Mise en reuvre d'une methode de volumes de controle a maillages non structures pour le calcul de modes propres acoustiques
Keywords:
control volume, finite element, acoustic, eigenvalueAbstract
This paper is devoted to the presentation of a control volume based finite element method (CVFEM). Its implementation is explicitedfor both Helmholtz and primitive variable formulations for planar and spatial problems. Application for solving acoustical eigenmode shows that the CVFEM is at least as accurate as the Galerkin FEM.
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References
[AST 79] ASTLEY R.J. and EVERSMAN W., <
in lined ducts with flow>>. J. Sound. Vib., vol. 65(1), 1979, p. 61-74.
[BAL 83] B.R.BALIGA, S.V.PATANKAR, «A Control Volume Finite-Element Method for
Two-Dimensional Fluid Flow and Heat Transfer>>, Num. Heat Transf., Vol. 6, p. 245-
, 1983.
[BAN 89] J. BANASZEK, <
ElementMethods for Diffusion-Type Problems>>, Num. Heat Transf, Part 8, vol. 16, p.
-78, 1989.
[BRI 62] J.F.BRIDGE and S.W. ANGRIST, <
J~ (X). Y~ (px)- J~ (px).Y~ (X)= 0 >>, Math.Comput. 16, p.198-204, 1962
[CRA 72] A. CRAGGS, «The use of simple three-dimensional finite elements for
determining the natural modes and frequencies of complex shaped enclosures>>, J. So.
And Vib., 23, p. 331-339, 1972.
[DHA 84] G.DHATT, G.TOUZOT, « Une presentation de Ia methode des elements finis>>,
Maloine. 1984.
[HOO 881] N. A. HOOKEY, B. R. BALIGA AND C. PRAKASH, << Evaluation and
Enhancements of Some Control-Volume Finite-Element Methods-Part I. ConvectionDiffusion
Problems>> , Num Heat Transf, vol. 14, p. 255-272,1988.
[HOO 882] N. A. HOOKEY AND B. R. BALIGA: <
Control-Volume Finite-Element Methods-Part 2. Incompressible Fluid Flow Problems>>,
Num. Heat Transf, vol. 14, p. 273-293, 1988.
[KET 89] C. F. KETTLEBOROUGH, S. R. HUSSAIN AND C. PRAKASH, << Solution of
Fluid Flow Problems with the Vorticity-Streamfunction Formulation and the Control
Volume-Based Finite-Element Method», Num. Heat Transf, Part B, vol. 16, p. 31-58,
[KRA 92] M. S. KRAKOV, <
Equations in Vortex-Streamfunction Formulation>>, Num. Heat Transf, Part B, vol. 21,
p. 125-145, 1992.
[PET 76] M. PETYT, J. LEA AND G. H. KOOPMANN, <
determining the acoustic modes of irregular shaped cavities >>, J. So. and Vib., 45, p. 495-
, 1976.
[PRI 93] J.P.PRIOU, E.REDON, Y.GERVAIS, and J.L.PEUBE, « Calcul des modes
acoustiques en milieu inhomogene par Ia methode des elements finis >> Proc.Inst of
Acoustics (UK) 1993, vol.l5 (3), p. 909-916.
[RAM 80] S. RAMADHYANI AND S. V. PATANKAR, <
equation: compariason of the Galerkin and control-volume methods>>, Int. J. for Num.
Meth. in Engineering, vo115, p. 1395-1418, 1980.
[SAD 97] H. SADAT, P.SALAGNAC, << Calcul des flux en parois presentant des
singularites >>,Int. Journal of Heat and Mass Transfer, vol. 40 n°18, p. 4255-4262, 1997.
[STE 72] G. W. STEWART, <>, SIAM J. Num.
Anal., 9(4):669-686, 1972.
[WHI 79] J. H. WILKINSON, «Kronecker's canonical form and the QZ algorithm>>, Lin.
AI g. Appl., 28:285-303, 1979.
