The numerical solution 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 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.
scientific article; zbMATH DE number 3909985
scientific article