Modelling, mathematical and numerical study of a solutal phase-field model
We investigate a thermodynamically consistent isothermal solutal phase-field mode1 describing the solidification of a binary alloy. The system is characterized by two variables: phase-field and concentration. The phase-field locally describes the phase state of the alloy (liquid, solid or intermediate). The evolution of these variables is described by a parabolic system with Neumann boundary conditions. After presenting the construction of the model, we investigate formal asymptotic limits when the liquid-solid interface width becomes small. Limit models are found in the form of generalized Stefan problems, which account for effects of the local interface curvature and velocity. We then introduce a finite element in space, semi-implicit Euler in time numerical scheme. The convergence of this scheme is proved thanks to the introduction of a generalized elliptic projector. We use this scheme to simulate dendritic growth in alloys, and investigate the stability of physical simulations with respect to various numerical parameters.
Faculté des sciences de base
Institut d'analyse et calcul scientifique
Chaire d'analyse et de simulation numérique
Jury: Erik Burman, Jürg Peter Buser, Pierluigi Colli, Alfio Quarteroni, Jean-François Scheid
Public defense: 2001-10-26
Record created on 2005-03-16, modified on 2016-08-08