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Effective boundary conditions for laminar flows over periodic rough boundaries. (English) Zbl 0917.76013
Summary: We propose effective boundary conditions or wall laws for a laminar flow over a rough wall with periodic roughness elements. These effective conditions are posed on a regularized boundary which allows to avoid the details of the wall and dramatically reduces computational cost. The effective conditions stem from an asymptotic expansion of the solution, which is presented here. Both first- and second-order conditions are discussed and tested numerically on two-dimensional cases. $$\copyright$$ Academic Press.

##### MSC:
 76D05 Navier-Stokes equations for incompressible viscous fluids 35B27 Homogenization in context of PDEs; PDEs in media with periodic structure 76M10 Finite element methods applied to problems in fluid mechanics
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##### References:
 [1] Achdou, Y., Effet d’un mince revêtement métallisé sur la réflexion d’une onde électromagnétique, C.R. acad. sci. Paris Sér. I, 314, 217, (1992) · Zbl 0800.78017 [2] Achdou, Y.; Pironneau, O., Analysis of wall laws, C.R. acad. sci. Paris Sér. I, 320, 541, (1995) · Zbl 0834.76014 [3] Achdou, Y.; Letallec, P.; Pironneau, O.; Valentin, F., Constructing wall laws with domain decomposition or asymptotics expansion techniques, Comput. methods appl. mech. eng., 151, 215, (1997) · Zbl 0920.76063 [4] Artola, M.; Cessenat, M., Diffraction d’une onde électromagnétique par une couche composite mince accolée à un conducteur épais, C.R. acad. sci. Paris Sér. I, 313, 231, (1991) · Zbl 0743.35081 [5] Benssousan, A.; Lions, J.L.; Papanicolaou, G., Asymptotic analysis for periodic structures, (1983) [6] Carrau, A., Modélisation numérique d’ un écoulement sur paroi rugueuse, (1992) [7] Carrau, A.; Gallice, G.; Letallec, P., Taking into account surface roughness in computing hypersonic reentry bodies, Applied sciences and engineering, 331, (1992) [8] G. Dury, Alziary, de Roquefort, Couche limite turbulente sur paroi rugueuse en regime supersonique, 1995 [9] Fournier, R., Vigie user guide, (1997) [10] Franca, L.P.; Frey, S.L., Stabilized finite element methods. II. the incompressible navier – stokes equations, Comput. methods appl. mech. engrg., 99, 209, (1992) · Zbl 0765.76048 [11] Glikson, F., Couche limite sur paroi rugueuse, (1996) [12] Hughes, T.J.R., The finite element method, (1987) [13] Keller, J.B., Removing small features from computational domains, J. comput. phys., 113, 148, (1994) · Zbl 0805.65111 [14] Landau, L.; Lifschitz, F., Fluid mechanics, (1953) [15] J. Nikuradse, Law of flow in rough pipe, Technical report, National advisory commitee for aeronautics, 1929 [16] Saad, Y., Numerical methods for large eigenvalue problems, (1992) · Zbl 0991.65039 [17] Sanchez-Palencia, E., Nonhomogeneous media and vibration theory, (1987) · Zbl 0637.73016 [18] F. Valentin, Université Paris 6, 1998 [19] F. Valentin, Méthode d’élement finis stabilisée pour les équations de Navier-Stokes incompressibles avec des conditions aux limites équivalentes
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