TRANSIENT SIMULATION OF INTERNAL SEPARATED FLOWS USING AN INTELLIGENT HIGHER-ORDER SPATIAL DISCRETIZATION SCHEME

Abstract

SUMMARY This paper summarizes the method-of-lines (MOL) solution of the Navier‐Stokes equations for an impulsively started incompressible laminar flow in a circular pipe with a sudden expansion. An intelligent higher-order spatial discretization scheme, which chooses upwind or downwind discretization in a zone-of-dependence manner when flow reversal occurs, was developed for separated flows. Stability characteristics of a linear advective‐diffusive equation were examined to depict the necessity of such a scheme in the case of flow reversals. The proposed code was applied to predict the time development of an impulsively started flow in a pipe with a sudden expansion. Predictions were found to show the expected trends for both unsteady and steady states. This paper demonstrates the ease with which the Navier‐Stokes equations can be solved in an accurate manner using sophisticated numerical algorithms for the solution of ordinary differential equations (ODEs). Solutions of the Navier‐Stokes equations in primitive variables formulation by using the MOL and intelligent higher-order spatial discretization scheme are not available to date. 1997 by John Wiley & Sons, Ltd.