Isogeometric analysis of the Cahn-Hilliard equation - a convergence study

JOURNAL OF COMPUTATIONAL PHYSICS

卷:305

Article

Kaestner, Markus^1,2  Metsch, Philipp¹  de Borst, Rene³ 

[1] Tech Univ Dresden, Inst Solid Mech, D-01062 Dresden, Germany

[2] Tech Univ Dresden, Dresden Ctr Computat Mat Sci DCMS, D-01062 Dresden, Germany

[3] Univ Glasgow, Sch Engn, Glasgow G12 8LT, Lanark, Scotland

关键词: Cahn-Hilliard equation;    Isogeometric analysis;    Bezier extraction;    Manufactured solutions;   

DOI  :  10.1016/j.jcp.2015.10.047

来源: Elsevier

【 摘 要 】

Herein, we present a numerical convergence study of the Cahn-Hilliard phase-field model within an isogeometric finite element analysis framework. Using a manufactured solution, a mixed formulation of the Cahn-Hilliard equation and the direct discretisation of the weak form, which requires a C-1-continuous approximation, are compared in terms of convergence rates. For approximations that are higher than second-order in space, the direct discretisation is found to be superior. Suboptimal convergence rates occur when splines of order p = 2 are used. This is validated with a priori error estimates for linear problems. The convergence analysis is completed with an investigation of the temporal discretisation. Second-order accuracy is found for the generalised-alpha method. This ensures the functionality of an adaptive time stepping scheme which is required for the efficient numerical solution of the Cahn-Hilliard equation. The isogeometric finite element framework is eventually validated by two numerical examples of spinodal decomposition. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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