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Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series B Année : 2007

Outflow boundary conditions for the incompressible non-homogeneous Navier-Stokes equations

Résumé

In this paper we propose the analysis of the incompressible non-homogeneous Navier-Stokes equations with nonlinear outflow boundary condition. This kind of boundary condition appears to be, in some situations, a useful way to perform numerical computations of the solution to the unsteady Navier-Stokes equations when the Dirichlet data are not given explicitly by the physical context on a part of the boundary of the computational domain. The boundary condition we propose, following previous works in the homogeneous case, is a relationship between the normal component of the stress and the outflow momentum flux taking into account inertial effects. We prove the global existence of a weak solution to this model both in 2D and 3D. In particular, we show that the nonlinear boundary condition under study holds for such a solution in a weak sense, even though the normal component of the stress and the density may not have traces in the usual sense.
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Dates et versions

hal-00112113 , version 1 (07-11-2006)

Identifiants

Citer

Franck Boyer, Pierre Fabrie. Outflow boundary conditions for the incompressible non-homogeneous Navier-Stokes equations. Discrete and Continuous Dynamical Systems - Series B, 2007, 7 (2), pp 219-250. ⟨10.3934/dcdsb.2007.7.219⟩. ⟨hal-00112113⟩
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