On a robust discontinuous Galerkin technique for the solution of compressible flow

Journal of Computational Physics

Volumn 224, Issue 1, 2007, Pages 208-221

  Feistauer, M ^a   Kucera V ^a  

^a CHARLES UNIVERSITY   (Czech Republic)

Author keywords

Compressible Euler equations; Discontinuous Galerkin space discretization; High speed flow; Low Mach number flow; Semi implicit linearized numerical scheme; Stabilization of the scheme; Vijayasundaram numerical flux

Indexed keywords

AERODYNAMICS; COMPUTATIONAL FLUID DYNAMICS; EULER EQUATIONS; FINITE ELEMENT METHOD; GALERKIN METHODS; INCOMPRESSIBLE FLOW; MACH NUMBER; NUMERICAL METHODS;

COMPRESSIBLE EULER EQUATIONS; DISCONTINUOUS GALERKIN; DISCONTINUOUS GALERKIN SPACE DISCRETIZATION; HIGH SPEED FLOWS; LOW-MACH-NUMBER FLOW; NUMERICAL FLUX; NUMERICAL SCHEME; SEMI-IMPLICIT; SEMI-IMPLICIT LINEARIZED NUMERICAL SCHEME; SPACE DISCRETIZATIONS; STABILIZATION OF THE SCHEME; VIJAYASUNDARAM NUMERICAL FLUX;

STABILIZATION;

EID: 34248187093     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.01.035     Document Type: Article

References (27)

1. Bassi F., and Rebay S. High-order accurate discontinuous finite element solution of the 2D Euler equations. J. Comput. Phys. 138 (1997) 251-285
2. Baumann C.E., and Oden J.T. A discontinuous hp finite element method for the Euler and Navier-Stokes equations. Int. J. Numer. Methods Fluids 31 (1999) 79-95
3. In: Cockburn B., Karniadakis G.E., and Shu C.-W. (Eds). Discontinuous Galerkin Methods, Lecture Notes in Computational Science and Engineering vol. 11 (2000), Springer, Berlin
4. Darwish M., Moukalled F., and Sekar B. A robust multi-grid pressure-based algorithm for multi-fluid flow at all speeds. Int. J. Numer. Methods Fluids 41 (2003) 1221-1251
5. Davis T.A., and Duff I.S. A combined unifrontal/multifrontal method for unsymmetric sparse matrices. ACM Trans. Math. Software 25 (1999) 1-19
6. Dolejši{dotless}́ V. Anisotropic mesh adaptation for finite volume and finite element methods on triangular meshes. Comput. Vis. Sci. 1 3 (1998) 165-178
7. Dolejši{dotless}́ V., and Feistauer M. On the discontinuous Galerkin method for the numerical solution of compressible high-speed flow. In: Brezzi F., Buffa A., Corsaro S., and Murli A. (Eds). Numerical Mathematics and Advanced Applications, ENUMATH 2001 (2003), Springer-Verlag Italia, Milano 65-84
8. Dolejši{dotless}́ V., and Feistauer M. A semi-implicit discontinuous Galerkin finite element method for the numerical solution of inviscid compressible flow. J. Comput. Phys. 198 (2004) 727-746
9. V. Dolejši{dotless}́, M. Feistauer, J. Hozman, Analysis of semi-implicit DGFEM for nonlinear convection-diffusion problems on nonconforming meshes. Comput. Methods Appl. Mech. Eng. (in press), doi:10.1016/j.cma.2006.09.025.
10. Dolejši{dotless}́ V., Feistauer M., and Schwab C. On some aspects of the discontinuous Galerkin finite element method for conservation laws. Math. Comput. Simul. 61 (2003) 333-346
11. Feistauer M. Mathematical Methods in Fluid Dynamics (1993), Longman Scientific & Technical, Harlow
12. Feistauer M., Felcman J., and Straškraba I. Mathematical and Computational Methods for Compressible Flow (2003), Clarendon Press, Oxford
13. Feistauer M., and Švadlenka K. Discontinuous Galerkin method of lines for solving nonstationary singularly perturbed linear problems. J. Numer. Math. 2 (2004) 97-117
14. Fraenkel L. On corner eddies in plane inviscid shear flow. J. Fluid Mech. 11 (1961) 400-406
15. Hauke G., and Hughes T.J.R. A comparative study of different sets of variables for solving compressible and incompressible flows. Comput. Methods Appl. Mech. Eng. 153 (1998) 1-44
16. Jaffre J., Johnson C., and Szepessy A. Convergence of the discontinuous Galerkin finite elements method for hyperbolic conservation laws. Math. Models Methods Appl. Sci. 5 (1995) 367-386
17. Klein R. Semi-implicit extension of a Godunov-type scheme based on low Mach number asymptotics 1: one-dimensional flow. J. Comput. Phys. 121 (1995) 213-237
18. Meister A. Viscous flow fields at all speeds: analysis and numerical simulation. J. Appl. Math. Phys. 54 (2003) 1010-1049
19. Meister A., and Struckmeier J. Hyperbolic Partial Differential Equations, Theory, Numerics and Applications (2002), Vieweg, Braunschweig
20. Park J.H., and Munz C.-D. Multiple pressure variables methods for fluid flow at all Mach numbers. Int. J. Numer. Methods Fluids 49 (2005) 905-931
21. Roller S., Munz C.-D., Geratz K.J., and Klein R. The multiple pressure variables method for weakly compressible fluids. Z. Angew. Math. Mech. 77 (1997) 481-484
22. van der Heul D.R., Vuik C., and Wesseling P. A conservative pressure-correction method for flow at all speeds. Comput. Fluids 32 (2003) 1113-1132
23. van der Vegt J.J.W., and van der Ven H. Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flow. J. Comput. Phys. 182 (2002) 546-585
24. Vijayasundaram G. Transonic flow simulation using upstream centered scheme of Godunov type in finite elements. J. Comput. Phys. 63 (1986) 416-433
25. Wenneker I., Segal A., and Wesseling P. A Mach-uniform unstructured staggered grid method. Int. J. Numer. Methods Fluids 40 (2002) 1209-1235
26. Wesseling P. Principles of Computational Fluid Dynamics (2001), Springer, Berlin
27. Wesseling P., and van der Heul D.R. Uniformly effective numerical methods for hyperbolic systems. Computing 66 (2001) 249-267