×

zbMATH — the first resource for mathematics

The numerical solution of the Navier-Stokes equations for 3-dimensional, unsteady, incompressible flows by compact schemes. (English) Zbl 0667.76051
This paper describes a numerical method for solving the Navier-Stokes equations for unsteady, incompressible, 3-dimensional flows using velocity-vorticity variables and irregular Cartesian grids. The method involves solving Cauchy-Riemann type equations for the velocity and transport-diffusion equations for the vorticity whose solenoidal vorticity components are obtained by solving a Poisson equation for a suitably chosen scalar potential. The importance of boundary conditions is examined. The difference equations are solved by iterations in order to permit exploitation of parallel and vector computing methods. Numerical experiments confirm the second-order spatial and temporal accuracy of the method.

MSC:
76D05 Navier-Stokes equations for incompressible viscous fluids
35Q30 Navier-Stokes equations
76M99 Basic methods in fluid mechanics
65N99 Numerical methods for partial differential equations, boundary value problems
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Anderson, D.A.; Tannehill, J.C.; Pletcher, R.H., Computational fluid mechanics and heat transfer, (1984), McGraw-Hill New York · Zbl 0569.76001
[2] Gunzburger, M.D., ()
[3] Teman, R., ()
[4] Wu, J.C.; Rich, Y.M.; Sanker, N.L., (), 137
[5] Onishi, K.; Kuroki, T.; Tanaka, M., (), 209
[6] Hussaini, M.Y.; Zang, T.A., Annu. rev. fluid mech., 19, 339, (1987)
[7] Patera, A.T., J. comput. phys., 54, 468, (1984)
[8] Leonard, A., Annu. rev. fluid mech., 17, 523, (1985)
[9] Gatski, T.B.; Grosch, C.E.; Rose, M.E., J. comput. phys., 48, 1, (1982)
[10] Dennis, S.C.R.; Ingham, D.B.; Cook, R.N., J. comput. phys., 33, 325, (1979)
[11] Fasel, H.F., Approximation methods for Navier-Stokes problems, (), 209
[12] Farouk, B.; Fusagi, T., Int. J. num. methods fluids, 5, 1017, (1985)
[13] Orlandi, P., Comput. and fluids, 15, No.2, 137, (1987)
[14] Osswald, G.A.; Ghia, K.N.; Ghia, U., ()
[15] Skerget, P.; Alujevic, A., Z. angew. math. mech., 65, T245, (1985)
[16] Fix, G.J.; Rose, M.E., SIAM J. numer. anal., 22, 250, (1985)
[17] Kaczmarz, S., Bull. acad. polon, sci. lett. A, 355, (1937)
[18] Tanabe, K., Num. math., 17, 203, (1971)
[19] Howarth, L., Philos. mag., 42, 1433, (1951)
[20] Rott, N., Z. angew. math. phys., 9, No.6, 543, (1958)
[21] Philips, R.B.; Rose, M.E., SIAM J. num. anal., 19, 698, (1982)
[22] Rose, M.E., J. comput. phys., 49, 420, (1983)
[23] Rose, M.E., Num. math., 24, 185, (1975)
[24] Orszag, S.A.; Israeli, M.; Deville, M.O., J. sci. comput., 1, 75, (1986)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.