Application of a Spectral Element Method to Two-Dimensional Forward-Facing Step Flow

In the present study, we investigate the two-dimensional laminar flow through a one-sided constriction of a plane channel with a ratio of h:H=1:4 (where h is the step height and H is the channel height). The computational approach employed is based on a mixed implicit/explicit time discretization scheme together with a highly accurate spatial discretization using a PN−PN−2 spectral-element method. It is well known that this so-called forward-facing step (FFS) flow exhibits a singularity in the pressure and the velocity derivatives at the corner point. We account for this singularity by a geometric mesh refinement strategy that was proposed in a hp-FEM context. A detailed numerical study of the FFS flow reveals that length and height of the recirculation zone in front of the step are almost constant for creeping flow. In the limit of high Reynolds numbers the length and height of the recirculation zone increase proportional to Re0.6 and Re0.2, respectively.