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, . APS. DOI: 10.1103/PhysRevE.83.026705.
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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 To develop unconditionally stable computational schemes, the Eyre theorem [D. J. Eyre, unpublished] proved for the classical equations, based on hypotheses of local equilibrium, is used.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.
|Title:||Unconditionally gradient-stable computational schemes in problems of fast phase transitions|
|Journal or Publication Title:||Physical Review E|
|In Open Access:||No|
|In ISI Web of Science:||Yes|
|HGF - Research field:||Aeronautics, Space and Transport|
|HGF - Program:||Space|
|HGF - Program Themes:||W FR - Forschung unter Weltraumbedingungen|
|DLR - Research area:||Space|
|DLR - Program:||W FR - Forschung unter Weltraumbedingungen|
|DLR - Research theme (Project):||W - Vorhaben Materialwissenschaftliche Forschung (old)|
|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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