An artificial compressibility flux for the discontinuous Galerkin solution of the incompressible Navier-Stokes equations

Journal of Computational Physics

Volumn 218, Issue 2, 2006, Pages 794-815

  Bassi, F ^a   Crivellini, A ^a   Di Pietro, D A ^a   Rebay, S ^b  

^a UNIVERSITY OF BERGAMO   (Italy)

^b UNIVERSITY OF BRESCIA   (Italy)

Author keywords

Artificial compressibility; Discontinuous Galerkin methods; Incompressible Navier Stokes equations; Riemann solver

Indexed keywords

COMPRESSIBILITY; GALERKIN METHODS; INCOMPRESSIBLE FLOW; NAVIER STOKES EQUATIONS; NUMERICAL METHODS; REYNOLDS NUMBER; VISCOUS FLOW;

ARTIFICIAL COMPRESSIBILITY; DISCONTINOUS GALERKIN METHODS; DISCONTINUOUS GALERKIN; DISCRETIZATIONS; HIGH-ORDER; HIGHER-ORDER; INCOMPRESSIBLE (NAVIER )STOKES EQUATION; INCOMPRESSIBLE NAVIER STOKES EQUATIONS; NUMERICAL SCHEME; RIEMANN SOLVER;

POLYNOMIAL APPROXIMATION;

EID: 33748895877     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.03.006     Document Type: Article

References (15)

1. Liu J.-G., and Shu C.-W. A high-order discontinuous Galerkin method for 2D incompressible flows. J. Comput. Phys. 160 (2000) 577-596
2. Cockburn B., Kanschat G., Schötzau D., and Schwab C. Local discontinuous Galerkin methods for the Stokes system. SIAM J. Numer. Anal. 40 1 (2002) 319-343
3. Cockburn B., Kanschat G., and Schötzau D. The local discontinuous Galerkin method for the Oseen equations. Math. Comp. 73 246 (2003) 569-593
4. Cockburn B., Kanschat G., and Schötzau D. A locally conservative LDG method for the incompressible Navier-Stokes equations. Math. Comp. 74 251 (2005) 1067-1095
5. Bassi F., and Rebay S. A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations. J. Comput. Phys. 131 (1997) 267-279
6. Bassi F., Rebay S., Mariotti G., Pedinotti S., and Savini M. A high-order accurate discontinuous finite element method for inviscid and viscous turbomachinery flows. In: Decuypere R., and Dibelius G. (Eds). Proceedings of the 2nd European Conference on Turbomachinery Fluid Dynamics and Thermodynamics (1997), Technologisch Instituut, Antwerpen, Belgium 99-108
7. Arnold D.N., Brezzi F., Cockburn B., and Marini D. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39 5 (2002) 1749-1779
8. Kovasznay L.S.G. Laminar flow behind a two-dimensional grid. Proc. Camb. Philos. Soc. 44 (1948) 58-62
9. Ghia U., Ghia K.N., and Shin C.T. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. J. Comp. Phys. 48 (1982) 387-411
10. Botella O., and Peyret R. Benchmark spectral results on the lid-driven cavity flow. Comput. Fluids 27 4 (1998) 421-433
11. Erturk E., Corke T.C., and Gokcol C. Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers. Int. J. Numer. Meth. Fluids 48 (2005) 747-774
12. D.A. Di Pietro, Discontinuous Galerkin methods for the incompressible Navier-Stokes equations, Ph.D. thesis, Università degli Studi di Bergamo, January 2006.
13. Cools R. An Encyclopædia of Cubature Formulas. J. Complexity 19 (2003) 445-453
14. S. Balay, K. Buschelman, W.D. Gropp, D. Kaushik, M.G. Knepley, L.C. McInnes, B.F. Smith, H. Zhang, PETSc Web page, , 2001.
15. D.T. Elsworth, E.F. Toro, Riemann solvers for solving the incompressible Navier-Stokes equations using the artificial compressibility method, College of Aeronautics Report 9208, Cranfield Institute of Technology, England, June 1992.