A Fast Marching Level Set Method for the Stefan Problem
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The Stefan problem describes the change in temperature distribution with respect to time in a medium undergoing phase change. In this thesis we provide a unique combination of established numerical techniques to solve the single phase Stefan problem in two dimensions. For this purpose it is necessary to solve the heat equation and to track the location of the free boundary as it moves. We define the finite difference method for approximating the solution to partial differential equations which forms the basis for our computations, and a collection algorithms using finite difference approximations that we use to find the solution. To track the free boundary we use a level set method, combined with a fast marching method to determine the velocity with which the boundary will move according to the Stefan condition. The heat equation is solved with a second order accurate implicit approach.