Un schema elements finis simple et adaptatif pour les ecoulements de Naviers-Stokes compressibles
Keywords:
Navier-Srokes, grid refinement, GMRES, diagonal preconditioningAbstract
We have developed a new, stable and simple formulation, based on the MINI element, to integrate the compressible Navier-Stokes equati011S by the finite element method. This element is well suited for grid refinement. The non-linear system is solved by GMRES, an iterative method, coupled with a new diagonal preconditioning. The resulting algorithme is very efficient and vectorizes well. The element converges quadratically in the L2 norm and has been tested against results of the GAMMWorkshop on Compressible Navier-Stokes Flows. on regular grids as well as on adapted grids.
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References
[ABF84]
[BGPV87)
[Bro87)
D.N. Arnold, F. Brezzi, and M. Fortin. A stable finite element for the Stokes
equations. Calcolo, 21, 1984.
M.O. Bristeau, R. Glowinski, J. Periaux, and H. Viviand, editors. Numerical
Simulation of Compre&&ible Navier-Stoke& Flow&. Volume 18 of NoteA on Numerical
Fluid MechanicA, Vieweg, 1987. Proceedings of the GAMM-Workshop
(Nice 1985).
P. N. Brown. A local convergence theory for combined inexact-Newton/finitedifference
projection methods. SIAM J. Numer. Anal., 24:410-434, 1987.
[BZGdA086) I. Babuska, O.C. Zienkiewicz, J. Gaga, and E.R. de A. Oliveira, editors. Accu-
[Cam87)
racy e&timate& and adaptative refinement• in finite element computation•. John
Whiley & Sons, 1986.
L. Gambier. Computation of viscous transonic flows using an unsteady type
method and a zonal grid refinement technique. In Numerical Simulation of
Compre .. ible Navier-Stoke• Flow•, pages 105-122, Vieweg, 1987.
[CJ84] T.F. Chan and K.R. Jackson. Nonlineary preconditionned Krylov subspace
methods for discrete Newton algorithms. SIAM J. Sci. Stat. Comput., 5:533-
, 1984.
[DT84] G. Dhatt and G. Touzot. Une pre&entation de Ia methode du element& fini&.
[Hir88]
[LMZ86]
[MBR87]
[ODSD86]
[PD86]
[SDN87]
[Sec86]
[Sec91]
[SS86]
[ZLMP85]
Collection Univer&iti de Compiegne, Maloine S.A., deuxieme edition, 1984.
Ch. Hirsch. Numerical Computation of Internal and Erternal Flow&. Volume 1
of Serie& in numerical method& in engineering, John Whiley &. Sons, 1988.
R. Lohner, K. Morgan, and 0. C. Zienkiewicz. Adaptative grid refinement for the
compressible Euler equations. In Accuracy E&timate& and Adaptive Refinement&
in Finite Element Computation&, pages 281-297, John Whiley &. Sons, 1986.
B. Miiller, T. Berglind, and A. Rizzi. Implicit central difference simulation
of compressible Navier-Stokes flow over a NACA-0012 airfoil. In Numerical
Simulation of Compreuible Navier-Stolce& Flow&, pages 183-200, Vieweg, 1987.
J.T. Oden, L. Demkowicz, T. Stouboulis, and P. Devloo. Adaptative methods
for problems in solid and fluid mechanics. In Accuracy E&timate& and Adaptive
Refinement& in Finite Element Computation&, pages 249-280, John Whiley &.
Sons, 1986.
B. Palmerio and A. Dervieux. Application of a FEM moving node adaptive
method to accurate dtock capuring. In Numerical Grid Generation in CFD,
pages 425-436, 1986.
Y. Secretan, G. Dhatt, and D. Nguyen. Compressible viscous flow around a
NACA-0012 airfoil. In Numerical Simulation of Compreuible Navier-Stoke&
Flow&, pages 219-236, Vieweg, 1987.
Y. Secretan. Modeli&ation par element& fini& de& equation& de Navier-Stolce&
compreuible& appliquee& aur ecoulement& erterne&. Master's thesis, Universite
Laval, Quebec, Canada, 1986.
Y. Secretan. Contribution ti Ia re&olution de& equation& de Navier-Stolce& compreuible&
par Ia methode du tilement& fini& adaptatij& ; Developpement d'un
eltiment &imp/e. PhD thesis, Eidgcnossische Technische Hochschule, Ziirich,
Switzerland, 1991.
Y. Saad and M. Schultz. GMRES: a generalized minimal residual algorithm for
solving nonsymetric linear systems. SIAM J. Sci. Stat. Comput., 7:856-869,
C. Zienkiewicz, R. LOhner, K. Morgan, and J. Perairc. High-speed compressible
flow and other advection-dominated problems of fluid dynamics. Finite
Element& in Fluid&, 6:41-88, 1985.
