Abstract
The development of fast iterative methods for the vorticitystreamfunction formulation of the Navier-Stokes equations is hampered by difficulties related to the treatment of the boundary conditions. When using the formula of Wood (see Roache (1972)) as a boundary condition for the vorticity no difficulties are encountered using multigrid acceleration of a block-iterative method, which updates vorticity and streamfunction simultaneously. Newton’s method is used to handle the nonlinearity, and the multigrid method is employed as an iterative linear systems solver. Numerical experiments on the square cavity flow problem show that the resulting method is considerably more efficient and robust than an earlier method (Roache (1975)) using a fast Poisson solver based on cyclic reduction and fast Fourier transformation, unless the Reynolds number is small.
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© 1984 Springer Fachmedien Wiesbaden
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Wesseling, P. (1984). Multigrid Solution of the Navier-Stokes Equations in the Vorticity-Streamfunction Formulation. In: Hackbusch, W. (eds) Efficient Solutions of Elliptic Systems. Notes on Numerical Fluid Mechanics, vol 10. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-14169-3_11
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DOI: https://doi.org/10.1007/978-3-663-14169-3_11
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
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