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Is the steady viscous incompressible two-dimensional flow over a backward-facing step at $$Re=800$$ stable? (English) Zbl 0784.76050
Summary: 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.

##### MSC:
 76M10 Finite element methods applied to problems in fluid mechanics 76M20 Finite difference methods applied to problems in fluid mechanics 76M25 Other numerical methods (fluid mechanics) (MSC2010) 76D05 Navier-Stokes equations for incompressible viscous fluids
ENTWIFE; PITCON
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