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Abstract
This article presents a method for solving moving-boundary problems associated with phase change. This method is an explicit interface-tracking scheme that involves the reconstruction and advection of the moving interface on a fixed grid. Three distinct steps are undertaken to handle the movement of the interface: advection and reconstruction (tracking); calculation of normal velocities; and the solution of the governing equations for different phases. Details of each step and its implementation are provided. The transient heat diffusion equation in two space dimensions is the governing equation for energy transport. In order to validate the approach, results obtained from the front-tracking scheme are compared with exact analytical solutions for melting problems in Cartesian and cylindrical coordinates. It is shown that the numerical and analytical results are in excellent agreement. Finally, problems involving the multidimensional solidification of a pure aluminum ingot subject to bi-directional heat extraction are presented. The results indicate that the algorithm was able to track the front accurately under these aggressive conditions which caused large curvature. In Part II, the front-tracking approach described herein is applied to directional solidification problems influenced by melt convection.