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An enriched finite element method and level sets for axisymmetric two‐phase flow with surface tension
Author(s) -
Chessa Jack,
Belytschko Ted
Publication year - 2003
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.946
Subject(s) - finite element method , discontinuity (linguistics) , extended finite element method , curvature , mixed finite element method , rotational symmetry , level set method , eulerian path , geometry , partition of unity , mathematics , mathematical analysis , mechanics , computer science , physics , structural engineering , engineering , lagrangian , segmentation , artificial intelligence , image segmentation
A finite element method for axisymmetric two‐phase flow problems is presented. The method uses an enriched finite element formulation, in which the interface can move arbitrarily through the mesh without remeshing. The enrichment is implemented by the extended finite element method (X‐FEM) which models the discontinuity in the velocity gradient at the interface by a local partition of unity. It provides an accurate representation of the velocity field at interfaces on an Eulerian grid that is not conformal to the weak discontinuity. The interface is represented by a level set which is also used in the construction of the element enrichment. Surface tension effects are considered and the interface curvature is computed from the level set field. The method is demonstrated by several examples. Copyright © 2003 John Wiley & Sons, Ltd.