New two-level leapfrog scheme for modeling the stochastic Landau-Lifshitz equations

作者：Glotov V Yu^*; Goloviznin V M; Karabasov S A; Markesteijn A P

来源：Computational Mathematics and Mathematical Physics, 2014, 54(2): 315-334.

DOI：10.1134/S0965542514020079

• stochastic Landau-Lifshitz equations
• fluctuating hydrodynamics
• multiscale problems
• leapfrog scheme

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.

• 出版日期2014-2