Semi-implicit Runge-Kutta schemes for non-autonomous differential equations in reactive flow computations

1996 Fluid Dynamics Conference

Volumn , Issue , 1996, Pages 1-12

  Wei Shen, Jian ^a   Zhong, Xiaolin ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY LAYERS; DELAY CONTROL SYSTEMS; DIFFERENTIAL EQUATIONS; FLUID DYNAMICS; HYPERSONIC FLOW; NUMERICAL METHODS; ORDINARY DIFFERENTIAL EQUATIONS;

AUTONOMOUS DIFFERENTIAL EQUATION; EXPLICIT RUNGE-KUTTA METHODS; IMPLICIT RUNGE-KUTTA METHOD; NON-AUTONOMOUS SYSTEM; NONAUTONOMOUS DIFFERENTIAL EQUATION; RUNGE-KUTTA SCHEMES; THERMO CHEMICAL PROCESS; THIRD ORDER ACCURACY;

RUNGE KUTTA METHODS;

EID: 84959232904     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (19)

1. C.-H. Chiu and X. Zhong. Numerical Simulation of Transient Hypersonic Flow Using the Essentialy Nonoscillatory Schemes. AIAA Journal, Vol. 34, No. 4, pp. 655-661, 1995. (Also AIAA paper 95-0469, 1995).
2. X. Zhong, X. Joubert, and T. K. Lee. The interaction of freestream disturbances and the bow shock in hypersonic flow past a cylinder. 1995. Presented in 20th International Symp. on Shock Waves, July 23-28, 1995, Pasadena, California.
3. P. Moin and J. Kim. On the numerical solution of the time-dependent viscous incompressible fluid flows involving solid boundaries. J. of Computational Physics, 35:381-392, 1980.
4. Thomas A. Zang and M. Y. Hussaini. Numerical experiments on subcritical transition mechanisms. AIAA Paper 81-1227, 1981.
5. R. S. Rogallo and P. Moin. Numerical simulation of turbulent flows. Ann. Rev. Fluid Mech., 16:99-137, 1984.
6. C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang. Spectral Methods in Fluid Dynamics. Springer-Verlag, 1988.
7. L. Kleiser and T. A. Zang. Numerical Simulation of Transition in Wall-Bounded Shear Flows. Ann. Rev. Fluid Mech., Vol. 23, pp. 495-535, 1991.
8. T. R. A. Bussing and E. M. Murman. A finite volume method for the calculation of compressible chemically reacting flows.47/1.4 Paper 85-0296, 1985.
9. J. P. Drummond, R. C. Rogers, and M. Y. Hussaini. Spectral methods for modeling supersonic chemically reacting flow fields. AIAA Paper 85- 0302, 1985.
10. H. C. Yee and J. L. Shinn. Semi-implicit and fully implicit shock capturing methods for hypersonic conservation laws with stiff source terms. AIAA Paper 87-1116, 1987.
11. R. J. Leveque and H. C. Yee. A study of numerical methods for hyperbolic conservation laws with stiff source terms. J. of Computational Physics, 86:187-210, 1990.
12. G. J. Cooper and A. Sayfy. Additive methods for numerical solutions of ordinary differential equations. Mathematics of Computation, 35(152):1159-1172, October 1980.
13. G. J. Cooper and A. Sayfy. Additive rungekutta methods for stiff ordinary differential equations. Mathematics of Computation, 40(161):207-218, January 1983.
14. X. Zhong. Semi-Implicit Runge-Kutta Schemes for Direct Numerical Simulation of Transient High- Speed Reactive Flows. To appear in the Journal of Computational Physics, 1996.
15. X. Zhong. New High-Order Semi-implicit Runge- Kutta Schemes for Computing Transient Nonequilibrium Hypersonic Flow. AIAA Paper 95-2007, 1995.
16. H. H. Rosenbrock. Some general implicit processes for the numerical solution of differential equations. Comput. J., 5:329, 1963.
17. J. D. Lambert. Computational Methods in Ordinary Differential Equations. John Wiley & Sons, 1973.
18. J. C. Butcher. Implicit Runge-Kutta processes. Math. Comp., 18:50-64, 1964.
19. E. Hairer, G. Bader, and CH. Lubich. On the stability of semi-implicit methods for ordinary differential equations. BIT, 22:211-232, 1982.