The influence of cell geometry on the accuracy of upwind schemes in the low mach number regime

Journal of Computational Physics

Volumn 228, Issue 8, 2009, Pages 2918-2933

  Rieper, Felix ^a   Bader, Georg ^b  

^a GOETHE UNIVERSITY   (Germany)

^b Institute for Applied Mathematics and Scientific Computing   (Germany)

Author keywords

Asymptotic analysis; Euler equations; Incompressible and compressible flow; Low Mach number flow; Numerical dissipation; Roe scheme

Indexed keywords

AERODYNAMICS; EULER EQUATIONS; INCOMPRESSIBLE FLOW; MACH NUMBER;

ACCURACY PROBLEMS; CELL GEOMETRIES; EULER'S EQUATION; FIXED MESH; LOW MACH NUMBERS; LOW-MACH-NUMBER FLOW; NUMERICAL DISSIPATION; ROE'S SCHEME; TRIANGULAR GRID; UP-WIND SCHEME;

ASYMPTOTIC ANALYSIS;

EID: 61549126915     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.01.002     Document Type: Article

References (13)

1. Leveque R.J. Finite Volume Methods for Hyperbolic Problems Cambridge Texts in Applied Mathematics (2002), Cambridge University Press, Cambridge
2. Sesterhenn J., Müller B., and Thomann H. On the cancellation problem in calculating compressible low Mach number flows. J. Comput. Phys. 151 2 (1999) 597-615
3. Turkel E. Preconditioned methods for solving the incompressible and low speed compressible equations. J. Comput. Phys. 72 (1987) 277-298
4. E. Turkel, A. Fiterman, B. van Leer, Preconditioning and the limit of the compressible to the incompressible flow equations for finite difference schemes, Frontiers of Computational Fluid Dynamics 1994, CMAS: Computational Methods in Applied Sciences, Chichester: Wiley, 1995
5. B. van Leer, W.-T. Lee, P. Roe, Characteristic time-stepping or local preconditioning of the euler equations, AIAA paper 91-1552, 1991.
6. Choi Y.-H., and Merkle C. The application of preconditioning in viscous flows. J. Comput. Phys. 105 2 (1993) 207-223
7. Guillard H., and Viozat C. On the behaviour of upwind schemes in the low Mach number limit. Comput. Fluids 28 1 (1999) 63-86
8. F. Rieper, On the behaviour of numerical schemes in the low Mach number regime, Ph.D. thesis, Brandenburg Technical University, Cottbus, 2008.
9. Klein R. Semi-implicit extension of a Godunov-type scheme based on low Mach number asymptotics I: one-dimensional flow. J. Comput. Phys. 121 2 (1995) 213-237
10. West D.B. Introduction to Graph Theory. second ed. (2005), Prentice-Hall of India, New Delhi
11. Guillard H., and Murrone A. On the behavior of upwind schemes in the low Mach number limit. II: Godunov type schemes. Comput. Fluids 33 4 (2004) 655-675
12. A. Meister, Analyse und Anwendung Asymptotik-basierter numerischer Verfahren zur Simulation reibungsbehafteter Strömungen in allen Mach-Zahlbereichen, Habilitationsschrift, Universität Hamburg, 2001.
13. Feistauer M., and Kucera V. On a robust discontinuous Galerkin technique for the solution of compressible flow. J. Comput. Phys. 224 1 (2007) 208-221