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Boundary conditions for incompressible flows. (English) Zbl 0648.76023

Summary: A general framework is presented for the formulation and analysis of rigid no-slip boundary conditions for numerical schemes for the solution of the incompressible Navier-Stokes equations. It is shown that fractional-step (splitting) methods are prone to introduce a spurious numerical boundary layer that induces substantial time differencing errors. High-order extrapolation methods are analyzed to reduce these errors. Both improved pressure boundary condition and velocity boundary condition methods are developed that allow accurate implementation of rigid no-slip boundary conditions.

MSC:

76D10 Boundary-layer theory, separation and reattachment, higher-order effects
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[1] Chorin, A. J. (1968).Math. Comp. 23, 341-354.
[2] Fortin, M., Peyret, R., and Temam, R. (1971).J. Mecanique 10, 357-390.
[3] Gottlieb, D., and Orszag, S. A. (1977). InNumerical Analysis of Spectral Methods, SIAM, Philadelphia. · Zbl 0412.65058
[4] Gottlieb, D., Hussaini, M. Y., and Orszag, S. A. (1984). In Voigt, R. G., Gottlieb, D., and Hussaini, M. Y. (eds.),Spectral Methods for Partial Differential Equations, SIAM, Philadelphia, pp. 1-54. · Zbl 0599.65079
[5] Harlow, F. H., and Welch, J. E. (1965).Phys. Fluids 8, 2182-2189. · Zbl 1180.76043
[6] Kim, J., and Moin, P. (1985).J. Comp. Phys. 59, 308-323. · Zbl 0582.76038
[7] Kleiser, L., and Schumann, U. (1980). In Hirscheil, E.H.,Proceedings Third GAMM Conference on Numerical Methods in Fluid Dynamics, Vieweg, Braunschweig, pp. 165-173.
[8] Marcus, P. S. (1984).J. Fluid Mech. 146, 45-64. · Zbl 0561.76037
[9] Moin, P., and Kim, J. (1980).J. Comp. Phys. 35, 381. · Zbl 0425.76027
[10] Orszag, S. A., and Israeli, M. (1974).Annu. Rev. Fluid Mech. 5, 281-318.
[11] Orszag, S. A., and Kells, L. (1980).J. Fluid Mech. 96, 159-205. · Zbl 0418.76036
[12] Temam, R. (1979).Navier-Stokes Equations, North-Holland, Amsterdam.
[13] Yanenko, N. N. (1971).The Method of Fractional Steps, Springer, New York. · Zbl 0209.47103
[14] Zang, T., and Hussaini, M. Y. (1986).Appl. Math. Comp., to appear.
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