RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Matem. Mod.: Year: Volume: Issue: Page: Find

 Matem. Mod., 2012, Volume 24, Number 1, Pages 109–128 (Mi mm3201)

Numerical analysis of new model of metals cristallization processes, two-dimensional case

V. T. Zhukov, N. A. Zaitsev, V. G. Lysov, Yu. G. Rykov, O. B. Feodoritova

M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, Moscow

Abstract: The paper is devoted to the numerical simulation of new model of metals crystallization processes. The difficulties of such simulation arise from the multiscale phenomenology of crystallization process. Nowadays the experimental researches establish the multiplicity of the details of crystallization process, however the general theoretical view of this process does not yet exist. The model which is used in the present paper is based on the description of a space occupied by the crystallizing alloy as the porous medium. The propagation of perturbations in such a medium is described by the equations of Biot’s type. The emergence of germs is described by modified Kahn-Hilliard equation. Previously the 1D numerical scheme has been constructed and its convergence property has been demonstrated. It is shown the possibility to model different crystallization regimes when changing the parameters of the model. In the presented paper 2D numerical model and results of computations are given. Due to multiscale phenomena the calculations require significant CPU time and hence the 2D model is based on explicit and explicit iteration algorithms which are implemented efficiently on multiprocessor computers.

Keywords: numerical simulation, metals crystallization, grid discretization, explicit iterations, time integration.

Full text: PDF file (776 kB)
References: PDF file   HTML file

English version:
Mathematical Models and Computer Simulations, 2012, 4:4, 440–453

Bibliographic databases:

Document Type: Article
UDC: 519.6

Citation: V. T. Zhukov, N. A. Zaitsev, V. G. Lysov, Yu. G. Rykov, O. B. Feodoritova, “Numerical analysis of new model of metals cristallization processes, two-dimensional case”, Matem. Mod., 24:1 (2012), 109–128; Math. Models Comput. Simul., 4:4 (2012), 440–453

Citation in format AMSBIB
\Bibitem{ZhuZaiLys12} \by V.~T.~Zhukov, N.~A.~Zaitsev, V.~G.~Lysov, Yu.~G.~Rykov, O.~B.~Feodoritova \paper Numerical analysis of new model of metals cristallization processes, two-dimensional case \jour Matem. Mod. \yr 2012 \vol 24 \issue 1 \pages 109--128 \mathnet{http://mi.mathnet.ru/mm3201} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2978093} \transl \jour Math. Models Comput. Simul. \yr 2012 \vol 4 \issue 4 \pages 440--453 \crossref{https://doi.org/10.1134/S2070048212040096} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84928997620}