Computational fluctuating fluid dynamics
Center for Computational Sciences and Engineering,
Lawrence Berkeley National Laboratory,
Berkeley, California, 94720, USA.
2 Department of Physics, San Jose State University, San Jose, California, 95192, USA. firstname.lastname@example.org
3 Carolina Center for Interdisciplinary Applied Mathematics, Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill NC 27599, USA.
This paper describes the extension of a recently developed numerical solver for the Landau-Lifshitz Navier-Stokes (LLNS) equations to binary mixtures in three dimensions. The LLNS equations incorporate thermal fluctuations into macroscopic hydrodynamics by using white-noise fluxes. These stochastic PDEs are more complicated in three dimensions due to the tensorial form of the correlations for the stochastic fluxes and in mixtures due to couplings of energy and concentration fluxes (e.g., Soret effect). We present various numerical tests of systems in and out of equilibrium, including time-dependent systems, and demonstrate good agreement with theoretical results and molecular simulation.
Mathematics Subject Classification: 35R60 / 60H10 / 60H35 / 82C31 / 82C80
Key words: Fluctuating hydrodynamics / Landau-Lifshitz-Navier-Stokes equations / stochastic partial differential equations / finite difference methods / binary gas mixtures
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