L'approximation quadratique et l'approche Taylor-Galerkin pour Ia modelisation des problemes transitoires d' advection -diffusion
Keywords:
advection-diffusion, splitting, Taylor-Galerkin, Fourier analysis, quadratic approximationAbstract
This paper presents a numerical study of the behaviour of a model based on quadratic finite element approximation for transient advection-diffusion problem modelling. This model is based on a classical splitting technique, the advection-diffusion equation being split in time. The advection part is computed by a &-weighting Taylor-Galerkin approach. As to the diffusion equation, it's discretized by a standard &-weighting Galerkin scheme. For these two phases and based on Fourier method, an error analysis is proposed using quadratics elements. Results of this analysis show interesting investigations on the behaviour of numerical schemes based on high approximations. These investigations are confirmed by some representative numerical examples in one and two dimensions.
Downloads
References
[BAT 86] BATES S., CATHERS B., << Analysis of spurious eigenmodes in finite element
equations », Int. 1. Num. Methods Eng., 23, p. 1131-1143, 1986.
[CUL 80] CuLLEN M.J.P., MORTON K.W., <
and other methods >>, J. Comp. Phys., 34, p. 245-267, 1980.
[CUL 82) CULLEN M.J.P., <
in the solution of hyperbolic problems>>, 1. Comp. Plzys., 45, p. 221-245, 1982.
[DON 84] DoNEA J., <>, Int. 1.
Nwn. Methods Eng., vol. 20, p. 101-119, 1984.
[DON 84) DONEA J., GIULIANI S., LAVAL H., QuARTAPELLE L., << Time-accurate solution of
advection-diffusion problems >>, Comp. Methods Appl. Mech. Eng., 45, p. 123-146, 1984.
[DON 87) DONEA J., QuARTAPELLE L., SELMIN V., << An analysis of time discretization in
finite element solution of hyperbolic problems>>, 1. Comp. Plzy., 70, p. 463-499, 1987.
[DON 92] DoNEA J., QUARTAPELLE L., << An introdution to finite clement methods for
transient advection problems>>, Comp. Methods Appl. Mech. Eng., 95, p. 169-203,1992.
[FIS 79) FiscHER H. B., !MBERGER J., LIST E.J., KoH R.C.Y., BROOKS N.H., Mixing in Inland
and Coastal Waters, Academic Press, California, 1979.
[HIR 88) HIRSCH C., Numerical computation of internal and external flows, VI, eel., Wiley,
[KHE 92) KHELIFA A., Nouvelle approche en elements finis pour Ia modelisation du
phenomcne de transport permanent et non permanent, these de maitrise, universite Laval,
Quebec, Canada, 127 p., 1992.
[KHE 92] KHELIFA A., RoBERT J.-L, OUELLET Y., << Mode!isation numerique de !'advectiondiffusion
d'un polluant: modeles TG2q et TG3q >>, 8<' C01zgres nigional de /'Est du
Canada, ACRPEM, Quebec, Canada, 1992.
[KHE -] KHELirA A., OliELLET Y., << Analysis of evolutionary errors in quadratic finite
element approximation of hyperbolic problems», Int. J. Num. Methods Eng., (soumis).
[LAY 88) Laval H., « Taylor-Galcrkin solution of the time-dependent Navicr-Stokes
equations >>, Complltational Methods in Flow Analysis, Eels. NIKI H., KAWAHARA M.,
Okayama, University of Science, p. 414-421, 1988.
[LA V 90] LA VAL H., QUARTAPELLE L., << A fractional-step Taylor-Galcrkin method for
unsteady incompressible t1ows >>,Int. J. Num. Methods Flui., 11, p. 501-513, 1990.
[MAR 75] MARCH UK G.J., Methods of numerical mathematics, Springer, Berlin,l975.
[MOR 801 MoRTON K.W., PARROT! A.K., «Generalized Galerkin methods for first-order
hyperbolic equations >>, 1. Camp. Phy., 36. p. 249-270, 1980.
[PAR 90] PARK N.S., LIGCEIT J.A., «Taylor-least-squares finite clement for two dimensional
advection-diffusion problems >>, Int . ./. Nwn. Methods Flui., vol. II, p. 21-3K, 1990.
