A series-expansion study of the Navier–Stokes equations with applications to three-dimensional separation patterns

Abstract

An algorithm has been developed which enables local Taylor-series-expansion solutions of the Navier-Stokes and continuity equations to be generated to arbitrary order. Much of the necessary algebra for generating these solutions can be done on a computer. Various properties of the algorithm are investigated and checked by making comparisons with known solutions of the equations of motion. A method of synthesizing nonlinear viscous-flow patterns with certain required properties is developed and applied to the construction of a number of two- and three-dimensional flow-separation patterns. These patterns are asymptotically exact solutions of the equations of motion close to the origin of the expansion. The region where the truncated series solution satisfies the full equations of motion to within a specified accuracy can be found.