[Techniques de calcul numérique pour frontières mobiles]
La méthode eulerienne–lagrangienne offre une approche populaire et efficace pour traiter des problèmes multi-fluidiques comportant des variations de forme. Spécialement, quand l'interface est considérée comme une discontinuité, consistante avec la théorie du milieu continu, ou comme une transition continue rapide, réduisant les difficultés numériques pour marquer les différentes régions. Dans ce papier, des éclaircissements sont apportés sur la performance des deux techniques. Sur le plan numérique, les deux approches sont développés sur des concepts similaires, l'interface est représentée par des marqueurs soumis à l'advection dans le sens lagrangien et les équations de conservation de la masse, de la quantité de mouvement et de l'énergies sont résolues sur une grille cartésienne fixe (eulerienne) à l'aide d'une méthode de projection de second ordre. La différence essentielle réside dans la manière de prendre en compte les conditions de transmission à l'interface. La méthode où l'interface est considérée comme une discontinuité demande un effort supplémentaire au sens numérique parce que le champ de vitesses dans chaque zone doit être couplé avec ceux dans les autres matériaux/phases, en assurant explicitement les conditions de transmission à l'interface par des procédures de raccordement. Par contre, une précision de second ordre pent être obtenue en comparaison avec le premier ordre de la méthode de l'interface continue. Néanmoins, pour des applications physiques, les deux approches peuvent être très efficaces pour traiter une variété de problèmes multi-fluides qui comportent des frontières mobiles. Plusieurs exemples sont apportés pour illustrer les performances des deux techniques.
The Eulerian–Lagrangian method is a popular and effective approach for handling multi-fluid problems involving substantial shape variations. Specifically, one can consider the interface either as a sharp discontinuity, consistent with the fundamental continuum theory, or as a smooth transition zone, reducing numerical difficulties in tracking distinct regions. In this article, we highlight the performance characteristics of both techniques. Computationally, both approaches can be devised using similar concepts, namely, the interface is represented by marker points and advected in a Lagrangian framework, and the mass, momentum, and energy conservation equations are solved on a fixed (Eulerian) Cartesian grid using a second-order projection method. The main difference lies in the way of accounting for the interfacial conditions and communication across the interface. The sharp interface method is more demanding computationally because the field equations in each zone need to be coupled with those in other materials/phases, by explicitly tracking the interfacial conditions via matching procedures. In return, second-order accuracy can be attained as compared to the first-order accuracy in the continuous interface method. Nevertheless, in physical applications, both approaches can be highly effective in handling a variety of multi-fluid problems involving moving boundaries. Several examples are presented to highlight the various performance characteristics of the two techniques.
Mot clés : Mécanique des fluides numérique, Problèmes des frontières mobiles, Système multiphase
@article{CRMECA_2004__332_5-6_375_0,
author = {Wei Shyy},
title = {Multiphase computations using sharp and continuous interface techniques for micro-gravity applications},
journal = {Comptes Rendus. M\'ecanique},
pages = {375--386},
publisher = {Elsevier},
volume = {332},
number = {5-6},
year = {2004},
doi = {10.1016/j.crme.2004.02.014},
language = {en},
}
Wei Shyy. Multiphase computations using sharp and continuous interface techniques for micro-gravity applications. Comptes Rendus. Mécanique, Volume 332 (2004) no. 5-6, pp. 375-386. doi : 10.1016/j.crme.2004.02.014. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.02.014/
[1] Numerical solution of free boundary problems in fluid mechanics, Parts I, II, III, J. Fluid Mech., Volume 148 (1984), pp. 1-43
[2] Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys. Fluids, Volume 8 (1965), pp. 2182-2189
[3] Effect of dynamic perturbation and contact condition on edge-defined fibre growth characteristics, Int. J. Heat Mass Transfer, Volume 37 (1994), pp. 977-987
[4] Computational Fluid Dynamics with Moving Boundaries, Hemisphere, Washington, DC, 1996
[5] Numerical analysis of blood flow in the heart, J. Comput. Phys., Volume 25 (1977), pp. 220-252
[6] Volume-of-fluid interface tracking with smoothed surface stress methods for three-dimensional flows, J. Comput. Phys., Volume 152 (1999), pp. 423-456
[7] Computational Modeling for Fluid Flow and Interfacial Transport, Elsevier, Amsterdam, Netherlands, 1994
[8] Moving boundaries in micro-scale biofluid dynamics, Appl. Mech. Rev., Volume 54 (2001), pp. 405-453
[9] Fronts propagating with curvature dependent speed: alogorithms based on Hamilton–Jacobi formulations, J. Comput. Phys., Volume 79 (1988), pp. 12-49
[10] Micro-scale drop dynamics for heat transfer enhancement, Prog. Aerospace Sci., Volume 38 (2002), pp. 275-304
[11] Accuracy and convergence of continuum surface-tension models (W. Shyy; R. Narayanan, eds.), Fluid Dynamics at Interfaces, Cambridge University Press, 1999
[12] Volume of fluid and immersed boundary investigations of a single rising droplet, 41st Aerospace Sciences Meeting & Exhibit, 2003 (Paper No. 2003-1282)
[13] The immersed interface method for elliptic equations with discontinuous coefficients and singular sources, SIAM J. Numer. Anal., Volume 31 (1994), p. 1019
[14] ELAFINT: a mixed, Eulerian–Lagrangian method for fluid flows with complex and moving boundaries, Int. J. Numer. Methods Fluids, Volume 22 (1996), pp. 691-712
[15] Computation of solid–liquid phase fronts in the sharp interface limit on fixed grids, J. Comput. Phys., Volume 153 (1999), pp. 535-574
[16] A fixed-grid, sharp-interface method for bubble dynamics and phase change, J. Comput. Phys., Volume 174 (2001), pp. 781-815
[17] An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries, J. Comput. Phys., Volume 156 (1999), pp. 209-240
[18] Curves and Surface for Computer-Aided Geometric Design, A Practical Guide, Academic Press, 1997
[19] D.B. Kothe, W.J. Rider, S.J. Mosso, J.S. Brock, J.I. Hochstein, Volume tracking of interfaces having surface tension in two and three dimensions, AIAA paper 96-0859, 1996
[20] T. Ye, W. Shyy, C.-F. Tai, J.N. Chung, Assessment of a sharp interface method for drop in equilibrium, Comput. & Fluids, in press
[21] The recoiling of liquid droplets upon collision with solid surfaces, Phys. Fluids, Volume 13 (2001), pp. 643-659
[22] Computations of drop dynamics with the immersed boundary method; Part 2 – Drop impact and heat transfer, Numer. Heat Transfer Part B, Volume 44 (2003), pp. 101-118
[23] Multigrid computations with the immersed boundary technique for multiphase flows, Int. J. Numer. Methods Heat and Fluid Flow, Volume 14 (2004), pp. 98-115
Cité par Sources :
Commentaires - Politique
The structure and mechanical properties of dragonfly wings and their role on flyability
Jiyu Sun; Bharat Bhushan
C. R. Méca (2012)