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Variational formulation of three‐dimensional viscous free‐surface flows: Natural imposition of surface tension boundary conditions
Author(s) -
Ho LeeWing,
Patera Anthony T.
Publication year - 1991
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650130603
Subject(s) - surface tension , free surface , mathematics , surface (topology) , compressibility , finite element method , no slip condition , mechanics , boundary value problem , geometry , boundary (topology) , mathematical analysis , classical mechanics , physics , thermodynamics , mixed boundary condition
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.