Isogeometric Analysis of Phase-Field Models: Application to the Cahn-Hilliard Equation

被引:0
|
作者
Gomez, H. [1 ]
Calo, V. M. [2 ]
Hughes, T. J. R. [2 ]
机构
[1] Univ A Coruna, Grp Numer Methods Engn, Dept Math Methods, Campus Elvina, La Coruna 15192, Spain
[2] Univ Texas Austin, Inst Computat Engineering & Scie, Austin, TX 78712 USA
来源
ECCOMAS MULTIDISCIPLINARY JUBILEE SYMPOSIUM: NEW COMPUTATIONAL CHALLENGES IN MATERIALS, STRUCTURES AND FLUIDS | 2009年 / 14卷
关键词
Phase-field; Cahn-Hilliard; Isogeometric Analysis; NURBS; GENERALIZED-ALPHA METHOD; DIFFERENCE SCHEME; CONTINUITY; REFINEMENT; SIMULATION; TURBULENCE; FLOWS;
D O I
暂无
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
The Cahn-Hilliard equation involves fourth-order spatial derivatives. Finite element solutions to the Cahn-Hilliard equation are not common because primal variational formulations of fourth-order operators are only well defined and integrable if the finite element basis functions are piecewise smooth and globally C-1-continuous. There are a very limited number of two-dimensional finite elements possessing C-1-continuity applicable to complex geometries, but none in three-dimensions. We propose isogeometric analysis as a technology that possesses a unique combination of attributes for complex problems involving higher-order differential operators, namely, higher-order accuracy, robustness, two- and three-dimensional geometric "exibility, compact support, and, most importantly, the possibility of C-1 and higher-order continuity. A NURBS-based variational formulation for the Cahn-Hilliard equation was tested on two- and three-dimensional problems. We present steady state solutions in two-dimensions and, for the first time, in three-dimensions. To achieve these results an adaptive time-stepping method is introduced. We also present a technique for desensitizing calculations to dependence on mesh refinement. This enables the calculation of topologically correct solutions on coarse meshes, opening the way to practical engineering applications of phase-field methodology.
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页码:1 / +
页数:3
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