A locally one-dimensional scheme for the solution of three-dimensional Navier-Stokes equations

An implicit locally one-dimensional scheme developed to solve the incompressible three-dimensional Navier-Stokes equations in primitive variables is described. The purpose of the study is to generate a fast, partly iterative scheme for the solution of laminar flow on an arbitrarily shaped body. The formulation does not require linearization, lagging of the mixed derivative terms, or a rectangular computational region. For data storage and analytical requirements, the physical and computational regions are divided into three subregions; the interface between the subregions is treated in a manner similar to that in Dietrich et al. (1975). The results of the Navier-Stokes computations are presented for low and intermediate Reynolds numbers for the flow over a sphere.