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A compact monotonic discretization scheme for solving second-order vorticity–velocity equations

✍ Scribed by Tony W.H. Sheu; T.P. Chiang; S.M. Liou

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
493 KB
Volume
190
Category
Article
ISSN
0045-7825

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✦ Synopsis

This paper presents a numerical method for solving the steady-state Navier±Stokes equations for incompressible ¯uid ¯ows using velocities and vorticity as working variables. The method involves solving a second-order dierential equation for the velocity and a convection±diusion equation for the vorticity in Cartesian grids. The key to the success of the numerical simulation of this class of ¯ow equations depends largely on proper simulation of vorticity transport equation subject to proper boundary vorticity. In this paper, we present a monotonic advection±diusion multi-dimensional scheme and a theoretically rigorous implementation of vorticity boundary conditions. While the derivation of the proposed integral vorticity boundary condition is more elaborate and is more dicult to solve than conventional local approaches, the present approach oers signi®cant advantages. In this study, both lid-driven and backward-facing step problems have been selected for comparison and validation purposes.

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