Stefan's problem and beyond

TL;DR

This paper challenges the traditional Stefan condition in phase change problems, develops a new numerical method, and models energy relaxation in ion beam technologies, emphasizing effects outside classical formulations.

Contribution

It introduces a novel approach to Stefan problems accounting for volumetric energy sources and demonstrates the importance of effects beyond classical Stefan conditions.

Findings

Traditional Stefan condition cannot be imposed with volumetric energy sources.

A new numerical method based on Tikhonov and Samarskii's ideas is developed.

Energy relaxation processes relevant to ion beam technologies are modeled.

Abstract

We argue that the celebrated Stefan condition on the moving interphase, accepted in mathematical physics up to now, can not be imposed if energy sources are spatially distributed in the volume. A method based on Tikhonov and Samarskii's ideas for numerical solution of the problem is developed. Mathematical modelling of energy relaxation of some processes useful in modern ion beam technologies is fulfilled. Necessity of taking into account effects completely outside the Stefan formulation is demonstrated.