The purpose of this paper is to carry out a finite element simulation of a physically non-linear phase change problem in a two-dimensional space without adaptive remeshing or moving-mesh algorithms. The extended finite element method (XFEM) and the level set method (LSM) were used to capture the transient solution and motion of phase boundaries. It was crucial to consider the effects of unequal densities of the solid and liquid phases and the flow in the liquid region.
The XFEM and the LSM are applied to solve non-linear transient problems with a phase change in a two-dimensional space. The model assumes thermo-dependent properties of the material and unequal densities of the phases; it also allows for convection in the liquid phase. A non-linear system of equations is derived and a numerical solution is proposed. The Newton-Raphson method is used to solve the problem and the LSM is applied to track the interface.
The robustness and utility of the method are demonstrated on several two-dimensional benchmark problems.
The novel procedure based on the XFEM and the LSM was developed to solve physically non-linear phase change problems with unequal densities of phases in a two-dimensional space.
Stapór, P. (2016), "A two-dimensional simulation of solidification processes in materials with thermo-dependent properties using XFEM", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 26 No. 6, pp. 1661-1683. https://doi.org/10.1108/HFF-01-2015-0018Download as .RIS
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