On the numerical treatment of viscous singularities in wall-confined thermocapillary convection

Abstract

Confined thermocapillary flows often present a viscous singularity where free and solid surfaces meet. Any computational treatment of these flows must filter this singularity, either explicitly by modifying the boundary conditions of the problem, or implicitly by using finite precision methods. The effect of an explicit polynomial filtering is here examined for an axisymmetric side-heated liquid bridge, leading to two results: (i) thermally convective flows converge very slowly with the filtering scale; the numerical experiments must therefore be conducted carefully in order to get physically relevant results; (ii) stream-function and temperature are not suitable test variables for estimating this convergence.