A mixed formulation of the Stefan problem with surface tension | Zendy

Christopher B. Davis | Zendy; Shawn W. Walker | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

A mixed formulation of the Stefan problem with surface tension

Author(s) -

Christopher B. Davis,

Shawn W. Walker

Publication year - 2016

Publication title -

interfaces and free boundaries mathematical analysis computation and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.964

H-Index - 39

eISSN - 1463-9971

pISSN - 1463-9963

DOI - 10.4171/ifb/349

Subject(s) - surface tension , stefan problem , discretization , mathematics , interface (matter) , saddle point , finite element method , a priori and a posteriori , mathematical analysis , stability (learning theory) , saddle , surface (topology) , constraint (computer aided design) , mechanics , thermodynamics , physics , mathematical optimization , geometry , computer science , gibbs isotherm , boundary (topology) , philosophy , epistemology , machine learning

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 solidliquid 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.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research