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Unconditionally gradient-stable computational schemes in problems of fast phase transitions

Lebedev, Vladimir and Sysoeva, Alena and Galenko, Peter (2011) Unconditionally gradient-stable computational schemes in problems of fast phase transitions. Physical Review E, 83, 026705-1-026705-11. APS. DOI: 10.1103/PhysRevE.83.026705.

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Abstract

Equations of fast phase transitions, in which the phase boundaries move with velocities comparable with the atomic diffusion speed or with the speed of local structural relaxation, are analyzed. These equations have a singular perturbation due to the second derivative of the order parameter with respect to time, which appears due to phenomenologically introduced local nonequilibrium. To develop unconditionally stable computational schemes, the Eyre theorem [D. J. Eyre, unpublished] proved for the classical equations, based on hypotheses of local equilibrium, is used. An extension of the Eyre theorem for the case of equations for fast phase transitions is given. It is shown that the expansion of the free energy on contractive and expansive parts, suggested by Eyre for the classical equations of Cahn-Hilliard and Allen-Cahn, is also true for the equations of fast phase transitions. Grid approximations of these equations lead to gradient-stable algorithms with an arbitrary time step for numerical modeling, ensuring monotonic nonincrease of the free energy. Special examples demonstrating the extended Eyre theorem for fast phase transitions are considered.

Document Type:Article
Title:Unconditionally gradient-stable computational schemes in problems of fast phase transitions
Authors:
AuthorsInstitution or Email of Authors
Lebedev, VladimirUdmurt State University
Sysoeva, AlenaUdmurt State University
Galenko, Peterpeter.galenko@dlr.de
Date:June 2011
Journal or Publication Title:Physical Review E
Refereed publication:Yes
In Open Access:No
In SCOPUS:Yes
In ISI Web of Science:Yes
Volume:83
DOI:10.1103/PhysRevE.83.026705
Page Range:026705-1-026705-11
Editors:
EditorsEmail
Lebedev, VladimirUdmurt State University
Sysoeva, AlenaUdmurt State University
Galenko, Peterpeter.galenko@dlr.de
Publisher:APS
Status:Published
Keywords:phase transformation,
HGF - Research field:Aeronautics, Space and Transport (old)
HGF - Program:Space (old)
HGF - Program Themes:W FR - Forschung unter Weltraumbedingungen (old)
DLR - Research area:Space
DLR - Program:W FR - Forschung unter Weltraumbedingungen
DLR - Research theme (Project):W - Vorhaben Materialwissenschaftliche Forschung (old)
Location: Köln-Porz
Institutes and Institutions:Institute of Materials Physics in Space
Deposited By: Dieter Herlach
Deposited On:13 Apr 2011 08:26
Last Modified:07 Feb 2013 20:39

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