Conservative multi-implicit spectral deferred correction methods for reacting gas dynamics

Journal of Computational Physics

Volumn 194, Issue 2, 2004, Pages 697-715

  Layton, Anita T ^a   Minion, Michael L ^a  

^a University of North Carolina at Chapel Hill   (United States)

Author keywords

Conservative methods; Operator splitting; Reactive flows; Semi implicit methods; Spectral defered correction methods

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DIFFERENCE EQUATIONS; GAS DYNAMICS;

CONSERVATIVE METHOD; CORRECTION METHOD; DEFERRED CORRECTION; MODELING EQUATIONS; OPERATOR-SPLITTING; REACTING GAS; REACTIVE FLOW; SEMI-IMPLICIT METHODS; SPECTRAL DEFERED CORRECTION METHOD; TIME-SCALES;

TIME MEASUREMENT;

EID: 1442282983     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2003.09.010     Document Type: Article

References (28)

1. S. Abarbanel, D. Gottlieb, M.H. Carpenter, On the removal of boundary errors caused by Runge-Kutta integration of nonlinear partial differential equations, SIAM J. Sci. Comput. 17 (1996) 777-782.
2. U.M. Ascher, L.R. Petzold, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, SIAM, Philadelphia, PA, 2000.
3. W. Bao, S. Jin, The random projection method for stiff multispecies detonation capturing, J. Comput. Phys. 178 (2002) 37-57.
4. A. Bourlioux, A.T. Layton, M.L. Minion, High-order multi-implicit spectral deferred correction methods for problems of reactive flow, J. Comput. Phys. 189 (2) (2003) 651-675.
5. M.H. Carpenter, D. Gottlieb, S. Abarbanel, W.-S. Don, The theoretical accuracy of Runge-Kutta time discretization for the initial boundary value problem: a study of the boundary error, SIAM J. Sci. Comput. 16 (1995) 1241-1252.
6. P. Colella, Multidimensional upwind methods for hyperbolic conservation laws, J. Comput. Phys. 87 (1990) 171-200.
7. P. Colella, A. Majda, V. Roytburd, Theoretical and numerical structure for reacting shock waves, SIAM J. Sci. Stat. Comput. 7 (4) (1986) 1059-1080.
8. P. Colella, P.R. Woodward, The piecewise parabolic method (PPM) for gas-dynamical simulations, J. Comput. Phys. 54 (1984) 174-201.
9. C.F. Curtiss, J.O. Hirschfelder, Integration of stiff equations, Proc. Natl. Acad. Sci. 38 (1952) 235.
10. A. Dutt, L. Greengard, V. Rokhlin, Spectral deferred correction methods for ordinary differential equations, BIT 40 (2) (2000) 241-266.
11. S.K. Godunov, A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics, Mat. Sbornik 47 (1959) 271-306.
12. E. Hairer, G. Wanner, Solving Ordinary Differential Equations II, Stiff and Differential-Algebraic Problems, Springer, Berlin, 1996.
13. F.K. Hebeker, R. Rannacher, An adaptive finite element method for unsteady convection-dominated flows with stiff source terms, SIAM J. Sci. Comput. 21 (3) (1999) 799-818.
14. C. Helzel, R.J. LeVeque, G. Warnecke, A modified fractional step method for the accurate approximation of detonation waves, SIAM J. Sci. Comput. 22 (4) (2000) 1489-1510.
15. R.J. Kee, F.M. Rupley, E. Meeks, J.A. Miller, CHEMKIN-III: A FORTRAN chemical kinetics for the analysis of gas-phase chemical and plasma kinetics, Sandia National Laboratories, Technical report SAND96-8216, 1996.
16. C.A. Kennedy, M.H. Carpenter, Additive Runge-Kutta schemes for convection-diffusion-reaction equations, Appl. Numer. Math. 44 (1-2) (2002) 139-181.
17. R. Klein, Semi-implicit extension of a Godunov-type scheme based on low Mach number asymptotics I: one-dimensional flow, J. Comput. Phys. 121 (1995) 213-237.
18. D. Lanser, J.G. Verwer, Analysis of operator splitting for advection-diffusion-reaction problems from air pollution modelling, J. Comput. Appl. Math. 111 (1-2) (1999) 201-216.
19. R.J. LeVeque, K.-M. Shyue, One-dimensional front tracking based on high resolution wave propagation methods, SIAM J. Sci. Comput. 16 (2) (1995) 348-377.
20. R.J. LeVeque, K.-M. Shyue, Two-dimensional front tracking based on high resolution wave propagation methods, J. Comput. Phys. 123 (1996) 354-368.
21. R. Liska, B. Wendroff, Comparison of several difference schemes on 1D and 2D test problems for the Euler equations, Technical Report LA-UR-01-6225, LANL, Los Alamos, 2001.
22. M.L. Minion, Semi-implicit spectral deferred correction methods for ordinary differential equations, Commun. Math. Sci. 1 (3) (2003) 471-500.
23. S. Osher, S. Chakravarthy, High resolution schemes and the entropy condition, SIAM J. Numer. Anal. 21 (1984) 984-995.
24. R.D. Richtmyer, K.W. Morton, Difference methods for initial value problems, second ed., Wiley Interscience, New York, 1967.
25. C.-W. Shu, S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes, J. Comput. Phys. 77 (1988) 439-469.
26. C.-W. Shu, S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes, II, J. Comput. Phys. 83 (1989) 32-78.
27. G. Strang, On the construction and comparison of difference schemes, SIAM J. Numer. Anal. 8 (3) (1968) 506-517.
28. N.N. Yanenko, The Method of Fractional Steps, Springer, New York, 1971.