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Solving thermal and phase change problems with the eXtended finite element method

Publication ,  Journal Article
Merle, R; Dolbow, J
Published in: Computational Mechanics
January 1, 2002

The application of the eXtended finite element method (X-FEM) to thermal problems with moving heat sources and phase boundaries is presented. Of particular interest is the ability of the method to capture the highly localized, transient solution in the vicinity of a heat source or material interface. This is effected through the use of a time-dependent basis formed from the union of traditional shape functions with a set of evolving enrichment functions. The enrichment is constructed through the partition of unity framework, so that the system of equations remains sparse and the resulting approximation is conforming. In this manner, local solutions and arbitrary discontinuities that cannot be represented by the standard shape functions are captured with the enrichment functions. A standard time-projection algorithm is employed to account for the time-dependence of the enrichment, and an iterative strategy is adopted to satisfy local interface conditions. The separation of the approximation into classical shape functions that remain fixed in time and the evolving enrichment leads to a very efficient solution strategy. The robustness and utility of the method is demonstrated with several benchmark problems involving moving heat sources and phase transformations.

Duke Scholars

Published In

Computational Mechanics

DOI

ISSN

0178-7675

Publication Date

January 1, 2002

Volume

28

Issue

5

Start / End Page

339 / 350

Related Subject Headings

  • Applied Mathematics
  • 4017 Mechanical engineering
  • 4005 Civil engineering
  • 0915 Interdisciplinary Engineering
  • 0913 Mechanical Engineering
  • 0905 Civil Engineering
 

Citation

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Merle, R., & Dolbow, J. (2002). Solving thermal and phase change problems with the eXtended finite element method. Computational Mechanics, 28(5), 339–350. https://doi.org/10.1007/s00466-002-0298-y
Merle, R., and J. Dolbow. “Solving thermal and phase change problems with the eXtended finite element method.” Computational Mechanics 28, no. 5 (January 1, 2002): 339–50. https://doi.org/10.1007/s00466-002-0298-y.
Merle R, Dolbow J. Solving thermal and phase change problems with the eXtended finite element method. Computational Mechanics. 2002 Jan 1;28(5):339–50.
Merle, R., and J. Dolbow. “Solving thermal and phase change problems with the eXtended finite element method.” Computational Mechanics, vol. 28, no. 5, Jan. 2002, pp. 339–50. Scopus, doi:10.1007/s00466-002-0298-y.
Merle R, Dolbow J. Solving thermal and phase change problems with the eXtended finite element method. Computational Mechanics. 2002 Jan 1;28(5):339–350.
Journal cover image

Published In

Computational Mechanics

DOI

ISSN

0178-7675

Publication Date

January 1, 2002

Volume

28

Issue

5

Start / End Page

339 / 350

Related Subject Headings

  • Applied Mathematics
  • 4017 Mechanical engineering
  • 4005 Civil engineering
  • 0915 Interdisciplinary Engineering
  • 0913 Mechanical Engineering
  • 0905 Civil Engineering