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This article is cited in 10 scientific papers (total in 10 papers)
New two-level leapfrog scheme for modeling the stochastic Landau–Lifshitz equations
V. Yu. Glotova, V. M. Goloviznina, S. A. Karabasovb, A. P. Markeshteijnb a Nuclear Safety Institute, Russian Academy of Sciences, Bol’shaya Tul’skaya ul. 52, Moscow, 115191, Russia
b School of Engineering and Materials Science, Queen Mary, University of London, Mule End Road, London, E1 4NS, UK
Abstract:
A two-level modification of the classical nondissipative leapfrog scheme with nonlinear flux correction has been developed for fluctuating hydrodynamics problems. The new algorithm has shown to satisfy the fluctuation-dissipation theorem to high accuracy. The results of various numerical tests, including equilibrium, nonequilibrium, one-, and two-dimensional systems, are compared with theoretical predictions, direct molecular simulations, and results produced by MacCormack’s schemes, the piecewise parabolic method, and a third-order Runge–Kutta scheme. The new algorithm is well suited for parallel computations due to its implementation simplicity and compact stencil.
Key words:
stochastic Landau–Lifshitz equations, fluctuating hydrodynamics, multiscale problems, leapfrog scheme.
Received: 06.05.2013 Revised: 28.08.2013
Citation:
V. Yu. Glotov, V. M. Goloviznin, S. A. Karabasov, A. P. Markeshteijn, “New two-level leapfrog scheme for modeling the stochastic Landau–Lifshitz equations”, Zh. Vychisl. Mat. Mat. Fiz., 54:2 (2014), 298–317; Comput. Math. Math. Phys., 54:2 (2014), 315–334
Linking options:
https://www.mathnet.ru/eng/zvmmf9993 https://www.mathnet.ru/eng/zvmmf/v54/i2/p298
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