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Boundary‐conforming mapping applied to computations of highly deformed solidification interfaces
Author(s) -
Tsiveriotis K.,
Brown R. A.
Publication year - 1992
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.1650140807
Subject(s) - computation , boundary (topology) , representation (politics) , directional solidification , finite element method , interface (matter) , boundary value problem , binary number , geometry , mechanics , grid , mathematical analysis , materials science , binary alloy , boundary representation , mathematics , physics , alloy , algorithm , thermodynamics , metallurgy , arithmetic , bubble , maximum bubble pressure method , politics , political science , law
Abstract A new boundary‐conforming mapping is developed for the calculation of highly deformed cellular solidification interfaces in a model of directional solidification of a binary alloy. The mapping is derived through a variational fomulation that is designed so that the grid penetrates the grooves between cells along the interface without causing a loss of ellipticity of the mapping equations. A finite element/Newton method is presented for simultaneous solution of the free boundary problem described by the solutal model of directional solidification and the mapping equations. Results are compared to previous calculations and demonstrate the importance of accurate representation of the interface shape for understanding the solution structure.