A XFEM Lagrange Multiplier Technique for Stefan Problems

Dave Martin, Hicham Chaouki, Jean-Loup Robert, Mario Fafard, Donald Ziegler
2016 Frontiers in Heat and Mass Transfer  
The two dimensional phase change problem was solved using the extended finite element method with a Lagrange formulation to apply the interface boundary condition. The Lagrange multiplier space is identical to the solution space and does not require stabilization. The solid-liquid interface velocity is determined by the jump in heat flux across the i nterface. Two methods to calculate the jump are used and c ompared. The first is based on an averaged temperature gradient near the interface. The
more » ... the interface. The second uses the Lagrange multiplier values to evaluate the jump. The Lagrange multiplier based approach was shown to be more robust and precise.
doi:10.5098/hmt.7.31 fatcat:6gnum6xpa5cdzif342frljlj7i