Isogeometric Analysis of the Cahn-Hilliard Phase-Field Model
Abstract
The Cahn-Hilliard equation involves fourth-order spatial derivatives. Finite element solutions are not common because primal variational formulations of fourth-order operators are well defined and integrable only if the finite element basis functions are piecewise smooth and globally C1-continuous. There are a very limited number of two-dimensional finite elements possessing C1-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 C1 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 11, 2007
- Accession Number
- ADA478639
Entities
People
- Hector Gomez
- Thomas J.R. Hughes
- Victor M. Calo
- Yuri Bazilevs
Organizations
- University of Texas at Austin