JournalsifbVol. 17, No. 4pp. 427–464

A mixed formulation of the Stefan problem with surface tension

  • Christopher B. Davis

    Tennessee Tech University, Cookeville, USA
  • Shawn W. Walker

    Louisiana State University, Baton Rouge, USA
A mixed formulation of the Stefan problem with surface tension cover
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Abstract

A dual formulation and finite element method is proposed and analyzed for simulating the Stefan problem with surface tension. The method uses a mixed form of the heat equation in the solid and liquid (bulk) domains, and imposes a weak formulation of the interface motion law (on the solid liquid interface) as a constraint. The basic unknowns are the heat fluxes and temperatures in the bulk, and the velocity and temperature on the interface. The formulation, as well as its discretization, is viewed as a saddle point system. Well-posedness of the time semi-discrete and fully discrete formulations is proved in three dimensions, as well as an a priori (stability) bound and conservation law. Simulations of interface growth (in two dimensions) are presented to illustrate the method.

Cite this article

Christopher B. Davis, Shawn W. Walker, A mixed formulation of the Stefan problem with surface tension. Interfaces Free Bound. 17 (2015), no. 4, pp. 427–464

DOI 10.4171/IFB/349