States)

Author keywords

Finite difference methods; Global asymptotic behavior; Reaction convection equation; Spurious asymptotes; Spurious numerical solutions; Spurious steady state numerical solutions; Stability

Indexed keywords

EID: 3142624971     PISSN: 10618562     EISSN: None     Source Type: Journal    
DOI: 10.1080/10618569608940776     Document Type: Article

References (21)

1. Colella, P., Majda, A. and Roytburd, V. (1986) Theoretical and Numerical Structure for Reacting Shock Waves, SIAM J. Sci. Stat. Comput., 7, 1059-1080.
2. Engquist, B. and Sjogreen, B. (1991) Robust Difference Approximations of Stiff Inviscid Detonation Waves, CAM Report 91-03, UCLA.
3. Fatemi, E. A. (1990) A New Splitting Method for Scaler Conservation Laws with Stiff Source Terms, IMA Preprint Series No. 755.
4. Gear, C. W. (1971) Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall.
5. Greenberg, J. B. (1988) Self-Regulating Finite-Difference Methods for the Computation of Reacting Flows with Nonlinear Kinetics, J. Scientific Computing, 3, 165-187.
6. Griffiths, D. F., Sturat, A. M. and Yee, H. C. (1992) Numerical Wave Propagation in Hyperbolic Problems with Nonlinear Source Terms, SIAM J. of Numer. Analysis.
7. Hale, J. and Kocak, H. (1991) Dynamics and Bifurcations, Springer-Verlag, New York.
8. Iserles, A. (1988) Stability and Dynamics of Numerical Methods for Nonlinear Ordinary differential Equations, DAMTP NA1, University of Cambridge, Cambridge England.
9. Lafon, A. and Yee, H. C. (1991) Dynamical Approach Study of Spurious Steady-State Numerical Solutions for Nonlinear Differential Equations, Part III: The Effects of Nonlinear Source Terms in Reaction-Convection Equations. NASA Technical Memorandum 103877, to appear, Intern. J. of CFD.
10. LeVeque, R. J. and Yee, H. C. (1990) A Study of Numerical Methods for Hyperbolic Conservation Laws with Stiff Source Terms, J. Comput. Phys., 86, 187-210.
11. Roe, P. L. and Arora, M. (1991) Design of Algorithms for a Dispersive Hyperbolic Problem, AIAA-91-1535, Proceedings of the AIAA 10th Computational Fluid Dynamics Conference, Honolulu, Hawaii.
12. Stewart, I. (1990) Bifurcation Theory Old and New, Proceedings of the IMA Conference on Dynamics of Numerics and Numerics of Dynamics, Bristol, England.
13. Sweby, P. K. (1988) TVD Schemes for Inhomogeneous Conservation Laws, Proceedings of the Second International Conference on Nonlinear Hyperbolic Problems, Aachen, Germany, ed. J. Ballman & R. Jeltsch, Vieweg, 599-607.
14. Sweby, P. K. (1989) Source Terms and Conservation Laws: A Preliminary Discussion, University of Reading, Department of Mathematics, Numerical Analysis Report 6/89.
15. Sweby, P. K. and Yee, H. C. (1994) On the Dynamics of Some Grid Adaptation Schemes, Proceedings of the 4th International Conference on Numerical Grid Generation in CFD and Related Fields, University College of Swansea, UK, also RIACS Technical Report 94.02, Feb. 1994.
16. Yee, H. C. (1989) A Class of High-Resolution Explicit and Implicit Shock-Capturing Methods, VKI Lecture Series 1989-04 March 6-10, 1989, also NASA TM-101088.
17. Yee, H. C. (1991) A Nonlinear Dynamical Approach to Algorithm Development in Hypersonic CFD, Proceedings of the 4th International Symposium on Computational Fluid Dynamics, Davis, Calif.
18. Yee, H. C., Sweby, P. K. and Griffiths, D. F. (1991) Dynamical Approach Study of Spurious Steady-State Numerical Solutions for Nonlinear Differential Equations, Part I: The dynamics of Time Discretiza- tions and Its Implications for Algorithm Development in Computational Fluid Dynamics, NASA TM-102820, April 1990, also J. Comput. Phys., 97, 249-310.
19. Yee, H. C., Sweby, P. K. and Lafon, A. (1992) Basins of Attraction and the Time-Dependent Approach to Obtaining Steady-State Numerical Solutions, Proceedings of the ICFD Conference of Numerical Methods for Fluid Dynamics, Reading, England.
20. Yee, H. C. and Sweby, P. K. (1992) Dynamical Approach Study of Spurious Steady-State Numerical Solutions for Nonlinear Differential Equations. Part II: Global Asymptotic Behavior of Time Discretizations, RNR-92-008, NASA Ames Research Center; to appear, Intern. J. of CFD, 1994.
21. Yee, H. C. and Sweby, P. K. (1993) Global Asymptotic Behavior of Iterative Implicit Schemes, RIACS Technical Report 93.11, NASA Ames Research Center, to appear, Intern. J. Bifurcation & Chaos, 1994.