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A projection scheme for incompressible multiphase flow using adaptive Eulerian grid: 3D validation
Author(s) -
Chen T.,
Minev P. D.,
Nandakumar K.
Publication year - 2005
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.964
Subject(s) - discretization , eulerian path , projection method , grid , compressibility , projection (relational algebra) , mathematics , incompressible flow , mesh generation , multiphase flow , computational fluid dynamics , finite element method , geometry , flow (mathematics) , computer science , mathematical analysis , mathematical optimization , mechanics , algorithm , physics , dykstra's projection algorithm , lagrangian , thermodynamics
A three‐dimensional finite element method for incompressible multiphase flows with capillary interfaces is developed based on a (formally) second‐order projection scheme. The discretization is on a fixed (Eulerian) reference grid with an edge‐based local h ‐refinement in the neighbourhood of the interfaces. The fluid phases are identified and advected using the level‐set function. The reference grid is then temporarily reconnected around the interface to maintain optimal interpolations accounting for the singularities of the primary variables. Using a time splitting procedure, the convection substep is integrated with an explicit scheme. The remaining generalized Stokes problem is solved by means of a pressure‐stabilized projection. This method is simple and efficient, as demonstrated by a wide range of difficult free‐surface validation problems, considered in the paper. Copyright © 2005 John Wiley & Sons, Ltd.