Remark on the pressure boundary condition for the projection method. (English) Zbl 0738.76054

Summary: Much has been said about the pressure boundary condition for the projection method, which is different from the actual boundary condition satisfied by the pressure in the Navier-Stokes equations. In this short note we present a different point of view which resolves the difficulty and we show how this point of view agrees with previous results.


76M20 Finite difference methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
65N15 Error bounds for boundary value problems involving PDEs
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[1] J. Bell, P. Colella, and H. Glaz (1989).
[2] A.J. Chorin (1967), Bull. Amer. Math. Soc., 73, 928-931. · Zbl 0168.46501
[3] A.J. Chorin (1968a), Math. Comp., 22, 745-762.
[4] A.J. Chorin (1968b), Stud. Numer. Anal., 2, 64-71.
[5] A.J. Chorin (1969), Math. Comp., 23, 341-353.
[6] M. Fortin, R. Peyret, and R. Temam (1971), J. Méc., 10, 357-390.
[7] P.M. Gresho and S.T. Chan (1990), Internat. J. Numer. Methods Fluids, 11, 621-659. · Zbl 0712.76036
[8] J. Kim and P. Moin (1985), J. Comp. Phys., 59, 308-323. · Zbl 0582.76038
[9] S.A. Orszag, M. Israeli, and M. Deville (1986), J. Sci. Comp., 1.
[10] J. Shen (1991), An optimal error estimate of the projection method for the Navier-Stokes equations: First-order schemes, Preprint, Institute for Applied Mathematics and Scientific Computating, Indiana University. To appear in SIAM J. Numer. Anal.
[11] R. Temam (1966), C. R. Acad. Sci. Paris Sér. A, 262, 219-221; 263, 241-244, 265-267, 459-462.
[12] R. Temam (1968a), Bull. Soc. Math. France, 98, 115-152.
[13] R. Temam (1968b), Ann. Mat. Pura Appl. (4), LXXIV, 191-380.
[14] R. Temam (1969a), Arch. Rational Mech. Anal., 32, 135-153. · Zbl 0195.46001
[15] R. Temam (1969b), Arch. Rational Mech. Anal. 33, 377-385. · Zbl 0207.16904
[16] R. Temam (1977), Navier-Stokes Equations, North-Holland, Amsterdam. · Zbl 0383.35057
[17] J. Van Kan (1986), SIAM J. Sci. Statist. Comput., 7, 870-891. · Zbl 0594.76023
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