Low-storage semi-implicit Runge-Kutta methods for reactive flow computations

36th AIAA Aerospace Sciences Meeting and Exhibit

Volumn , Issue , 1998, Pages

  Yob, Jack Jai Ick ^a   Zhong, Xiaolin ^a,b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b Mechanical and Aerospace Engineering Department   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AEROSPACE ENGINEERING; BOUNDARY LAYERS; DIFFERENTIAL EQUATIONS; DIRECT NUMERICAL SIMULATION; DISCRETE EVENT SIMULATION; HYPERSONIC BOUNDARY LAYERS; HYPERSONIC FLOW; LAMINAR BOUNDARY LAYER; NAVIER STOKES EQUATIONS; NUMERICAL METHODS; NUMERICAL MODELS;

EFFICIENT COMPUTATION; EXPLICIT METHOD; HIGH-ORDER ACCURACY; IMPLICIT METHODS; LAMINAR TURBULENT TRANSITIONS; REACTIVE SOURCES; TEMPORAL DISCRETIZATION METHODS; THERMO CHEMICAL PROCESS;

RUNGE KUTTA METHODS;

EID: 84983189321     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (27)

1. Zhong, X., "Direct Numerical Simulation of Hypersonic Boundary Layer Transition Over Blunt Leading Edges, Part I: A New Numerical Method and Validation," AIAA Paper 97-0755, 1997.
2. Zhong, X., "Direct Numerical Simulation of Hypersonic Boundary Layer Transition Over Blunt Leading Edges, Part II: Receptivity to Sound," AIAA Paper 97-0756, 1997.
3. Zhong, X., "Additive Semi-implicit Runge-Kutta Methods for Computing High-Speed Nonequilibrium Reactive Flows," Journal of Computational Physics, Vol. 128, 1996, pp. 19-31.
4. Shen, J.-W., and Zhong, X., "Semi-Implicit Runge-Kutta Schemes for Non-Autonomous Differential Equations in Reactive Flow Computations," AIAA Paper 96-1969, 1996.
5. Canuto, C., Hussaini, M. Y., Quarteroni, A., and Zang, T. A., Spectral Methods in Fluid Dynamics, Springer-Verlag, New York/Berlin, 1988.
6. Moin, P., and Kim, J., "On the Numerical Solution of Time-dependent Viscous Incompressible Fluid Flows Involving Solid Boundaries," Journal of Computational Physics, Vol. 35, 1980, pp. 381-392.
7. Hairer, E., and Wanner, G., Solving Ordinary Differential Equations II, Springer-Verlag, Berlin Heidelberg, 1991.
8. Hairer, E., Norsett, S. P., and Wanner, G., Solving Ordinary Differential Equations I, Springer-Verlag, Berlin Heidelberg, 1993.
9. Yee, H. C., and Shin, J. L., "Semi-Implicit and Fully Implicit Shock-Capturing Methods for Nonequilibrium Flows," AIAA Journal, Vol. 27, 1989, pp. 299-307.
10. LeVeque, R. J., and Yee, H. C., "A Study of Numerical Methods for Hyperbolic Conservation Laws with Stiff Source Terms," Journal of Computational Physics, Vol. 86, 1990, pp. 187-210.
11. Yanenko, N. N., The Method of Fractional Steps, Springer-Verlag, 1971.
12. Oran, E. S., and Boris, J. P., Numerical Simulation of Reactive Flow, Elsevier Science Publishing, New York, 1987.
13. Strang, G., "On the Construction and Comparison of Difference Schemes," SIAM J. Numer. Anal., Vol. 5, 1968, pp. 506-517.
14. Jin, S., "Runge-Kutta Methods for Hyperbolic Conservation Laws with Stiff Relaxation Terms," Journal of Computational Physics, Vol. 122, 1995, pp. 51-67.
15. Yoh, J. J., and Zhong, X., "Semi-Implicit Runge-Kutta Schemes for Stiff Multi-Dimensional Reacting Flows," AIAA Paper 97-0803, 1997.
16. Yoh, J. J., and Zhong, X., "Low-Storage Semi-Implicit Runge-Kutta Schemes for Transient Reacting Flow Simulations," submitted to the Journal of Computational Physics, 1997.
17. Williamson, J. H., "Low-Storage Runge-Kutta Schemes," Journal of Computational Physics, Vol. 35, 1995, pp. 48-56.
18. Engquist, B. E., and Sjögreen, B., "Robust Difference Approximations of Stiff Inviscid Detonation Waves," UCLA CAM Report 91-03, 1991.
19. Wray, A. A., "Very Low Storage Time-Advancement Schemes," NASA Internal Report Moffet Field, CA, 1986.
20. Dekker, K., and Verwer, J. G., Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations, Elsevier Science Publishers B. V., Amsterdam Netherlands, 1984.
21. Lambert, J. D., Numerical Methods for Ordinary Differential Systems, Wiley, New York, 1991.
22. Lambert, J. D., Computational Methods in Ordinary Differential Equations, Wiley, New York, 1973.
23. Butcher, J. C., Numerical Analysis of Ordinary Differential Equations, Wiley, New York, 1987.
24. Butcher, J. C., and Wanner, G., "Runge-Kutta Methods: Some Historical Notes," Applied Numerical Mathematics, Vol. 22, 1996, pp. 113-151.
25. Chen, G.-Q., Levermore, C. D., and Liu, T.-P., "Hyperbolic Conservation Laws with Stiff Relaxation Terms and Entropy," Comm. Pure Appl. Math., Vol. 47, 1994, p. 787.
26. Jin, S., and Levermore, C. D., "Numerical Schemes for Hyperbolic Conservation Laws with Stiff Relaxation Terms," Journal of Computational Physics, Vol. 126, 1996, pp. 449-467.
27. Sjögreen, B., "Numerical Computation of Three Dimensional Detonation Waves on Parallel Computers," Uppsala University Report 162-1994, 1994.