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

We present a new surface-intrinsic linear form for the treatment of normal and tangential surface tension boundary conditions in C0-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.