Variational formulation of three‐dimensional viscous free‐surface flows: Natural imposition of surface tension boundary conditions

Abstract

Abstract We present a new surface‐intrinsic linear form for the treatment of normal and tangential surface tension boundary conditions in C 0 ‐geometry variational discretizations of viscous incompressible free‐surface flows in three space dimensions. The new approach is illustrated by a finite (spectral) element unsteady Navier‐Stokes analysis of the stability of a falling liquid film.