An effective conduction length model in the enthalpy formulation for the stefan problem

In the fixed-grid finite-volume formulation, so called the enthalpy formulation, for the Stefan problem, the temperature and the front movement show step-like history, which is a well-known characteristic of the enthalpy method. This paper presents an effective conduction length model to mitigate such an oscillatory behavior as well as to support the physical reasoning. The proposed model is based on the simple fact that the heat flux across the boundary of phase-change cells should be estimated with the distance between the phase front and the center of neighboring cell. The model is applied to one-dimensional Stefan problems with various Stefan numbers. The numerical results show that the proposed model can smooth the spurious oscillation of the history of temperature and the evolution of front movement.