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Approximation of Cahn–Hilliard diffuse interface models using parallel adaptive mesh refinement and coarsening with C 1 elements
Author(s) -
Stogner Roy H.,
Carey Graham F.,
Murray Bruce T.
Publication year - 2008
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.2337
Subject(s) - spinodal decomposition , cahn–hilliard equation , finite element method , transformation (genetics) , jump , interface (matter) , phase (matter) , mathematics , computer science , mathematical optimization , mathematical analysis , adsorption , thermodynamics , physics , chemistry , partial differential equation , gibbs isotherm , biochemistry , quantum mechanics , gene
A variational formulation and C 1 finite element scheme with adaptive mesh refinement and coarsening are developed for phase‐separation processes described by the Cahn–Hilliard diffuse interface model of transport in a mixture or alloy. The adaptive scheme is guided by a Laplacian jump indicator based on the corresponding term arising from the weak formulation of the fourth‐order non‐linear problem, and is implemented in a parallel solution framework. It is then applied to resolve complex evolving interfacial solution behavior for 2D and 3D simulations of the classic spinodal decomposition problem from a random initial mixture and to other phase‐transformation applications of interest. Simulation results and adaptive performance are discussed. The scheme permits efficient, robust multiscale resolution and interface characterization. Copyright © 2008 John Wiley & Sons, Ltd.