Multidomain hybrid RKDG and WENO methods for hyperbolic conservati on laws

SIAM Journal on Scientific Computing

Volumn 35, Issue 2, 2013, Pages

  Cheng, Jian ^a   Lu, Yaowen ^a   Liu, Tiegang ^a  

^a BEIHANG UNIVERSITY   (China)

Author keywords

Conservation laws; Multidomain hybrid method; Runge Kutta discontinuous Galerkin method; Weighted essentially nonoscillatory scheme

Indexed keywords

FINITE DIFFERENCE METHOD; GALERKIN METHODS; NUMERICAL METHODS; PHYSICAL PROPERTIES; RUNGE KUTTA METHODS; SHOCK WAVES;

CONSERVATION LAW; ESSENTIALLY NON-OSCILLATORY SCHEMES; HYBRID METHOD; MULTI-DOMAINS; MULTIDOMAIN HYBRID METHOD; RUNGE-KUTTA DISCONTINUOUS GALERKIN; RUNGE-KUTTA DISCONTINUOUS GALERKIN METHODS; THIRD ORDER; WEIGHTED ESSENTIALLY NONOSCILLATORY; WEIGHTED ESSENTIALLY NONOSCILLATORY SCHEME;

COMPUTATIONAL EFFICIENCY;

EID: 84880631532     PISSN: 10648275     EISSN: 10957200     Source Type: Journal    
DOI: 10.1137/110855156     Document Type: Article

References (32)

1. W. H. REED AND T. R. HILL, Triangular Mesh Methods f or the Neutron Transport Equation, Tech. report LA-UR-73-479, Los Alamos Scientific Laboratory, Los Alamos, NM, 1973.
2. C.-W. SHU, High Order Finite Difference and Finite Volume WENO Schemes and Discontinuous Galerkin Methods for CFD, Tech. report NASA/CR-2001-210865, ICASE Report 2001-11, NASA, 2001.
3. A. HARTEN, B. ENGQUIST, S. OSHER, AND S. CHAKRAVATHY, Uniformly high order accurate essentially nonoscillatory schemes III, J. Comput. Phys., 71(1987), pp. 231-303.
4. C.-W. SHU AND S. OSHER, Efficient implementation of essentially non-oscillatory shock capturing schemes I, J. Comput. Phys., 77(1987), pp. 439-471.
5. C.-W. SHU AND S. OSHER, Efficient implementation of essentially non-oscillatory shock capturing schemes II, J. Comput. Phys., 83(1989), pp. 32-78.
6. C.-W. SHU, Essentially Non-oscillatory and Weighted Essentially Non-oscillatory Schemes for Hyperbolic Conservation Laws, Tech. report NASA/CR-97-206253, ICASE Report 97-65, NASA, 1997.
7. G. S. JIANG AND C.-W. SHU, Efficient implementation of weighted ENO schemes, J. Comput. Phys., 126(1996), pp. 202-228.
8. O. FRIEDRICH, Weighted essentially non-oscillatory schemes for the interpolation of mean values on unstructured grids, J. Comput. Phys., 144(1998), pp. 194-212.
9. C. HU AND C.-W. SHU, Weighted essentially non-oscillatory schemes on triangular meshes, J. Comput. Phys., 150(1999), pp. 97-127.
10. B. COCKBURN AND C.-W. SHU, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for scalar conservation laws II: Ge neral f ramework, Math. Comp., 52(1989), pp. 411-435.
11. B. COCKBURN AND C.-W. SHU, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for scalar conservation laws III: One dimensional systems, J. Comput. Phys., 84(1989), pp. 90-113.
12. B. COCKBURN AND C.-W. SHU, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for scalar conservation laws IV: The multidimensional case, Math. Comp., 54(1990), pp. 545-581.
13. B. COCKBURN AND C.-W. SHU, The Runge-Kutta local projection discontinuous Galerkin finite element method for scalar conservation laws V: Multidimensional systems, J. Comput. Phys., 141(1998), pp. 199-224.
14. B. COCKBURN AND C.-W. SHU, Runge-Kutta discontinuous Galerkin methods for convectiondominated problems, J. Sci. Comput., 16(2001), pp. 173-261.
15. J. QIU AND C.-W. SHU, Runge-Kutta discontinuous Galerkin method using WENO limiters, SIAM J. Sci. Comput., 26(2005), pp. 907-929.
16. J. QIU AND C.-W. SHU, Hermite WENO schemes and their application as limiter for Runge-Kutta discontinuous Galerkin method: One dimensional case, J. Comput. Phys., 193(2004), pp. 115-135.
17. G. CHESSHIRE AND W. D. HENSHAW, Composite overlapping meshes for the solution of partial differential equations, J. Comput. Phys., 90(1990), pp. 1-64.
18. M. J. BERGER, On conservation at grid interfaces, SIAM J. Numer. Anal., 24(1987), pp. 967-984.
19. H. S. TANG AND T. ZHOU, On nonconservation algorithms for grid interfaces, SIAM J. Numer. Anal., 37(1999), pp. 173-193.
20. Z. N. WU, S. S. XU, B. GAO, AND L. S. ZHUANG, Review of numerical computation of compressible flows with artificial interfaces, Comput. & Fluids., 36(2007), pp. 1657-1679.
21. K. SEBASTIAN AND C.-W. SHU, Multidomain WENO finite difference method with interpolation at subdomain interfaces, J. Sci. Comput., 19(2003), pp. 405-438.
22. P. D. LAX AND B. WENDROFF, Systems of conservation laws, Comm. Pure Appl. Math., 13(1960), pp. 217-237.
23. P. WOODWARD AND P. COLELLA, The numerical simulation of two-dimensional fluid flow with strong shocks, J. Comput. Phys., 54(1984), pp. 115-173.
24. M. DUMBSER, D. S. BALSARA, AND E. F. TORO, A unified framework for the construction of one step finite volume and discontinuous Galerkin schemes on unstructured meshes, J. Comput. Phys., 227(2008), pp. 8209-8253.
25. L. P. ZHANG, W. LIU, L. X. HE, AND X. G. DENG, A new class of DG/FV hybrid schemes for one-dimensional conservation law, in the 8th Asian Conference on Computational Fluid Dynamics, Hong Kong, 2010, pp. 10-14.
26. L. P. ZHANG, W. LIU, L. X. HE, X. G. DENG, AND H. X. ZHANG, A new class of DG/FV hybrid methods for conservation laws I: Basic formulation and one-dimensional systems, J. Comput. Phys., 231(2011), pp. 1081-1103.
27. L. P. ZHANG, W. LIU, L. X. HE, X. G. DENG, AND H. X. ZHANG, A class of hybrid DG/FV methods for conservation laws II: Two dimensional cases, J. Comput. Phys., 231(2011), pp. 1104-1120.
28. D. S. BALSARA, C. ALTMANN, C.-D. MUNZ, AND M. DUMBSER, A sub-cell based indicator for troubled zones in RKDG schemes and a novel class of hybrid RKDG+HWENO schemes, J. Comput. Phys., 226(2007), pp. 586-620.
29. H. LUO, L. LUO, R. NOURGALIEV, AND V. MOUSSEAU, A reconstructed discontinuous Galerkin method for the compressible Euler equations on arbitrary grids, in Proceedings of the 19th AIAA Computational Fluid Dynamics Conference, INL/CON-09-16255, 2009.
30. J. ZHU, J. QIU, C.-W. SHU, AND M. DUMBSER, Runge-Kutta discontinuous Galerkin method using WENO limiters II: Unstructured meshes, J. Comput. Phys., 227(2008), pp. 4330-4353.
31. H. LUO AND J. D. BAUM, A Hermite WENO-based limiter for discontinuous Galerkin method on unstructured grids, J. Comput. Phys., 225(2007), pp. 686-713.
32. H. LUO, H. XIAO, R. NOURGALIEV, AND C. CAI, A comparative study of different reconstruction schemes for a reconstructed discontinuous Galerkin method on arbitrary grids, in Proceedings of the 20th AIAA Computational Fluid Dynamics Conference, INL/CON-11-22524, 2011.