The numerical solution of two-dimensional flow in a branching channel
type: Item
instance of: scholarly article
title: The numerical solution of two-dimensional flow in a branching channel
zbMATH Open document ID: 0569.76041
DOI: 10.1016/0045-7930(84)90014-8
author: J. S. Bramley
author: S. C. R. Dennis
published in: Computers and Fluids
publication date: 1984-01-01T00:00:00Z
review text: A numerical method for treating the steady two-dimensional flow of a viscous incompressible fluid in a branching channel is given. The Navier- Stokes equations are written in terms of the stream function and vorticity, giving the usual two coupled partial differential equations. These equations are solved using the difference scheme of the second author and \textit{J. D. Hudson} [in: \textit{C. Taylor}, \textit{K. Morgan} and \textit{C. A. Brebbia} (eds.), Numerical methods in laminar and turbulent flow. Proc. first int. Conf. Univ. Swansea (1978; Zbl 0403.76002) on pp. 69 ff.] and a solution to the resulting large system of algebraic equations is obtained using a Gauss-Seidel iteration technique. The upstream and downstream boundary conditions are discussed and a logarithmic transformation is applied to coordinate measuring distance downstream in order to extend the numerical solution far enough downstream. Two methods are presented for dealing with the singularity in the vorticity at the sharp corners where the channel bifurcates.
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 76M99
zbMATH DE Number: 3909985
zbMATH Keywords: stream function vorticity formulation
zbMATH Keywords: steady two-dimensional flow
zbMATH Keywords: branching channel
zbMATH Keywords: difference scheme
zbMATH Keywords: system of algebraic equations
zbMATH Keywords: Gauss-Seidel iteration technique
zbMATH Keywords: logarithmic transformation
zbMATH Keywords: singularity in the vorticity
MaRDI profile type: Publication
full work available at URL: 0045-7930(84)90014-8
OpenAlex ID: W2047267851
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description: scientific article; zbMATH DE number 3909985