Open Access

ARTICLE

MODELLING OF PHASE CHANGE WITH NON-CONSTANT DENSITY USING XFEM AND A LAGRANGE MULTIPLIER

Dave Martin^a,b,† , Hicham Chaouki^a,b, Jean-Loup Robert^a, Donald Ziegler^c, Mario Fafard^a,b

a Department of Civil and Water Engineering, Laval University, Quebec, QC, G1V 0A6, Canada
b NSERC/Alcoa Industrial Research Chair MACE3 and Aluminium Research Centre - REGAL, Laval University, Quebec, QC, G1V 0A6, Canada
c Alcoa Primary Metals, Alcoa Technical Center, 100 Technical Drive, Alcoa Center, PA, 15069-0001, USA
† Corresponding author. Email: dave.martin.1@ulaval.ca

Frontiers in Heat and Mass Transfer 2016, 7, 1-11. https://doi.org/10.5098/hmt.7.40

Abstract

A two phase model for two-dimensional solidification problems with variable densities was developed by coupling the Stefan problem with the Stokes problem and applying a mass conserving velocity condition on the phase change interface. The extended finite element method (XFEM) was used to capture the strong discontinuity of the velocity and pressure as well as the jump in heat flux at the i nterface. The melting temperature and velocity condition were imposed on the interface using a Lagrange multiplier and the penalization method, respectively. The resulting formulations were then coupled using a fixed point iteration a lgorithm. Three examples were investigated and the results were compared to numerical results coming from a commercial software using ALE techniques to track the solid/liquid interface. The model was able to reproduce the benchmark simulations while maintaining a sharp phase change interface and conserving mass.

---

Keywords

---