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Variational formulation of three-dimensional viscous free-surface flows: Natural imposition of surface tension boundary conditions. (English) Zbl 0739.76057
Summary: 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.

##### MSC:
 76M30 Variational methods applied to problems in fluid mechanics 76M25 Other numerical methods (fluid mechanics) (MSC2010) 76D45 Capillarity (surface tension) for incompressible viscous fluids 76D05 Navier-Stokes equations for incompressible viscous fluids
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