Axially symmetric steady motion of a viscous incompressible fluid: some numerical experiments

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Abstract
This paper considers the numerical solution of axially symmetric steady motion of a viscous incompressible fluid in a circular cylinder of constant radius. A boundary-layer type assumption is made which reduces the Navier-Stokes equation from elliptic to parabolic and renders the solution independent of downstream data. Explicit methods of solution are shown to be unsatisfactory, and in practice the fully implicit method has advantages over the Crank-Nicolson method. Hagen-Poiseuille flow is used as a test case. An example is solved with an initial flow of arbitrary form, which correctly tends to Hagen-Poiseuille flow as the numerical solution is continued downstream.

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