CFL Conditions for Runge-Kutta discontinuous Galerkin methods on triangular grids

Journal of Computational Physics

Volumn 230, Issue 12, 2011, Pages 4657-4678

  Toulorge, T ^a   Desmet, W ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

CFL condition; Discontinuous Galerkin; Linear stability; Runge Kutta

Indexed keywords

COMPUTATIONAL EFFICIENCY; RUNGE KUTTA METHODS; STABILITY CRITERIA; WAVE PROPAGATION;

ADVECTION EQUATIONS; CFL-CONDITION; DISCONTINUOUS GALERKIN; LINEAR STABILITY; RUNGE-KUTTA DISCONTINUOUS GALERKIN METHODS; RUNGE-KUTTUM; SCALAR ADVECTION; STABILITY CONSTRAINTS; TIME STEP; TRIANGULAR GRID;

GALERKIN METHODS;

EID: 79955674274     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2011.02.040     Document Type: Article

References (24)

1. Cockburn B., Shu C.-W. Runge-Kutta discontinuous Galerkin methods for convection-dominated problems. J. Sci. Comput. 2001, 16:173-261.
2. Hesthaven J.S., Warburton T. Nodal discontinuous Galerkin methods: algorithms, analysis, and applications. Texts in Applied Mathematics 2008, vol. 54. Springer Verlag, New York, USA.
3. Cockburn B., Shu C.-W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework. Math. Comput. 1989, 52:411-435.
4. 1-discontinuous-Galerkin finite element method for scalar conservation laws. RAIRO Modél. Math. Anal. Numér. 1991, 25:337-361.
5. Kubatko E.J., Westerink J.J., Dawson C. Semi discrete discontinuous Galerkin methods and stage-exceeding-order, strong-stability-preserving Runge-Kutta time discretizations. J. Comput. Phys. 2007, 222:832-848.
6. Cockburn B., Hou S., Shu C.-W. The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. iv: the multidimensional case. Math. Comput. 1990, 54:545-581.
7. Kubatko E.J., Dawson C., Westerink J.J. Time step restrictions for Runge-Kutta discontinuous Galerkin methods on triangular grids. J. Comput. Phys. 2008, 227:9697-9710.
8. Atkins H.L., Shu C.-W. Quadrature-free implementation of discontinuous Galerkin method for hyperbolic equations. AIAA J. 1998, 36:775-782.
9. Reddy S.C., Trefethen L.N. Stability of the method of lines. Numer. Math. 1992, 62:235-267.
10. Kreiss H.O., Wu L. On the stability definition of difference approximations for the initial boundary value problem. Appl. Numer. Math. 1993, 12:213-227.
11. C.P.A. Blom, Discontinuous Galerkin Method on Tetrahedral Elements for Aeroacoustics, Ph.D. Thesis, University of Twente, 2003.
12. Engquist B., Osher S. One-sided difference approximations for nonlinear conservation laws. Math. Comput. 1981, 36:321-351.
13. Osher S., Solomon F. Upwind difference schemes for hyperbolic systems of conservation laws. Math. Comput. 1982, 38:339-374.
14. M.H. Carpenter, C.A. Kennedy, Fourth-Order 2N-Storage Runge-Kutta Schemes, Technical Memorandum NASA-TM-109112, NASA Langley Research Center, 1994.
15. Mead J.L., Renaut R.A. Optimal Runge-Kutta methods for first order pseudospectral operators. J. Comput. Phys. 1999, 152:404-419.
16. Allampalli V., Hixon R., Nallasamy M., Sawyer S.D. High-accuracy large-step explicit Runge-Kutta (HALE-RK) schemes for computational aeroacoustics. J. Comput. Phys. 2009, 228:3837-3850.
17. Hu F.Q., Hussaini M.Y., Manthey J.L. Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics. J. Comput. Phys. 1996, 124:177-191.
18. Stanescu D., Habashi W.G. 2N-storage low dissipation and dispersion Runge-Kutta schemes for computational acoustics. J. Comput. Phys. 1998, 143:674-681.
19. Berland J., Bogey C., Bailly C. Low-dissipation and low-dispersion fourth-order Runge-Kutta algorithm. Comput. Fluids 2006, 35:1459-1463.
20. Calvo M., Franco J.M., Rández L. A new minimum storage Runge-Kutta scheme for computational acoustics. J. Comput. Phys. 2004, 201:1-12.
21. Tselios K., Simos T. Optimized Runge-Kutta methods with minimal dispersion and dissipation for problems arising from computational acoustics. Phys. Lett. A 2007, 363:38-47.
22. Gottlieb S., Shu C.-W., Tadmor E. Strong stability-preserving high-order time discretization methods. SIAM Rev. 2001, 43:89-112.
23. Ruuth S.J. Global optimization of explicit strong-stability-preserving Runge-Kutta methods. Math. Comput. 2006, 75:183-207.
24. Jameson A. Solution of the euler equations for two dimensional transonic flow by a multigrid method. Appl. Math. Comput. 1983, 13:327-355.