A third-order-accurate upwind scheme for Navier-Stokes solutions in three dimensions

A finite-difference method, accurate and stable at high Reynolds numbers, is described for the numerical solution of the steady Navier-Stokes equations in three dimensions. The basic governing equations are expressed in terms of three equations for the velocity components and three equations for the vorticity components. The equations for the velocity components are of Poisson type and are differenced using the conventional three-point central differences. Convective terms in the transport equations for the vorticity components are differenced using a third-order-accurate upwind scheme. Difference equations thus obtained are solved by an alternating direction, line-iterative algorithm. Numerical results are presented for flow inside a cubic box resulting from the motion of one of its sides moving parallel to itself for Reynolds numbers up to 400. Comparison is made with the computations of other investigators based on the second-order methods. A thorough documentation of the flow structure for this important model problem is provided.