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A new technique for numerical simulation of dendritic solidification using a meshfree interface finite element method
Author(s) -
Ghoneim Adam
Publication year - 2016
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.5185
Subject(s) - finite element method , diffuse element method , meshfree methods , level set method , smoothed finite element method , interface (matter) , computer science , extended finite element method , kronecker delta , algorithm , mathematics , computational science , mathematical optimization , boundary knot method , bubble , boundary element method , finite element limit analysis , structural engineering , physics , parallel computing , maximum bubble pressure method , engineering , segmentation , artificial intelligence , quantum mechanics , image segmentation
Summary A new technique for sharp‐interface modeling of dendritic solidification is proposed using a meshfree interface finite element method such that the liquid–solid interface is represented implicitly and allowed to arbitrarily intersect the finite elements. At the interface‐embedded elements, meshfree interface points without connectivity are imposed directly at the zero level set while meshfree interpolants are constructed using radial basis functions. This ensures both the partition of unity and the Kronecker delta properties are satisfied allowing for precise and easy imposition of Dirichlet boundary conditions at the interface. The constructed meshfree interpolants are also used for solving a variational level set equation based on the Ginzburg–Landau energy functional minimization such that reinitialization is completely eliminated and fast marching algorithms for interfacial velocity extension are not necessary resulting in an efficient algorithm with excellent volume conservation. The meshfree interface finite element method is used for modeling dendritic solidification in a pure melt where it is found suitable in handling the complex interfacial dynamics often encountered in dendritic growth. Mathematical formulation and implementation followed by numerical results and analysis will be presented and discussed. Copyright © 2016 John Wiley & Sons, Ltd.