New two-level leapfrog scheme for modeling the stochastic Landau-Lifshitz equations |
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| Authors: | V Yu Glotov V M Goloviznin S A Karabasov A P Markesteijn |
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| Institution: | 1. Nuclear Safety Institute, Russian Academy of Sciences, Bol’shaya Tul’skaya ul. 52, Moscow, 115191, Russia
2. School of Engineering and Materials Science, Queen Mary, University of London, Mule End Road, London, E1 4NS, UK
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| 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. |
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