A Runge-Kutta discontinuous Galerkin method for the Euler equations

Computers and Fluids

Volumn 34, Issue 3, 2005, Pages 375-398

  Tang, Huazhong ^a   Warnecke, Gerald ^b  

^a PEKING UNIVERSITY   (China)

^b OTTO VON GUERICKE UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

DECOMPOSITION; FINITE ELEMENT METHOD; GALERKIN METHODS; GAS DYNAMICS; INTEGRAL EQUATIONS; KINETIC THEORY OF GASES; OSCILLATIONS; PROBLEM SOLVING;

EULER EQUATIONS; NON-LINEAR FLUX; RIEMANN SOLVER; RUNGE-KUTTA DISCONTINUOUS GALERKIN (RKDG) METHOD;

RUNGE KUTTA METHODS;

EQUATION; FLUID FLOW; MATHEMATICAL ANALYSIS; MODELING;

EID: 10944272687     PISSN: 00457930     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compfluid.2004.01.004     Document Type: Article

References (32)

1. Atkins H.L. Shu C.W. Quadrature-free implementation of discontinuous Galerkin method for hyperbolic equations AIAA J. 36 1998 775-782
2. Azarenok B.N. Ivanenko S.A. Tang T. Adaptive mesh redistribution method based on Godunov's scheme Commun. Math. Sci. 1 2003 152-179
3. Biswas F. Devine K. Flaherty J.E. Parallel adaptive finite element method for conservation laws Appl. Numer. Math. 14 1984 255-283
4. Burbeau A. Sagaut P. Bruneau C.H. A problem-independent limiter for high-order Runge-Kutta discontinuous Galerkin methods J. Comput. Phys. 169 2001 111-150
5. Cercignani C. The Boltzmann equation and its applications 1998 Springer-Verlag Berlin
6. Chapman S. Cowling T.W. The mathematical theory of non-uniform gases 3rd ed. 1990 Cambridge University Press Cambridge
7. tCockburn B. Discontinuous Galerkin methods for convection-dominated problems Earth T.J. Deconinck H. High-order methods for computational physics Lecture notes in computational science and engineering vol. 9 1999 69-224 Springer Berlin
8. Cockburn B. Shu C.W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: General framework Math. Comput. 52 1989 411-435
9. 2AN) 25 1991 337-361.
10. Cockburn B. Shu C.W. The Runge-Kutta discontinuous Galerkin method for conservation laws V: Multidimensional systems J. Comput. Phys. 141 1998 199-224.
11. Cockburn B. Shu C.W. Runge-Kutta discontinuous Galerkin method for convection-dominated problems J. Sci. Comput. 16 2001 173-261
12. Cockburn B. Karniadakis G. Shu C.W. The development of discontinuous Galerkin methods Cockburn B. Karniadakis G. Shu C.W. Discontinuous Galerkin methods: Theory, computation and applications. Lecture notes in computational science and engineering vol. 11 2000 3-50 Springer Berlin
13. 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. 54 1990 545-581
14. Cockburn B. Lin S.Y. Shu C.W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One dimensional systems J. Comput. Phys. 84 1989 90-113
15. Jiang G.S. Shu C.W. On a cell entropy inequality for discontinuous Galerkin methods Math. Comput. 62 1994 531-538
16. Kunik M. Qamar S. Warnecke G. Kinetic schemes for the ultra-relativistic Euler equations J. Comput. Phys. 187 2003 572-596
17. Mandal J.C. Despande S.M. Kinetic flux vector splitting for the Euler equations Comput. Fluids 23 1994 447-478
18. Remade J.F. Flaherty J.E. Shephard M.S. An adaptive discontinuous Galerkin technique with an orthogonal basis applied to compressible flow problems SIAM Rev. 45 2003 53-72
19. Reed WH, Hill TR. Triangular mesh methods for neutron transport equation. Technical Report LA-UR-73-479, Los Alamos Scientific Laboratory; 1973
20. Shu C.W. TVB uniformly high-order schemes for conservation laws Math. Comp. 49 1987 105-121
21. Shu C.W. Osher S. Efficient implementation of essentially non-oscillatory shock capturing schemes, II J. Comput. Phys. 77 1988 439-471
22. Shu C.W. Osher S. Efficient implementation of essentially non-oscillatory shock capturing schemes, II J. Comput. Phys. 83 1989 32-78
23. Tang H.Z. Tang T. Moving mesh methods for one- and two-dimensional hyperbolic conservation laws SIAM J. Num. Anal. 41 2003 487-515
24. Tang H.Z. Wu H.M. High resolution KFVS finite volume methods and Its applications in CFDs Chinese J. Numer. Math. Appl. 21 1999 93-103
25. Tang H.Z. Wu H.M. Kinetic flux vector splitting for radiation hydrodynamical equations Comput. Fluids 29 2000 917-934
26. Tang H.Z. Xu K. A high-order gas-kinetic method for multidimensional ideal magnetohydrodynamics J. Comput. Phys. 165 2000 69-88
27. Tang H.Z. Xu K. On positivity of a class of flux-vector splitting methods I. Explicit difference schemes Math. Num. Sin. 23 2001 469-476
28. Tang T. Xu K. Gas-kinetic schemes for the compressible Euler equations: Positivity-preserving analysis Z. Angew Math. Phys. 50 1999 258-281
29. Woodward P.R. Colella P. The numerical simulation of two-dimensional fluid flow with strong shocks J. Comput. Phys. 54 1984 115-173
30. Xu K. A gas-kinetic scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method J. Comput. Phys. 171 2001 289-335
31. Xu K. Gas-kinetic schemes for unsteady compressible flow simulations. VKI for fluid dynamics lecture series 1998-03; 1998
32. Zhou T. Li Y.F. Shu C.W. Numerical comparison of WENO finite volume and Runge-Kutta discontinuous Galerkin methods J. Sci. Comput. 16 2001 145-171