Boundary layer for a penalization method for viscous incompressible flow

Advances in Differential Equations

Volumn 8, Issue 12, 2003, Pages 1453-1480

  Carbou, Gilles ^a   Fabrie, Pierre ^a  

^a UNIVERSITÉ BORDEAUX 1   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4344692753     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (23)

1. Ph. Angot and J.P. Caltagirone, Natural convection through periodic porous media, Proceeding 9th Int. Heat Transfer Conf., Jerusalem, Hemisphere, 5 (1990), 219-224.
2. Ph. Angot, Analysis of singular perturbation on the Brinkman problem for fictitious domain models of viscous flow, Math. Methods Appl. Sci., 22 (1999), 1395-1412.
3. Ph. Angot, C.-H. Bruneau, and P. Fabrie, A penalization method to take into account obstacles in incompressible viscous flows, Numer. Math., 81 (1999), 497-520.
4. E. Arquis and J.P. Caltagirone, Sur les conditions hydrodynamiques au voisinage d'une interface milieu fluide-milieu poreux: application à la convection naturelle, C.R. Acad. Sci Paris, 299, No 1, Série II (1984), 1-4.
5. Ch.-H. Bruneau, Numerical simulation and analysis of the transition to turbulence, Lecture Notes in Physics, 490 (1997).
6. Ch.-H. Bruneau and P. Fabrie, Effective downstream boundary conditions for incompressible Navier-Stokes equations, Int. J. Numer. Methods in Fluids, 19 (1994), 693-705.
7. Ch.-H. Bruneau and P. Fabrie, New efficient boundary conditions for incompressible Navier-Stokes equations: a well-posedness result, M2AN, 30 (1996), 815-840.
8. Ch.-H. Bruneau and I. Mortazavi, Contrôle passif d'écoulemnts incompressibles autour d'obstacles à l'aide de milieux poreux, C. R. Acad. Sci. Paris, 329, série II (2001), 517-521.
9. V. Bruneau and G. Carbou, Asymptotic expansion for large limit coupling, Asymptot. Anal., 29 (2002), 91-113.
10. G. Carbou, P. Fabrie, and O. Guès, Couches limites dans un modèle de ferromagn étisme, Comm. Partial Differential Equations, 27 (2002), 1467-1495.
11. J.P. Caltagirone, Sur l'interaction fluide-milieux poreux: application au calcul des efforts exercés sur un obstacle par un fluide visqueux, C. R. Acad. Sci. Paris, 318 Série II (1994), 571-577.
12. L. Cattabriga, Su un problema al contorno relativo al sistema di equazioni di Stokes, Rend. Semin. Mat. Univ. Padova, 31 (1961), 308-340.
13. P. Constantin and C. Foias, "Navier-Stokes Equations," Chicago Lectures in Mathematics, University of Chicago Press, 1988.
14. D. Goldstein, R. Handler, and L. Sirovich, Modeling a no-slip flow boundary with an external force field, J. Comput. Phys, 105 (1993), 354-366.
15. E. Grenier and O. Guès, Boundary layers for viscous perturbations of noncharacteristic quasilinear hyperbolic problems, J. Differential Equations 143 (1998), 110-146.
16. K. Khadra, S. Parneix, Ph. Angot, and J.P. Caltagirone, Fictitious domain approach for numerical modeling of Navier-Stokes equation, Int. J. Numer. Meth. in Fluids, 34 (2000), 651-684.
17. N. Kevlahan and J.M. Ghidaglia, Computation of turbulent flow past an array of cylinders using a spectral method with Brinkman penalization, Eur. J. Mech., B, Fluids, 20 (2001), 333-350.
18. J.L. Lions, "Quelques méthodes de résolution de problèmes aux limites non linéaires," Dunod, Paris, 1969.
19. C. Peskin, Numerical analysis of blood flow in the heart, J. Comput. Phys., 25 (1977), 220-252.
20. C. Peskin, The fluid dynamics of heart valves: Experimental, theoretical and comptutational method, Annu. Rev. Fluid Mech., 14 (1982), 235-259.
21. E.M. Saiki and S. Biringen, Numerical simulation of a cylinder in uniform flow: application of a virtual boundary method, J. Comput. Phys., 123 (1996), 450-465.
22. L. Tartar, Topics in nonlinear analysis, preprint, Orsay (1978).
23. R. Temam, "Navier-Stokes Equations and Numerical Analysis," North-Holland, Amsterdam, 1979.