Gradient Stability of Numerical Algorithms in Local Nonequilibrium Problems of Critical Dynamics
Galenko, Peter and Lebedev, Vladimir and Sysoeva, A. (2011) Gradient Stability of Numerical Algorithms in Local Nonequilibrium Problems of Critical Dynamics. Computational Mathematics and Mathematical Physics, 51 (6), pp. 1074-1090.
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The critical dynamics of a spatially inhomogeneous system are analyzed with allowance for local nonequilibrium, which leads to a singular perturbation in the equations due to the appearance of a second time derivative. An extension is derived for the Eyre theorem, which holds for classical critical dynamics described by first-order equations in time and based on the local equilibrium hypothesis. It is shown that gradient-stable numerical algorithms can also be constructed for second-order equations in time by applying the decomposition of the free energy into expansive and contractive parts, which was suggested by Eyre for classical equations. These gradient-stable algorithms yield a monotonically nondecreasing free energy in simulations with an arbitrary time step. It is shown that the gradient stability conditions for the modified and classical equations of critical dynamics coincide in the case of a certain time approximation of the inertial dynamics relations introduced for describing local nonequilibrium. Model problems illustrating the extended Eyre theorem for critical dynamics problems are considered.
|Title:||Gradient Stability of Numerical Algorithms in Local Nonequilibrium Problems of Critical Dynamics|
|Journal or Publication Title:||Computational Mathematics and Mathematical Physics|
|In ISI Web of Science:||Yes|
|Page Range:||pp. 1074-1090|
|Keywords:||Undercooling of Materials|
|HGF - Research field:||Aeronautics, Space and Transport|
|HGF - Program:||Raumfahrt|
|HGF - Program Themes:||R FR - Forschung unter Weltraumbedingungen|
|DLR - Research area:||Raumfahrt|
|DLR - Program:||R FR - Forschung unter Weltraumbedingungen|
|DLR - Research theme (Project):||R - Vorhaben Materialwissenschaftliche Forschung|
|Institutes and Institutions:||Institute of Materials Physics in Space|
|Deposited By:||Dieter Herlach|
|Deposited On:||28 Jul 2011 14:57|
|Last Modified:||26 Feb 2013 15:05|
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