THE BOUNDARY ELEMENT METHOD APPLIED TO FREEZING AND MELTING PROBLEMS - Vick, Brian; Nelson, D. J. (Numerical heat transfer. Part B, Fundamentals, 1993)
Solutions for problems involving phase change have been attempted using a variety of techniques, including finite-difference, finite element, and approximate analytical methods. In all these methods the main difficulty is tracking the phase front, since it evolves as a nonlinear function of the temperature distribution. The objective of this article is to demonstrate the numerical advantages of the boundary element method (BEM)for this class of problems. The proposed BEM reduces the problem to a nonlinear set of integral equations for the location of the phase front. These integral equations can be solved numerically using simple basis functions for the unknown boundary data, with no need to discretize the entire domain. A general solution for multidimensional problems is proposed. The numerical accuracy and characteristics of the method are demonstrated using a one-dimensional freezing problem. It is shown that accurate, computationally efficient, and numerically stable solutions can be obtained using implicit time discretization