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.
Mots-clés : fluctuating hydrodynamics, Landau-Lifshitz-Navier-Stokes equations, stochastic partial differential equations, finite difference methods, binary gas mixtures
@article{M2AN_2010__44_5_1085_0,
author = {Bell, John B. and Garcia, Alejandro L. and Williams, Sarah A.},
title = {Computational fluctuating fluid dynamics},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {1085--1105},
publisher = {EDP-Sciences},
volume = {44},
number = {5},
year = {2010},
doi = {10.1051/m2an/2010053},
mrnumber = {2731404},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2010053/}
}
TY - JOUR AU - Bell, John B. AU - Garcia, Alejandro L. AU - Williams, Sarah A. TI - Computational fluctuating fluid dynamics JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2010 SP - 1085 EP - 1105 VL - 44 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2010053/ DO - 10.1051/m2an/2010053 LA - en ID - M2AN_2010__44_5_1085_0 ER -
%0 Journal Article %A Bell, John B. %A Garcia, Alejandro L. %A Williams, Sarah A. %T Computational fluctuating fluid dynamics %J ESAIM: Modélisation mathématique et analyse numérique %D 2010 %P 1085-1105 %V 44 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2010053/ %R 10.1051/m2an/2010053 %G en %F M2AN_2010__44_5_1085_0
Bell, John B.; Garcia, Alejandro L.; Williams, Sarah A. Computational fluctuating fluid dynamics. ESAIM: Modélisation mathématique et analyse numérique, Special Issue on Probabilistic methods and their applications, Tome 44 (2010) no. 5, pp. 1085-1105. doi : 10.1051/m2an/2010053. http://www.numdam.org/articles/10.1051/m2an/2010053/
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