@Article{hmt.7.40,
AUTHOR = {Dave Martin
, Hicham Chaouki, Jean-Loup Robert, Donald Ziegler, Mario Fafard},
TITLE = {MODELLING OF PHASE CHANGE WITH NON-CONSTANT DENSITY USING XFEM AND A LAGRANGE MULTIPLIER},
JOURNAL = {Frontiers in Heat and Mass Transfer},
VOLUME = {7},
YEAR = {2016},
NUMBER = {1},
PAGES = {1--11},
URL = {http://www.techscience.com/fhmt/v7n1/54645},
ISSN = {2151-8629},
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.},
DOI = {10.5098/hmt.7.40}
}