Numerical comparison of WENO finite volume and Runge-Kutta discontinuous Galerkin methods

Journal of Scientific Computing

Volumn 16, Issue 2, 2001, Pages 145-171

  Zhou, Tie ^a   Li, Yinfan ^b   Shu, Chi Wang ^c  

^a PEKING UNIVERSITY   (China)

^b INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

^c BROWN UNIVERSITY   (United States)

Author keywords

Comparison; Discontinuous Galerkin; Finite volume; WENO

Indexed keywords

ALGORITHMS; BOUNDARY VALUE PROBLEMS; COMPUTER SIMULATION; EIGENVALUES AND EIGENFUNCTIONS; FINITE VOLUME METHOD; GALERKIN METHODS; INTEGRATION; MATHEMATICAL MODELS;

DISCONTINUOS GALERKIN; DISCRETE KINETIC THEORY; LATTICE BOLTZMAN METHOD; WEIGHTED ESSENTIALLY NON-OSCILLATORY (WENO);

DIFFUSION;

EID: 7544220935     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1012282706985     Document Type: Review

References (19)

1. Biswas, R., Devine, K. D., and Flaherty, J. (1994). Parallel, Adaptive Finite Element Methods for Conservation Laws, Applied Numerical Mathematics, Vol. 14, pp. 255-283.
2. Cockburn, B. (1998). An introduction to the discontinuous Galerkin method for convection dominated problems. In Cockburn, B., Johnson, C., Shu, C.-W., and Tadmor, E. (Quarteroni, A., ed.), Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, Lecture Notes in Mathematics, Springer, Vol. 1697, pp. 151-268.
3. Cockburn, B. (1999). Discontinuous Galerkin methods for convection-dominated problems. In Barth, T. J. and Deconinck, H. (eds.), High-Order Methods for Computational Physics, Lecture Notes in Computational Science and Engineering, Springer, Vol. 9, pp. 69-224.
4. Cockburn, B., Karniadakis, G., and Shu, C.-W. (2000). The development of discontinuous Galerkin methods. In Cockburn, B., Karniadakis, G., and Shu, C.-W. (eds.), Discontinuous Galerkin Methods: Theory, Computation and Applications, Lecture Notes in Computational Science and Engineering, Springer, Vol. 11, Part I: Overview, pp. 3-50.
5. 2AN) 25, 337-361.
6. Cockburn, B., and Shu, C.-W. (1989). TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: General framework. Math. Comp. 52, 411-435.
7. Cockburn, B., Lin, S.-Y., and Shu, C.-W. (1989). TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One dimensional system. J. Comput. Phys. 84, 90-113.
8. Cockburn, B., Hou, S., and Shu, C.-W. (1990). The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: The multidimensional case. Math. Comp. 54, 545-581.
9. Cockburn, B., and Shu, C.-W. (1998). The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws V: multidimensional systems. J. Comput. Phys. 141, 199-224.
10. Cockburn, B., and Shu, C.-W. (1998). The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM J. Numer. Anal. 35, 2440-2463.
11. Harten, A., Engquist, B., Osher, S., and Chakravarthy, S. (1987). Uniformly high order essentially non-oscillatory schemes, III. J. Comput. Phys. 71, 231-303.
12. Hu, C., and Shu, C.-W. (1999). Weighted essentially non-oscillatory schemes on triangular meshes. J. Comput. Phys. 150, 97-127.
13. Jiang, G.-S., and Shu, C.-W. (1996). Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202-228.
14. Liu, X.-D., Osher, S., and Chan, T. (1994). Weighted essentially non-oscillatory schemes. J. Comput. Phys. 115, 200-212.
15. Shu, C.-W. (1999). High order ENO and WENO schemes for computational fluid dynamics. In Barth, T. J., and Deconinck, H. (eds.), High-Order Methods for Computational Physics, Lecture Notes in Computational Science and Engineering, Springer, Vol. 9, pp. 439-582.
16. Shu, C.-W. (1998). Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. In Cockburn, B., Johnson, C., Shu, C.-W., and Tadmor, E. (Quarteroni, A., ed.), Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, Lecture Notes in Mathematics, Springer, Vol. 1697, pp. 325-432.
17. Shu, C.-W., and Osher, S. (1988). Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 77, 439-471.
18. Shu, C.-W., and Osher, S. (1989). Efficient implementation of essentially non-oscillatory shock-capturing schemes II. J. Comput. Phys. 83, 32-78.
19. Woodward, P., and Colella, P. (1984). The numerical simulation of two-dimensional fluid flow with strong shocks. J. Comput. Phys. 54, 115-173.