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On the advantages of the vorticity-velocity formulation of the equations of fluid dynamics. (English) Zbl 0632.76049
The purpose of the present note is to explore in more detail the properties of some disparate numerical approaches. It will be shown that the vorticity-velocity formulation has a striking advantage when applied to problems in non-inertial frames of reference. More specifically, there exists an intrinsic vorticity-velocity formulation wherein all non- inertial effects (arising from both the rotation and translation of the frame of reference relative to an inertial framing) only enter into the solution of the problem through the implementation of initial and boundary conditions. This is in stark contrast to the pressure-velocity formulation, where non-inertial effects appear directly in the momentum equation in the form of Coriolis and Eulerian accelerations - a state of affairs which can give rise to a variety of numerical problems. A detailed exposition of this interesting property of the vorticity- velocity formulation will be presented along with a brief discussion of other advantages of this approach.

76D10 Boundary-layer theory, separation and reattachment, higher-order effects
35Q30 Navier-Stokes equations
Full Text: DOI
[1] Chorin, A.K., Math. comput., 22, 745, (1968)
[2] Williams, G.P., J. fluid mech., 37, 727, (1969)
[3] Anderson, D.A.; Tannehill, J.C.; Pletcher, R.H., Computational fluid dynamics and heat transfer, (1984), McGraw-Hill New York · Zbl 0569.76001
[4] Dennis, S.C.R.; Ingham, D.B.; Cook, R.N., J. comput. phys., 33, 325, (1979)
[5] Fasel, H.F., ()
[6] \scT. B. Gatski, C. E. Grosch, and \scM. E. Rose, to be published.
[7] Batchelor, G.K., An introduction to fluid dynamics, (1967), Cambridge Univ. Press London · Zbl 0152.44402
[8] Gatski, T.B.; Grosch, C.E.; Rose, M.E., J. comput. phys., 48, 1, (1982)
[9] Levich, E.; Tsinober, A., Phys. lett. A, 93, 293, (1983)
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