Numerical Integration of the Navier-Stokes Equations for Steady Two-Dimensional Flow

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Abstract
A summary is given of a numerical method of solving steady‐flow problems for the symmetrical motion of a viscous fluid past a fixed cylinder in two dimensions. The stream function and vorticity are used as dependent variables. Two features which have not previously been mentioned are considered. The first is concerned with the convergence of the iterative procedure which is used to obtain successive approximations to the stream function and vorticity. The second is the method of approximating the equation which governs the vorticity by finite‐difference schemes. The latter is discussed in the light of recent suggestions that approximations whose accuracy is demonstrably lower than that of the usual central‐difference scheme should be used in order to secure a matrix which is diagonally dominant. It is shown that the diagonally dominant system can be used while still retaining the higher accuracy of central differences. The results of some illustrative calculations are given for flow past a finite flat plate for Reynolds numbers up to 200, and for flow past elliptic cylinders of various ratios of major to minor axes at Reynolds number 40.

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