Boundary conditions on artificial frontiers for incompressible and compressible Navier-Stokes equations

Abstract

Abstract.Non reflecting boundary conditions on artificial frontiers of the domain are proposed for both incompressible and compressible Navier-Stokes equations. For incompressible flows, the boundary conditions lead to a well-posed problem, convey properly the vortices without any reflections on the artificial limits and allow to compute turbulent flows at high Reynolds numbers. For compressible flows, the boundary conditions convey properly the vortices without any reflections on the artificial limits and also avoid acoustic waves that go back into the flow and change its behaviour. Numerical tests illustrate the efficiency of the various boundary conditions. Mathematics Subject Classification. 35Q30, 65C20, 65M99. Résumé. Leséquations de

Revisiting open boundary conditions from the point of view of characteristic variables

“…Note also that several possible improvements have been proposed, which need to be extended to realistic test cases : generalized characteristic variables (Lie, 2001), absorbing conditions taking into account the viscous terms (Halpern, 1991), transmission (or weak formulation) methods (Bruneau andFabrie, 1994, 1996).…”

On pressure boundary conditions for steady flows of incompressible fluids with pressure and shear rate dependent viscosities

“…including (5.1) were proposed (for unsteady incompressible Navier-Stokes equations) in order to perform long-time simulations at high Reynolds numbers. See also [4], [5], [7]. Note that b 1 given by (5.1) meets (B1), (B2) with γ 1 = 3 and…”

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

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