A new finite difference front tracking method for two phase 1- D moving boundary problems

摘要

A front tracking finite difference method is developed for a two phase one dimensional classical Stefan problem. The method, to start with, requires two time step sizes needed for the front to move a fixed spatial distance each. Two equations are derived applying Green's theorem of vector calculus for two regions of the problem and solved by bisection method to obtain these time steps. Subsequent steps are obtained, one by one, by applying bisection method to the discrete form of the Stefan condition. This front tracking method is much simpler and natural than the methods based on enthalpy formulation and can take care of source or sink terms on the front. Enthalpy formalism overlooks the Stefan condition which is a vital ingredient in the development of our method, Problem of freezing of a slab as well as freezing of a spherical droplet is presented as examples.