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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Original Russian Text © V.Yu. Glotov, V.M. Goloviznin, S.A. Karabasov, A.P. Markesteijn, 2014, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2014, Vol. 54, No. 2, pp. 298–317.
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Glotov, V.Y., Goloviznin, V.M., Karabasov, S.A. et al. New two-level leapfrog scheme for modeling the stochastic Landau-Lifshitz equations. Comput. Math. and Math. Phys. 54, 315–334 (2014). https://doi.org/10.1134/S0965542514020079
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DOI: https://doi.org/10.1134/S0965542514020079