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Boundary conditions on artificial frontiers for incompressible and compressible Navier-Stokes equations. (English) Zbl 0954.76014
Summary: We propose non-reflecting boundary conditions on artificial boundaries for 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 boundaries and allow to compute turbulent flows at high Reynolds numbers. For compressible flows, the boundary conditions also convey properly the vortices without reflections on the artificial boundaries and additionally avoid the creation of acoustic waves that go back into the flow and change its behaviour. Numerical tests illustrate the efficiency of various boundary conditions.

MSC:
76D05 Navier-Stokes equations for incompressible viscous fluids
35Q30 Navier-Stokes equations
76N15 Gas dynamics (general theory)
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References:
[1] Ph. Angot, Ch.-H. Bruneau and P. Fabrie, A penalization method to take into account obstacles in incompressible viscous flows. Numer. Math.81 (1999). · Zbl 0921.76168
[2] 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. Paris299, Série II (1984).
[3] Ch.-H. Bruneau, Numerical Simulation and Analysis of the Transition to Turbulence. 15th ICNMFD, Lect. Notes in Phys.490 (1996).
[4] Ch.-H. Bruneau, Numerical Simulation of incompressible flows and analysis of the solutions. CFD Review Vol. I (1998). Zbl0945.76057 · Zbl 0945.76057
[5] Ch.-H. Bruneau and E. Creusé, Towards a transparent boundary condition for compressible Navier-Stokes equations (submitted). Zbl1017.76050 · Zbl 1017.76050
[6] Ch.-H. Bruneau and P. Fabrie, Effective downstream boundary conditions for incompressible Navier-Stokes equations. Int. J. Numer. Methods in Fluids19 (1994). Zbl0816.76024 · Zbl 0816.76024
[7] 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). Zbl0865.76016 · Zbl 0865.76016
[8] 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. E60, No. 2, (1999).
[9] 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. Paris318, Série II, (1994). Zbl0795.76080 · Zbl 0795.76080
[10] J.R. Chasnov, The viscous-convective subrange in nonstationary turbulence. Phys. Fluids10, No. 5, (1998). · Zbl 1185.76743
[11] T. Colonius, S.K. Lele and M. Parviz, Boundary conditions for direct computation of aerodynamic sound generation. AIAA journal31 (1993). · Zbl 0785.76069
[12] B. Enquist and A. Majda, Absorbing boundary conditions for the numerical simulation of waves. Math. Comp.31 (1977). · Zbl 0367.65051
[13] P.M. Gresho, Incompressible fluid dynamics: some fundamental formulation issues. Ann. Rev. Fluid Mech.23 (1991). · Zbl 0717.76006
[14] 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).
[15] H. Kellay, X.L. Wu and W. I. Goldburg, Experiments with turbulent soap films. Phys. Rev. Lett.74 (1995).
[16] H. Kellay, X.L. Wu and W.I. Goldburg, Vorticity measurements in turbulent soap films. Phys. Rev. Lett.80 (1998).
[17] H.O. Kreiss, Initial boundary value problems for hyperbolic systems. Comm. P. App. Math.23 (1970). · Zbl 0193.06902
[18] M. Marion and R. Temam, Navier-Stokes equations: theory and approximation. Handbook of numerical analysis, Vol. VI, (1998). · Zbl 0921.76040
[19] T.J. Poinsot and S.K. Lele, Boundary conditions for direct simulations of compressible viscous flows. J. Comp. Phys.101 (1992). · Zbl 0766.76084
[20] D.H. Rudy and J.C. Strikwerda, A nonreflecting outflow boundary condition for subsonic Navier-Stokes calculations. J. Comp. Phys.36 (1980). · Zbl 0425.76045
[21] J.C. Strikwerda, Initial boundary value problems for incompletely parabolic systems. Comm. P. App. Math.30 (1977). · Zbl 0351.35051
[22] R. Temam, Navier-Stokes equations and numerical analysis. North-Holland (1979). · Zbl 0426.35003
[23] 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 Fluids26 (1997). · Zbl 0962.76067
[24] 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).
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