zbMATH — the first resource for mathematics

New efficient boundary conditions for incompressible Navier-Stokes equations: A well-posedness result. (English) Zbl 0865.76016
Summary: Efficient natural conditions on open boundaries for incompressible flows are derived from a weak formulation of Navier-Stokes equations. Energy estimates in velocity-pressure formulation are established from a mixed formulation, and a rigorous proof of existence of solutions is given. As an illustration, the conditions are written down for the flow behind an obstacle in a channel. Moreover, numerical tests have shown the accuracy and robustness of such conditions.

76D05 Navier-Stokes equations for incompressible viscous fluids
35Q30 Navier-Stokes equations
Full Text: DOI EuDML
[1] R. A. ADAMS, 1975, Sobolev spaces, Academic press, New-York. Zbl0314.46030 MR450957 · Zbl 0314.46030
[2] C. BÈGUE, C. CONCA, F. MURAT and O. PIRONNEAU, 1987, A nouveau sur les équations de Stokes et de Navier-Stokes avec des conditions aux limites sur la pression, C. R. Acad. Sci. Parts, 304 série I, pp. 23-28. Zbl0613.76029 MR878818 · Zbl 0613.76029
[3] Ch.-H. BRUNEAU and P. FABRIE, 1994, Effective downstream boundary conditions for incompressible Navier-Stokes equations. Int. J. for Num. Methods in Fluids, 19, pp. 693-705. Zbl0816.76024 · Zbl 0816.76024
[4] C. CONCA, 1984, Approximation de quelques problèmes de type Stokes par une méthode d’éléments finis mixtes. Numer. Math., 45, pp. 75-91. Zbl0523.34009 MR761881 · Zbl 0523.34009
[5] G. DUVAUD, J. L. LIONS, 1972, Les inéquations en mécanique et en physique, Dunod. Zbl0298.73001 MR464857 · Zbl 0298.73001
[6] V. GlRAULT et P. A. RAVIART, 1986, Finite elements method for Navier Stokes equations, Springer Series in Computational Mathematics. MR851383
[7] P. M. GRESHO, 1991, Incompressible fluid dynamics: Some fundamental formulation issues. Annu. Rev. Fluid Mech., 23, pp. 413-453. Zbl0717.76006 MR1090333 · Zbl 0717.76006
[8] L. HALPERN, 1986, Artificial boundary conditions for the linear advection diffusion equation, Math. Comp., 46, pp. 425-438. Zbl0649.35041 MR829617 · Zbl 0649.35041
[9] L. HALPERN and M. SCHATZMAN, 1989, Artificial boundary conditions for incompressible viscous flows. SIAM J. Math. Anal., 20, pp. 308-353. Zbl0668.76048 MR982662 · Zbl 0668.76048
[10] J. L. LIONS, 1979, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris. Zbl0189.40603 · Zbl 0189.40603
[11] R. PEYRET and B. REBOURCET, 1982, Développement de jets en fluides stratifiés, Journal de Mécanique Théorique et Appliquée, 1, pp. 467-491. Zbl0543.76014 · Zbl 0543.76014
[12] O. PIRONNEAU, 1986, Conditions aux limites sur la pression pour les équations de Stokes et de Navier-Stokes, C. R. Acad. Sci. Paris, 303, série I, pp. 403-40. Zbl0613.76028 MR862203 · Zbl 0613.76028
[13] R. TEMAM, 1993, Navier-Stokes Equations and Nonlinear Functional Analysis, Regional conference series in applied mathematics. Zbl0833.35110 · Zbl 0833.35110
[14] R. TEMAM, 1979, Navier-Stokes Equations and numencal Analysis, 2nd ed. North-Holland, Amsterdam. Zbl0426.35003 MR603444 · Zbl 0426.35003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.