Finite volume solver; Low Mach number flows; AUSM schemes
Abstract :
[en] This paper presents a cell-centered high order finite volume scheme for the solution of the three-dimensional (3D) Navier–Stokes equations with low Mach number. The system of non-linear equations is solved by means of a fully implicit pseudo-transient scheme. Each pseudo-time step is solved by a Newton-GMRes procedure. A local preconditioning technique is used to scale the speed of sound and to improve the system condition number for low Mach number and low cell Reynolds number. This preconditioning is applied to the AUSM+up flux vector splitting function. The method is tested on 2D and 3D low Mach number laminar flows.
Disciplines :
Aerospace & aeronautics engineering
Author, co-author :
Vigneron, Didier ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > A&M
Vaassen, Jean-Marc; Université de Liège - ULiège > Aérospatiale et mécanique > Aérodynamique
Essers, Jean-André ; Université de Liège - ULiège > Aérospatiale et mécanique > Aérodynamique
Language :
English
Title :
An implicit finite volume method for the solution of 3D low Mach number viscous flows using a local preconditioning technique
Batchelor G.K. An Introduction to Fluid Dynamics (1967), Cambridge University Press, Cambridge
Choi Y.-H., and Merkle C.L. The application of preconditioning in viscous flows. J. Comput. Phys. 105 (1993) 207-223
Chorin A.J. A numerical method for solving incompressible viscous flow problems. J. Comput. Phys. 2 (1967) 12-26
W.J. Coirier, An adaptively-refined, Cartesian, cell-based scheme for the Euler and Navier-Stokes equations, Ph.D. Thesis, University of Michigan, June 1994.
Ghia U., Ghia K.N., and Shin C.T. High-resolutions for incompressible flow using the Navier-Stokes equations and a multigrid method. J. Comput. Phys. 48 (1982) 387-441
I. Lepot, F. Meers, J.-A. Essers, Multilevel parallel high order schemes for inviscid flow computations on 3D unstructured meshes, in: Proceedings of the ECCOMAS Computational Fluid Dynamics Conference, September 2001.
M.-S. Liou, A further development of the ausm + scheme towards robust and accurate solutions for all speeds, June 2003, AIAA Paper 2003-4116.
Merkle C.L. Computation of flows with arbitrary equations of state. AIAA J. 36 (1998) 515-521
K. Morgan, J. Periaux, F. Thomasset, Analysis of laminar flow over a backward facing step, Notes on Numerical Fluid Mechanics, vol. 9, Vieweg, Braunschweig, 1984.
Saad Y. Iterative Methods for Sparse Linear Systems (1996), PWS Publishing Company
Turkel E. Preconditioned methods for solving the incompressible and low speed compressible equations. J. Comput. Phys. 72 (1987) 277-298
J.-M. Vaassen, D. Vigneron, J.-A. Essers, An implicit high order finite volume scheme for the solution of 3d Navier-Stokes equations with new discretisation of diffusive terms, Juin 2005, Proceedings of Acomen 2005 Conference, Ghent.
Vierendeels J., Riemslagh K., and Dick E. A multigrid semi-implicit line method for viscous incompressible and low-Mach-number flows on high aspect ratio grids. J. Comput. Phys. 154 (1999) 310-341
Volpe G. Performance of compressible flow codes at low mach numbers. AIAA J. 31 (1993) 49-56
Weiss J.M., and Smith W.A. Preconditioning applied to variable and constant density flows. AIAA J. 33 11 (1995) 2050-2057
