Une methode d'elements finis pour le calcul des ecoulements compressibles utilisant les variables conservatives et Ia methode SUPG

Authors

  • Azzeddine Soulaimani Ecole de technologie superieure Universite du Quebec, departement de genie mecanique 4750 avenue Henri-Julien Montreal, H2T 2C8, Canada
  • Nacer-Eddine Elkadri Elyamani Universite Laval, departement de genie mecanique Ecole de technologie superieure, departement de genie mecanique
  • Claire Deschenes Universite Laval, departement de genie mecanique Ste-Foye, GJK 7P4, Canada

Keywords:

Navier-Stokes and Euler equations, conservation variables, SUPG, shock capturing, engine intake

Abstract

The Navier-Stokes and Euler equations are solved in a conservative form and using the conservation variables. The variational formulation and the corresponding finite element approximations are discussed. For high speed flows, the numerical model has to be stabilized. We used a SUPG method along with a shock capturing operator. The stabilization techniques and the solution algorithm are described. Some numerical tests are carried out to validate the code. This model is employed to simulate the flow in an engine intake.

 

Downloads

Download data is not yet available.

References

T.J .R. Hughes and T.E. Tezduyar, Finite element methods for first-order

hyperbolic systems with particular emphasis on the compressible Euler equations.

Computer Methods in Applied Mechanics and Engineering, 45 (1984)

-284.

T.J .R. Hughes, L.P. Franca and M. Mallet, A new finite element formulation

for computational fluid dynamic: I. Symmetric forms of the compressible

Euler and N avier-Stokes equations and the second law of the thermodynamics.

Computer Methods in Applied Mechanics and Engineering, 54 (1986) 223-234.

0. Pironneau, On the transport-diffusion algorithm and its applications to

the Navier-Stokes equation. Num. Math. 38 (1982) 309-332.

J. Donea, A Taylor-Galerkin method for conservative transport problems.

Internat. J. Numer. Methods Engrg. 20 (1984) 101-120.

A.N. Brooks, T.J .R. Hughes, Streamline upwind Petrov-Galerkin formulations

for convection dominated flows with particular emphasis on the compressible

N avier-Stokes equations, Computer Methods in Applied Mechanics

and Engineering, 32 (1982) 199-259.

M.-0. Bristeau, R. Glowinski and J. Periaux, Numerical methods for the

Navier-Stokes equations. Applications to the simulation of compressible and

incompressible viscous flows, Computer Physics Report, 6, North Holland, Amsterdam,

(1987) 73-187.

N .E. E. Elkadri, Modelisation des ecoulements compressibles visqueux par

Ia methode des elements finis. Memoire de maitrise, Universite Laval, Quebec,

Canada (1992).

A. Soulaimani and M. Fortin, Finite element solution of compressible viscous

flows using conservative variable. To appear in: Computer Methods in Applied

Mechanics and Engineering.

M. Fortin, H. Manouzi and A. Soulaimani, On finite element approximations

and stabilization methods for compressible viscous flows. International Journal

of Numerical Methods in fluids, vol. 17, no 6, (1993) 477-499.

G.J. Le Beau, S.E. Ray, S.K. Aliabadi and T.E. Tezduyar, SUPG finite

element computation of compressible flows with the entropy and conservation

variables formulations. Computer Methods in Applied Mechanics and Engineering,

(1993) 397-422.

(11] M.-0. Bristeau, R. Glowinski, L. C. Dutto, J. Periaux and G. Roge, Compressible

viscous flow calculations using compatible finite element approximations.

International Journal of Numerical Methods in fluids, 11 (1990) 719-749.

(12] 0. Pironneau and J. Rappaz, Numerical analysis for compressible viscous

abiabatic stationary flows. Impact of Computing in Science and Engineering,

Academic Press, Boston, MA, 1, (1989) 109-137.

(13] M. Fortin and A. Soulaimani, Finite element approximation of compressible

viscous flows, Proc. Compt. Meth. in Flow Analysis, 2, in H. Niki and M.

Kawahara (eds.), Okayama University of Sciences Press, (1988) 951-956.

(14] D .N. Arnold, F. Brezzi and M. Fortin, A stable finite element for the Stokes

equations. Calcolo 23 (1984), 337-344.

(15] A. Soulaimani, M. Fortin, Y. Ouellet, G. Dhatt and F. Bertrand, Simple

continuous pressure elements for two- and three-dimensional incompressible

flows. Computer Methods in Applied Mechanics and Engineering, 62 (1987)

-69.

F. Brezzi, M.O. Bristeau, L.P. Franca, M. Mallet and G. Roge, A relationship

between stabilized finite element methods and the Galerkin Method with

bubble functions. Computer Methods in Applied Mechanics and Engineering,

(1992) 117-129.

A. Soulaimani, Contribution a la resolution numerique des problemes hydrodynamiques

a surface libre. These de Ph.D., Universite Laval, 1987.

R. Lohner, K. Morgan and J. Peraire, A simple extension to multidimensional

problems of the artificial viscosity due to Lapidus. Comm. Appl. Numer.

Methods, 1 (1985) 141- 147.

(19] M. Mallet," A finite element method for computational fluid dynamics,"

Ph.D. Thesis, Division of Applied Mechanics, Stanford University, CA, 1985.

F. Shakib," Finite element analysis of the compressible Euler and NavierStokes

equations,"Ph.D. Thesis, Division of Applied Mechanics, Stanford University,

CA, 1989.

Y. Saad and M. H. Schultz, GMRES: a generalized minimal residual algorithm

for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comp., 7

(1986) 856-869.

Z. Johan, T.J.R. Hughes and F. Shakib, A globally convergent matrix-free

algorithm for implicit time-marching schemes arising in finite element analysis

in fluids. Computer Methods in Applied Mechanics and Engineering, 87 (1991)

-304.

L. Cambier, Computation of Viscous Transonic Flows Using and Unsteady

Type Method and a Zonal Grid Refinement Technique, O.N.E.R.A, France,

(1985).

A. Rizzi and H. Viviand editors, Numerical methods for the computation

of inviscid transonic flows with shock waves, a GAMM-Workshop. Volume 3

of notes on numerical fluid mechanics, Vieweg Verlag, 1981.

F .Fortin, Simulation d'ecoulements compressibles non-visqueux et visqueux

par les methodes de fractionnement des flux. These de doctorat, Universite de

Sherbrooke, 1991.

T. J. Barth. Computational fluid dynamics, on unstructured grids and

solvers. von Karman Institute for fluid dynamics, NASA Ames Research Center,

USA, Lecture Series 1990-03, March 5-9, 1990.

A. Soulaimani, D. Chasse and L. Lamarche, Simple adaptive mesh method

for compressible flows. Accepted for the Eleventh Canadian Symposium on

Fluid Dynamics, Edmonton, 1994.

Downloads

Published

1994-02-27

How to Cite

Soulaimani, A. ., Elyamani, N.-E. E. ., & Deschenes, C. . (1994). Une methode d’elements finis pour le calcul des ecoulements compressibles utilisant les variables conservatives et Ia methode SUPG. European Journal of Computational Mechanics, 3(2), 211–245. Retrieved from https://journals.riverpublishers.com/index.php/EJCM/article/view/3623

Issue

Section

Original Article