Artículos de revistas
Weak Solutions Of A Phase-field Model With Convection For Solidification Of An Alloy
Registro en:
Communications In Applied Analysis. , v. 8, n. 4, p. 503 - 532, 2004.
10832564
2-s2.0-10644222028
Autor
Planas G.
Boldrini J.L.
Institución
Resumen
In recent years, the phase-field methodology has achieved considerable importance in modeling and numerically simulating a range of phase transitions that occur during solidification processes. In attempt to understand the mathematical aspects of such methodology, in this article we consider a simplified model of this sort for a nonstationary process of solidification/melting of a binary alloy with thermal properties. The model includes the possibility of occurrence of natural convection in non-solidified regions and, therefore, leads to a free-boundary value problem for a highly non-linear system of partial differential equations consisting of a phase-field equation, a heat equation, a concentration equation and a modified Navier-Stokes equations by a penalization term of Carman-Kozeny type, which accounts for the mushy effects, and Boussinesq terms to take in consideration the effects of variations of temperature and concentration in the flow. A proof of existence of weak solutions for the system is given. The problem is firstly approximated and a sequence of approximate solutions is obtained by Leray-Schauder's fixed point theorem. 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