Finite difference solution of one-dimensional Stefan problem with periodic boundary conditions

A finite difference method is used to solve the one-dimensional Stefan problem with periodic Dirichlet boundary condition. The temperature distribution, the position of the moving boundary and its velocity are evaluated. It is shown that, for given oscillation frequency, both the size of the domain and the oscillation amplitude of the periodically oscillating surface temperature, strongly influence the temperature distribution and the boundary movement. Furthermore, good agreement between the present finite difference results and numerical results obtained previously using the nodal integral method is seen.