A numerical treatment of two-dimensional flow in a branching channel
A numerical method for treating the steady two-dimensional flow of a viscous incompressible fluid in a branching channel is given. The upstream and downstream boundary conditions are discussed and a logarithmic transformation is applied to the 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 associated with the geometrical division of the flow. The Navier-Stokes equations are written in terms of the stream function and vorticity giving the usual two coupled nonlinear partial differential equations. These equations are solved using the method of Dennis and Hudson (1978). The effect of the relative widths of the channels upstream and downstream of the branch on the separation of the flow is discussed using results obtained from three separate grid sizes.
KeywordsReynolds Number Logarithmic Transformation Poiseuille Flow Sharp Corner Extra Point
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