Archive of Issues
Germany; Russia Izhevsk; Jena; Karlsruhe
Section  Computer science 
Title  Computer simulation of the rapid solidification for diluted melt SiAs 
Author(s)  Lebedev V.G.^{a}, Sysoeva A.A.^{a}, Knyazheva I.S.^{a}, Danilov D.A.^{b}, Galenko P.K.^{c} 
Affiliations  Udmurt State University^{a}, Karlsruhe Institute of Technology^{b}, University of Jena^{c} 
Abstract  We consider a locally nonequilibrium process of solidification for a supercooled binary melt. For sake of simplicity, it is assumed, that the solidifying binary system is at constant temperature and pressure. Also there are two phases corresponding to the solid and the liquid states. The mathematical description of the solidification process is based on the phasefield model that generalizes the approach of Plapp (M. Plapp, Phys. Rev. E 84, 031601 (2011)) to the case of locally nonequilibrium processes. We use the method of extended irreversible thermodynamics to derive thermodynamically consistent equations of the model, in contrast to the phenomenological approach of Plapp. A concentration as a dynamic variable (and not the chemical potential of the impurity) is another difference from Plapp's model. The equivalence of describing the process of solidification through the concentration field and through the chemical potential of the system is shown in the framework of the resulting model. In view of the smallness of the relaxation times, the present model is reduced to the singularperturbed system of partial differential parabolic equations describing the dynamics of concentration and phase fields. In the paper, it is assumed that the description of the thermodynamic equilibrium states on the basis of the experimentally obtained Gibbs potentials is given. To verify the model, the numerical simulation of the onedimensional problem of solidification of the melt was performed in the approximation of the diluted melt SiAs, which had been repeatedly investigated experimentally. In this paper, we propose a gradientstable explicit method of integrating equations of the second order of accuracy in time in order to solve the system of singularlyperturbed equations numerically. We reduced an infinite space interval to a finite interval by the method of “periodic translation”. The estimation of stability was performed using numerical experiments. The concentration profile, the phasefield profile and the distribution coefficient of the impurity at the front of solidification depending upon the value of supercooling were obtained from the numerical simulation of the solidification process for diluted melt SiAs. An analytical expression for the distribution coefficient as a function of supercooling that follows from the locally nonequilibrium model with a sharp interface was used to test the adequacy of the results of numerical experiments. The effect of the model parameters on the solidification process and behavior of the numerical solutions near the diffuse boundary were investigated. 
Keywords  diluted solution, rapid solidification, phase field, grand potential, modeling 
UDC  538.911 
MSC  74N20 
DOI  10.20537/vm140111 
Received  7 October 2013 
Language  Russian 
Citation  Lebedev V.G., Sysoeva A.A., Knyazheva I.S., Danilov D.A., Galenko P.K. Computer simulation of the rapid solidification for diluted melt SiAs, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2014, issue 1, pp. 123140. 
References 

Full text 