Open Access

ARTICLE

A XFEM LAGRANGE MULTIPLIER TECHNIQUE FOR STEFAN PROBLEMS

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

Frontiers in Heat and Mass Transfer 2016, 7, 1-9. https://doi.org/10.5098/hmt.7.31

Abstract

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 second uses the Lagrange multiplier values to evaluate the jump. The Lagrange multiplier based approach was shown to be more robust and precise.

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Keywords

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