Concepts and Application of Time-Limiters to High Resolution Schemes

Journal of Scientific Computing

Volumn 19, Issue 1-3, 2003, Pages 139-162

  Duraisamy, Karthikeyan ^a   Baeder, James D ^a   Liu, Jian Guo ^b  

^a UNIVERSITY OF MARYLAND   (United States)

^b University of Maryland   (United States)

Author keywords

High resolution schemes; Non linear time integration; Time limiting

Indexed keywords

HIGH RESOLUTION SCHEMES; NON-LINEAR TIME INTEGRATION; TIME-LIMITING;

FINITE DIFFERENCE METHOD; FUNCTIONS; INTEGRATION; INTERPOLATION; NUMERICAL METHODS; PROBLEM SOLVING;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 0346640292     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1025395707090     Document Type: Article

References (15)

1. Gottlieb, S., and Shu, C.-W. (1998). Total variation diminishing Runge-Kutta schemes. Math. Comp. 67, 73-85.
2. Gottlieb, S., Shu, C.-W., and Tadmor, E. (2001). Strong stability preserving high order time discretization methods. SIAM Rev. 43, 89-112.
3. Hairer, E., and Wanner, G. (1991). Solving Ordinary Differential Equations, Vol. 2, Springer-Verlag.
4. Harten, A. (1983). High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49, 357-393.
5. Harten, A., and Osher, S. (1987). Uniformly high order accurate non-oscillatory schemes 1. SIAM J. Numer. Anal. 24.
6. Harten, A., Hyman, J., and Lax, P. (1976). On finite difference approximations and entropy conditions for shocks. Comm. Pure Appl. Math. 29, 297-322.
7. Hyunh, H. (1993). Accurate monotone cubic interpolation. SIAM J. Numer. Anal. 30, 57-100.
8. Laney, C. B. (1998). Computational Gasdynamics, Cambridge University Press.
9. Pulliam, T. (1993). Time Accuracy and the Use of Implicit Methods, AIAA Paper 93-3360.
10. Roe, P. (1985). Some contributions to the modelling of discontinuous flows. Lectures Appl. Math. 22, 163-193.
11. Shu, C.-W. (1998). Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws in advanced numerical approximation of nonlinear hyperbolic equations. In Cockburn, B., Johnson, C., Shu, C.-W., and Tadmor, E. (eds.), Lecture Notes in Mathematics, Vol. 1697, Springer, pp. 325-432.
12. Suresh, A., and Huynh, H. (1997). Accurate monotonicity-preserving schemes with Runge-Kutta time stepping. J. Comput. Phys. 136.
13. Van Leer, B. (1979). Towards the ultimate conservative difference scheme v. a second order sequel to Godunov's method. J. Comput. Phys. 32, 101-136.
14. Wada, W., and Liou, M.-S. (1997). An accurate and robust flux splitting scheme for shock and contact discontinuities. SIAM J. Sci. Comput. 18, 633-657.
15. Yoon, S., and Jameson, A. (1988). Lower-upper symmetric Gauss-Seidel method for the Euler and Navier-Stokes equations. AIAA J. 26, 1025-1026.