INTRODUCTION 1. - The problem for analysis and requirements 2. - Results 3. - Comparison of computer times 4. - Conclusion. INTRODUCTION In 1981 it appeared to the organizers that a workshop to compare codes to solve the Navier -Stokes equations would be of great interest to the community of numerical analysts and users working on CFD (Computer fluid Dynamics}. A test problem would have to be selected with the following features : 1. it should be suited for all known methods (finite differences, finite elements, spectral ... ) thus the geometry should be simple. 2. it should be simple so that scientists with small computer facilities can test it and the gradients in the flow should be reasonable in size so that algo rithms don't blow up with a limited number of points and iterations. In practice one would have to select a stationary flow at moderate Reynolds number. 3. it should be a real flow to allow experimental ~asurements. The simplest problem used previously was the cavity flow problem ; however the singularity of the data at the boundary (point A and B on figure 1} makes it difficult for the Finite Element and Spectral methods ; furthermore it is not such an easy experiment to set up. A B .... u = 2 Flow around a cylinder, although most interesting of all, is too difficult because it is unbounded (many grid points) and very quickly unsteady {Re ~30).

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Recent Developments in the Numerical Solution of the Navier-Stokes Equations.- Viscous Flow over Backward Facing Steps An Experimental Investigation.- Numerical Predictions of Laminar Flow behind a Step.- The Backward-Facing Step Comparison of Two Algorithms for Unsteady NavierStokes Equations.- A Finite Element Method for Numerical Analysis of Laminar Flow over a Step.- Numerical Analysis of Laminar Flow over a Step.- Calculation of Laminar Flow over a Step by a Finite Element Method Based on the Stream Function-Vorticity Formulation.- An Efficient Quasi-Linear Finite Element Method for Solving the Incompressible Navier-Stokes Equations at Large Reynolds Numbers.- Laminar Flow over a Backward Facing Step: Numerical Solutions for a Test Problem.- Study of Incompressible Flow over a Backward Facing Step Using a Triangular Penalty Element.- Calculations of Flow over a Step.- Calculation of Laminar Backward-Facing Step Flow with Four Discretization Schemes for the Convection Terms.- Laminar Flow past a Backward Step.- Finite Element Simulations of Flow past a Backward Facing Step.- Finite Element Analysis of Laminar Viscous Flow over a Step by Nonlinear Least Squares and Alternating Direction Methods.- Calculation of Flow over a Backward Facing Step.- Use of Divergence Free Basis in Finite Element Methods.- Viscous Flow over Backward Facing Steps Computations with the LEONARD and the TEACH Algorithms.- Separated Flow Calculations Using an Eigenfunction Expansion Method.- Abstract Least Square in ?-? Discretized with Piecewise Linear Conforming Elements.- Finite Element Analysis of Laminar Viscdus Flow over a Step by the Penalty Function Formulation.- Laminar Flow over a Backward Facing Step Finite-Difference Solution with Fast Fourier Transform forRegions Consisting of Rectangular Subdomains.- Numerical Analysis of Laminar Flow over a Step by a Finite Element Method with Divergence Free Elements.- Numerical Analysis of Flow over a Step.