Application of Charlie's method to the one-phase stefan problem

Abstract

Charlie’s method [2-4], an explicit predictor-corrector ?nite di?erence-based scheme, is applied to the one-phase moving boundary problem with a Neumann-type boundary condition known as the Stefan problem. A front-tracking method is used to simulate the location of the moving boundary. A simple example of the one-dimensional melting of ice [5] is taken into consideration. In general, the nonlinearity associated with the moving boundary signi?cantly complicates the analysis of this class of problems. A suitable range of the ?lter parameter ? in Charlie’s scheme is established, so that the numerical algorithm is stable and the time execution for the simulation is e?cient than the standard explicit scheme. The result of this study will give an insight to the future application of Charlie’s method in the simulation of the electrofusion joining process which involves a change of phase