INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS Int. J. Numer. Meth. Fluids 28: 1073–1091 (1998) ANALYSIS OF 3D BACKWARD-FACING STEP INCOMPRESSIBLE FLOWS VIA A LOCAL AVERAGE-BASED NUMERICAL PROCEDURE G. DE STEFANO, F.M. DENARO* AND G. RICCARDI Dipartimento di Ingegneria Aerospaziale, Seconda Uniersita ` di Napoli, Aersa (Ce), Italy SUMMARY The study of the flow over a three-dimensional backward-facing step still provides interesting research when a new numerical method is developed and an investigation of the flow topology is performed. From a numerical point of view, accurate solutions are required, preferably with little computational effort, and the numerical results must lead to the understanding of the main features of the flow. The guidelines of an integrated framework are presented in this paper, starting with the description of the numerical methods for solving three-dimensional incompressible flows, based on a local-average procedure, up to the investigation of the flow structure by means of vortex lines reconstruction and vortices identification. Several results are reported concerning an analytical benchmark, simulation of flows in laminar and incipient transitional regimes and detection of vortical structures. Preliminary results for highly unsteady flows are also presented. © 1998 John Wiley & Sons, Ltd. KEY WORDS: three-dimensional backward-facing step incompressible flow; local average procedure; multidimensional fluxes reconstruction; vortex lines; vortices identification 1. INTRODUCTION The backward-facing step (BFS) flow in a channel has been extensively studied both numeri- cally (e.g. [1 – 6]) and experimentally (e.g. [7,8]) during the last two decades. Despite its simple geometry, flow over the BFS shows some features of more complex geometry flows (i.e. separation, recirculation, reattachment), depending on Reynolds number (Re ) and some geometrical parameters. Due to this fact, and also because the results of the numerical computations can be usefully compared with experimental data, it represents a good test case for any new numerical methodology. The flow regime can be varied by maintaining relatively moderate Reynolds numbers, ranging from laminar to fully developed turbulent flow. 3D numerical simulations are required, as the experiments of Armaly et al. [8] revealed that 2D flow conditions are only a particular case of a more general and complex situation. This fact can justify the lack of accordance between experimental and 2D numerical simulations, starting from Re 600 (based upon the mean inlet velocity, defined as U  =2/3U max , and the full channel height H ). However, the appearance of a recovered two-dimensionality at Re 6000, although it is only in an average meaning, justified some authors to perform 2D simulations of turbulent flows with and without turbulence modelling (e.g. [2,4,5]). * Correspondence to: Dipartimento di Ingegneria Aerospaziale, Seconda Universita ` di Napoli, via Roma, 29, 81031 Aversa (Ce), Italy. CCC 0271–2091/98/171073 – 22$17.50 © 1998 John Wiley & Sons, Ltd. Receied January 1997 Reised June 1997