Is the steady viscous incompressible two‐dimensional flow over a backward‐facing step at <i>Re</i> = 800 stable?

Abstract

Abstract A detailed case study is made of one particular solution of the 2D incompressible Navier–Stokes equations. Careful mesh refinement studies were made using four different methods (and computer codes): (1) a high‐order finite‐element method solving the unsteady equations by time‐marching; (2) a high‐order finite‐element method solving both the steady equations and the associated linear‐stability problem; (3) a second‐order finite difference method solving the unsteady equations in streamfunction form by time‐marching; and (4) a spectral‐element method solving the unsteady equations by time‐marching. The unanimous conclusion is that the correct solution for flow over the backward‐facing step at Re = 800 is steady—and it is stable, to both small and large perturbations.