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Stable Fourth-Order Stream-Function Methods for Incompressible Flows with Boundaries

Stable Fourth-Order Stream-Function Methods for Incompressible Flows with Boundaries
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Year:    2009

Journal of Computational Mathematics, Vol. 27 (2009), Iss. 4 : pp. 441–458

Abstract

Fourth-order stream-function methods are proposed for the time dependent, incompressible Navier-Stokes and Boussinesq equations. Wide difference stencils are used instead of compact ones and the boundary terms are handled by extrapolating the stream-function values inside the computational domain to grid points outside, up to fourth-order in the no-slip condition. Formal error analysis is done for a simple model problem, showing that this extrapolation introduces numerical boundary layers at fifth-order in the stream-function. The fourth-order convergence in velocity of the proposed method for the full problem is shown numerically.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2009.27.4.012

Journal of Computational Mathematics, Vol. 27 (2009), Iss. 4 : pp. 441–458

Published online:    2009-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Incompressible flow Stream-function formulation Finite difference methods.

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