Hostname: page-component-77c89778f8-9q27g Total loading time: 0 Render date: 2024-07-22T13:25:33.506Z Has data issue: false hasContentIssue false
  • English
  • Français

Boundary conditions on artificial frontiers for incompressibleand compressible Navier-Stokes equations

Published online by Cambridge University Press:  15 April 2002

Charles-Henri Bruneau
Charles-Henri Bruneau*
Affiliation:
Mathématiques Appliquées de Bordeaux, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence, France. (bruneau@math.u-bordeaux.fr)
Get access

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.

Keywords

Navier-Stokes equationsartificial boundary conditions.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 2: Special issue for R. Teman's 60th birthday , March 2000 , pp. 303 - 314
Copyright
© EDP Sciences, SMAI, 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ph. Angot, Ch.-H. Bruneau and P. Fabrie, A penalization method to take into account obstacles in incompressible viscous flows. Numer. Math. 81 (1999).
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, Série II (1984).
Ch.-H. Bruneau, Numerical Simulation and Analysis of the Transition to Turbulence. 15th ICNMFD, Lect. Notes in Phys. 490 (1996).
Ch.-H. Bruneau, Numerical Simulation of incompressible flows and analysis of the solutions. CFD Review Vol. I (1998).
Ch.-H. Bruneau and E. Creusé, Towards a transparent boundary condition for compressible Navier-Stokes equations (submitted).
Ch.-H. Bruneau and P. Fabrie, Effective downstream boundary conditions for incompressible Navier-Stokes equations. Int. J. Numer. Methods in Fluids 19 (1994).
Ch.-H. Bruneau and P. Fabrie, New efficient boundary conditions for incompressible Navier-Stokes equations: a well-posedness result. Mod. Math. Anal. Num. 30 (1996).
Ch.-H. Bruneau, O. Greffier and H. Kellay, Numerical study of grid turbulence in two dimensions and comparison with experiments on turbulent soap films. Phys. Rev. E 60, No. 2, (1999).
J.P. Caltagirone, Sur l'interaction fluide-milieu poreux: application au calcul des efforts exercés sur un obstacle par un fluide visqueux. C.R. Acad. Sci. Paris 318, Série II, (1994).
J.R. Chasnov, The viscous-convective subrange in nonstationary turbulence. Phys. Fluids 10, No. 5, (1998).
T. Colonius, S.K. Lele and M. Parviz, Boundary conditions for direct computation of aerodynamic sound generation. AIAA journal 31 (1993).
B. Enquist and A. Majda, Absorbing boundary conditions for the numerical simulation of waves. Math. Comp. 31 (1977).
P.M. Gresho, Incompressible fluid dynamics: some fundamental formulation issues. Ann. Rev. Fluid Mech. 23 (1991).
H. Kellay, Ch.-H. Bruneau, A. Belmonte and X. L. Wu, Probability density functions of the enstrophy flux in two dimensional grid turbulence. Phys. Rev. Lett. (to appear).
H. Kellay, X.L. Wu and W. I. Goldburg, Experiments with turbulent soap films. Phys. Rev. Lett. 74 (1995).
H. Kellay, X.L. Wu and W.I. Goldburg, Vorticity measurements in turbulent soap films. Phys. Rev. Lett. 80 (1998).
H.O. Kreiss, Initial boundary value problems for hyperbolic systems. Comm. P. App. Math. 23 (1970).
M. Marion and R. Temam, Navier-Stokes equations: theory and approximation. Handbook of numerical analysis, Vol. VI, (1998).
T.J. Poinsot and S.K. Lele, Boundary conditions for direct simulations of compressible viscous flows. J. Comp. Phys. 101 (1992).
D.H. Rudy and J.C. Strikwerda, A nonreflecting outflow boundary condition for subsonic Navier-Stokes calculations. J. Comp. Phys. 36 (1980).
J.C. Strikwerda, Initial boundary value problems for incompletely parabolic systems. Comm. P. App. Math. 30 (1977).
R. Temam, Navier-Stokes equations and numerical analysis. North-Holland (1979).
B. Wasistho, B.J. Geurts and J.G.M. Kuerten, Simulation techniques for spatially evolving instabilities in compressible flows over a flat plate. Computers and Fluids 26 (1997).
C.H. Williamson, Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers. J. Fluid Mech. 206 (1989).