A numerical technique for the solution of the Navier–Stokes equations of unsteady flow

Abstract

A numerical technique is developed on the solution of the Navier–Stokes equations of unsteady axisymmetric flow of a viscous incompressible fluid in any orthogonal system of coordinates. Using a finite difference scheme for time and spatial derivatives the discretization of equations of motion leads to a convergent and efficient algorithm for the unkown values of the functions of the flow at the ( n + 1)th time level in terms of the known values at the nth time level for any nodal point. Accordingly this technique is used for the numerical simulation of Taylor vortices stable or time dependent in spherical annular gaps at large aspect ratios σ = 0.4, 0.44, 0.48 and 0.5 for the first time. The method also applies to more composite problems such as MHD flows, flows with heat transfer etc. Our computations are compared with available numerical results and experimental measurements with very good agreement in all cases.