An efficient method for temporal integration of the Navier-Stokes equations in confined axisymmetric geometries

A method for temporal integration of the Navier-Stokes equations written in cylindrical coordinates is described. The objective is to avoid the severe time-step limitation usually encountered in confined axisymmetric geometries (e.g., pipe flow), caused by a fine azimuthal grid spacing around the centerline and the desire to refine the grid in the radial direction near walls. Avoiding severe time-step limitations usually involves treating all terms with derivatives in the radial and azimuthal directions with an implicit time-integration scheme. However, this leads to a set of coupled nonlinear equations which generally require complex and costly solution procedures. The scheme described in this paper decomposes the computational domain into two regions. Within each region only the derivatives in one coordinate direction is treated implicitly. Conditions at the interface between the regions are determined to maintain the overall temporal accuracy of the basic time-integration schemes. Results from a direct numerical simulation (DNS) of turbulent pipe flow a re validated against computational and experimental results from the literature. It is demonstrated that this new scheme allows for larger time-steps than other schemes, leading to significant CPU savings. (C) 1996 Academic Press, Inc.