AN EFFICIENT METHOD FOR TEMPORAL INTEGRATION OF THE NAVIER-STOKES EQUATIONS IN CONFINED AXISYMMETRICAL GEOMETRIES

A method for temporal integration of the Navier-Stokes equations writt en in cylindrical coordinates is described. The objective is to avoid the severe time-step limitation usually encountered in confined axisym metric geometries (e.g., pipe flow), caused by a fine azimuthal grid s pacing around the centerline and the desire to refine the grid in the radial direction near walls. Avoiding severe time-step limitations usu ally involves treating all terms with derivatives in the radial and az imuthal directions with an implicit time-integration scheme. However, this leads to a set of coupled nonlinear equations which generally req uire complex and costly solution procedures. The scheme described in t his paper decomposes the computational domain into two regions. Within each region only the derivatives in one coordinate direction is treat ed implicitly. Conditions at the interface between the regions are det ermined to maintain the overall temporal accuracy of the basic time-in tegration schemes. Results from a direct numerical simulation (DNS) of turbulent pipe flow a re validated against computational and experime ntal results from the literature. It is demonstrated that this new sch eme allows for larger time-steps than other schemes, leading to signif icant CPU savings. (C) 1996 Academic Press, Inc.