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Computational fluctuating fluid dynamics

Published online by Cambridge University Press:  26 August 2010

John B. Bell ,
Alejandro L. Garcia  and
Sarah A. Williams
John B. Bell
Affiliation:
Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, California, 94720, USA.
Alejandro L. Garcia
Affiliation:
Department of Physics, San Jose State University, San Jose, California, 95192, USA. algarcia@algarcia.org
Sarah A. Williams
Affiliation:
Carolina Center for Interdisciplinary Applied Mathematics, Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill NC 27599, USA.
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Abstract

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.

Keywords

Fluctuating hydrodynamicsLandau-Lifshitz-Navier-Stokes equationsstochastic partial differential equationsfinite difference methodsbinary gas mixtures
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 44 , Issue 5: Special Issue on Probabilistic methods and their applications , September 2010 , pp. 1085 - 1105
Copyright
© EDP Sciences, SMAI, 2010

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