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A variationally consistent finite element approach to the two‐fluid internal contact‐line problem
Author(s) -
Hadjiconstantinou Nicolas G.,
Patera Anthony T.
Publication year - 2000
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 - 10.1002/1097-0363(20001230)34:8<711::aid-fld77>3.0.co;2-5
Subject(s) - mechanics , finite element method , discontinuity (linguistics) , compressibility , internal pressure , incompressible flow , fluid dynamics , classical mechanics , mathematics , surface tension , physics , mathematical analysis , geometry , thermodynamics
A new method for simulating incompressible viscous fluid flow involving moving internal contact lines is presented. The steady state interface shape is determined by a variationally consistent formulation of the surface tension contribution to the equations of motion adapted to the case of internal contact lines through the application of a global force balance compatibility condition that consistently removes the pressure indeterminacy. The Crouzeix–Raviart element is chosen to capture the pressure discontinuity at the two‐fluid interface. The resulting discrete equations are solved by an iterative procedure which displays fast convergence characteristics for small capillary numbers. Numerical results for the case of the steady movement of a fluid meniscus in a two‐dimensional channel are presented. Copyright © 2000 John Wiley & Sons, Ltd.