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Abstract
The enthalpy method is one of the most widely used methods for solving phase change problems with a moving boundary. In the application of the enthalpy method, systems of nonlinear equations have to be solved at each time step when implicit time discretization is being used. In this article, we propose to use Broyden 's algorithm as an efficient method for solving these systems of nonlinear equations based on a direct discretization of the enthalpy equation. Numerical experiments are conducted to verify the efficiency of our scheme for a one-dimensional, two-phase solidification problem.
Notes
Address correspondence to Dr. James Caldwell, Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong.