Application of Broyden's method to the enthalpy method for phase change problems

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.