An enthalpy formulation based on an arbitrarily deforming mesh for solution of the Stefan problem

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Abstract

Traditionally schemes for dealing with the Stefan phase change problem are separated into fixed grif or front tracking (deforming grid) schemes. A standard fixed grid scheme is to use an enthalpy formulation and track the movement of the phase front via a liquid fraction variable. In this paper, an enthalpy formulation is applied on a continuously deforming finite element grid. This approach results in a general numerical scheme that incorporates both front tracking and fixed grid schemes. It is shown how on appropriate setting of the grid velocity a fixed or deforming grid solution can be generated from the general scheme. In addition an approximate front tracking scheme is developed which can produce accurate non-oscillatory predictions at a computational cost close to an efficient fixed grid scheme. The versatility of the general scheme and the approximate front tracking scheme are demonstrated on solution of a number of Stefan problems in both one and two dimensions.

Original languageEnglish (US)
Pages (from-to)492-502
Number of pages11
JournalComputational Mechanics
Volume14
Issue number5
DOIs
StatePublished - Aug 1 1994

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