A comparison of troubled-cell indicators for Runge-Kutta discontinuous Galerkin methods using weighted essentially nonoscillatory limiters

SIAM Journal on Scientific Computing

Volumn 27, Issue 3, 2006, Pages 995-1013

  Qiu, Jianxian ^a,b   Shu, Chi Wang ^c  

^a NANJING UNIVERSITY   (China)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^c BROWN UNIVERSITY   (United States)

Author keywords

High order accuracy; Limiters; Runge Kutta discontinuous Galerkin method; Weighted essentially nonoscillatory finite volume scheme

Indexed keywords

COSTS; PARAMETER ESTIMATION; PROBLEM SOLVING; RUNGE KUTTA METHODS;

HIGH-ORDER ACCURACY; RUNGE-KUTTA DISCONTINUOUS GALERKIN METHOD; WEIGHTED ESSENTIALLY NONOSCILLATORY FINITE VOLUME SCHEME;

NUMERICAL METHODS;

EID: 33646565327     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/04061372X     Document Type: Article

References (24)

1. R. BISWAS, K.D. DEVINE, AND J. FLAHERTY, Parallel, adaptive finite element methods for conservation laws, Appl. Numer. Math., 14 (1994), pp. 255-283.
2. A. BURBEAU, P. SAGAUT, AND C.H. BRUNEAU, A problem-independent limiter for high-order Runge-Kutta discontinuous Galerkin methods, J. Comput. Phys., 169 (2001), pp. 111-150.
3. B. COCKBURN, S. HOU, AND C.-W. SHU, The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: The multidimensional case, Math. Comp., 54 (1990), pp. 545-581.
4. B. COCKBURN, S.-Y. LIN, AND C.-W. SHU, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One dimensional systems, J. Comput. Phys., 84 (1989), pp. 90-113.
5. B. COCKBURN AND C.-W. SHU, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: General framework, Math. Comp., 52 (1989), pp. 411-435.
6. B. COCKBURN AND C.-W. SHU, The Runge-Kutta local projection Pi-discontinuous Galerkin finite element method for scalar conservation laws, RAIRO Model. Math. Anal. Numér., 25 (1991), pp. 337-361.
7. B. COCKBURN AND C.-W. SHU, The Runge-Kutta discontinuous Galerkin method for conservation laws V: Multidimensional systems, J. Comput. Phys., 141 (1998), pp. 199-224.
8. A. HARTEN, High resolution schemes for hyperbolic conservation laws, J. Comput. Phys., 49 (1983), pp. 357-393.
9. A. HARTEN, ENO schemes with subcell resolution, J. Comput. Phys., 83 (1989), pp. 148-184.
10. A. HARTEN, B. ENGQUIST, S. OSHER, AND S. CHAKRAVATHY, Uniformly high order accurate essentially non-oscillatory schemes, III, J. Comput. Phys., 71 (1987), pp. 231-303.
11. G. JIANG AND C.-W. SHU, Efficient implementation of weighted ENO schemes, J. Comput. Phys., 126 (1996), pp. 202-228.
12. L. KRJVODONOVA, J. XIN, J.-F. REMACLE, N. CHEVAUGEON, AND J.E. FLAHERTY, Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws, Appl. Numer. Math., 48 (2004), pp. 323-338.
13. J. QIU AND C.-W. SHU, Runge-Kutta discontinuous Galerkin method using WENO limiters, SIAM J. Sci. Comput., 26 (2005), pp. 907-929.
14. J. QIU AND C.-W. SHU, Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method: One dimensional case, J. Comput. Phys., 193 (2003), pp. 115-135.
15. J. Qiu AND C.-W. SHU, Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method II: Two dimensional case, Comput. Fluids, 34 (2005), pp. 642-663.
16. W.H. REED AND T.R. HILL, Triangular Mesh Methods for Neutron Transport Equation, Technical report LA-UR-73-479, Los Alamos Scientific Laboratory, Los Alamos, NM, 1973.
17. W.J. RIDER AND L.G. MARGOLIN, Simple modifications of monotonicity-preserving limiters, J. Comput. Phys., 174 (2001), pp. 473-488.
18. C.-W. SHU, TVB uniformly high-order schemes for conservation laws, Math. Comp., 49 (1987), pp. 105-121.
19. C.-W. SHU, Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, in Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, Lecture Notes in Math. 1697, A. Quarteroni, ed., Springer, New York, 1998, pp. 325-432.
20. C.-W. SHU AND S. OSHER, Efficient implementation of essentially non-oscillatory shock-capturing schemes, J. Comput. Phys., 77 (1988), pp. 439-471.
21. C.-W. SHU AND S. OSHER, Efficient implementation of essentially non-oscillatory shock capturing schemes II, J. Comput. Phys., 83 (1989), pp. 32-78.
22. A. SURESH AND H.T. HUYNH, Accurate monotonicity-preserving schemes with Runge-Kutta time stepping, J. Comput. Phys., 136 (1997), pp. 83-99.
23. P.K. SWEBY, High resolution schemes using flux limiters for hyperbolic conservation laws, SIAM J. Numer. Anal., 21 (1984), pp. 995-1011.
24. P. WOODWARD AND P. COLELLA, The numerical simulation of two-dimensional fluid flow with strong shocks, J. Comput. Phys., 54 (1984), pp. 115-173.