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A Galerkin method for a class of steady, two-dimensional, incompressible, laminar boundary-layer flows

Published online by Cambridge University Press:  29 March 2006

Chen-Chi Hsu
Chen-Chi Hsu
Affiliation:
Department of Applied Mechanics and Engineering Science, University of Michigan, Ann Arbor
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Abstract

A Galerkin method is proposed for a class of boundary-layer flow problems. In this method, the assumed solution is composed of an auxiliary function and a series solution. The representing functions used in the series solution are orthonormal eigenfunctions, closely related to that of the boundary-layer equation, and are independent of the initial condition, as well as the boundary conditions. The reduced system of stiff, first-order, nonlinear, ordinary differential equations then has diagonal dominance for the first part of the flow region. The proposed method has been tested on two representative flows. Numerical experiments show that highly accurate results can be obtained for the entire boundary-layer flow region, if the auxiliary function satisfying the initial and boundary conditions is chosen to satisfy the first compatibility condition of the upstream flow region. In fact the computation is rather simple, and the numerical integration of the reduced initial-value problem can be carried out up to separation with a fairly large step.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 69 , Issue 4 , 24 June 1975 , pp. 783 - 802
Copyright
© 1975 Cambridge University Press

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