Numerical solution of a Stefan-like problem in Bingham rheology

Authors:
Jiří Nedoma
Affiliations:
Institute of Computer Science AS CR, Pod vodárenskou vezí 2, 182 00 Prague 8, Czech Republic
Venue:
Mathematics and Computers in Simulation - MODELLING 2001 - Second IMACS conference on mathematical modelling and computational methods in mechanics, physics, biomechanics and geodynamics
Year:
2003

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Abstract

Many physical as well as geodynamical and technological processes connected with heat and diffusion involving phase-change phenomena lead to solve free boundary problems of Stefan-like type. In this paper, a generalized two-phase Stefan-like problem is formulated and discussed. The method used is based on the weak formulation in enthalpy formulation, on Bingham rheology, on concentration of solid (visco-plastic) and liquid (strongly viscoplastic with very low threshold of plasticity) components and the finite element technique. The existence of the solution of the continuous problem and of its FE approximation are presented and discussed.