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The XFEM for nonlinear thermal and phase change problems

Pawel Stapór (Faculty of Management and Computer Modelling, Kielce University of Technology, Kielce, Poland)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 2 March 2015




Of particular interest is the ability of the extended finite element method (XFEM) to capture transient solution and motion of phase boundaries without adaptive remeshing or moving-mesh algorithms for a physically nonlinear phase change problem. The paper aims to discuss this issue.


The XFEM is applied to solve nonlinear transient problems with a phase change. Thermal conductivity and volumetric heat capacity are assumed to be dependent on temperature. The nonlinearities in the governing equations make it necessary to employ an effective iterative approach to solve the problem. The Newton-Raphson method is used and the incremental discrete XFEM equations are derived.


The robustness and utility of the method are demonstrated on several one-dimensional benchmark problems.


The novel procedure based on the XFEM is developed to solve physically nonlinear phase change problems.



Stapór, P. (2015), "The XFEM for nonlinear thermal and phase change problems", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 25 No. 2, pp. 400-421.



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