EXPLICIT RUNGE-KUTTA METHOD FOR 3-DIMENSIONAL INTERNAL INCOMPRESSIBLE FLOWS

A computer code has been developed to obtain the steady-state solutions for three-dimensional laminar incompressible flow governed by the Navier-Stokes equations. A central difference finite-volume formulation with an explicit one-step multistage Runge-Kutta time-stepping scheme for the primitive variables (i.e., velocity components and pressure) is used. The preconditioning matrix method, which is a generalized version of the artificial compressibility method, is used to construct a pressure equation from the continuity equation. Fourth-order artificial dissipation is used to suppress high-frequency oscillations. Numerical techniques to accelerate the rate of convergence include local time stepping and implicit residual smoothing. The code is validated by determining its ability to accurately predict 1) boundary-layer growth in a square duct with established and entry flow upstream conditions, 2) secondary now in a 90-deg bend of a square cross section, and 3) separation and reattachment in flow over a backward-facing step. The calculations are found to compare favorably with experimental data and numerical calculations available in the literature.