Isogeometric analysis of phase-field models: Application to the cahn-hilliard equation

H. Gomez, V. M. Calo, T. J.R. Hughes

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

5 Scopus citations

Abstract

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 inte-grable if the finite element basis functions are piecewise smooth and globally l1 -continuous. There are a very limited number of two-dimensional finite elements possessing l1 -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 flexibility, compact support, and, most importantly, the possibility of l1 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.

Original languageEnglish (US)
Title of host publicationECCOMAS Multidisciplinary Jubilee Symposium
Subtitle of host publicationNew Computational Challenges in Materials, Structures, and Fluids
EditorsJosef Eberhardsteiner, Christian Hellmich, Herbert A. Mang, Jacques Périaux
PublisherSpringer
Pages1-16
Number of pages16
ISBN (Print)9781402092305
DOIs
StatePublished - Jan 1 2009
EventInternational ECCOMAS Multidisciplinary Jubilee Symposium - New Computational Challenges in Materials, Structures, and Fluids, EMJS 2008 - Vienna, Austria
Duration: Feb 18 2008Feb 20 2008

Publication series

NameComputational Methods in Applied Sciences
Volume14
ISSN (Print)1871-3033

Other

OtherInternational ECCOMAS Multidisciplinary Jubilee Symposium - New Computational Challenges in Materials, Structures, and Fluids, EMJS 2008
CountryAustria
CityVienna
Period02/18/0802/20/08

Keywords

  • Cahn-Hilliard
  • Isogeometric analysis
  • NURBS
  • Phase-field

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Modeling and Simulation
  • Biomedical Engineering
  • Computer Science Applications
  • Fluid Flow and Transfer Processes
  • Computational Mathematics
  • Electrical and Electronic Engineering

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