The XFEM for nonlinear thermal and phase change problems
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 2 March 2015
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
The robustness and utility of the method are demonstrated on several one-dimensional benchmark problems.
Originality/value
The novel procedure based on the XFEM is developed to solve physically nonlinear phase change problems.
Keywords
Citation
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. https://doi.org/10.1108/HFF-02-2014-0052
Publisher
:Emerald Group Publishing Limited
Copyright © 2015, Emerald Group Publishing Limited