Enriched Finite Volume Approximations of the Plane-Parallel Flow at a Small Viscosity

Abstract

We investigate viscous boundary layers of the plane-parallel flow, governed by the stationary Navier-Stokes equations under a certain symmetry. Following the analysis in Gie et al. (Annales de l'Institut Henri Poincare C. Analyse Non Lineaire, 2018), we first construct the so-called corrector, which is an analytic approximation of the velocity vector field near the boundary. Then, by embedding the corrector function into the classical Finite Volume schemes, we construct the semi-analytic enriched Finite Volume schemes for the plane-parallel flow, and numerically verify that our new enriched schemes reduce significantly the computational error of classical schemes especially near the boundary, and hence produce more accurate approximations without introducing any finer mesh near the boundary.