Computational fluctuating fluid dynamics

John B. Bell; Alejandro L. Garcia; Sarah A. Williams

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 44, Issue: 5, page 1085-1105
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Bell, John B., Garcia, Alejandro L., and Williams, Sarah A.. "Computational fluctuating fluid dynamics." ESAIM: Mathematical Modelling and Numerical Analysis 44.5 (2010): 1085-1105. <http://eudml.org/doc/250763>.

@article{Bell2010,
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. },
author = {Bell, John B., Garcia, Alejandro L., Williams, Sarah A.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Fluctuating hydrodynamics; Landau-Lifshitz-Navier-Stokes equations; stochastic partial differential equations; finite difference methods; binary gas mixtures; fluctuating hydrodynamics},
language = {eng},
month = {8},
number = {5},
pages = {1085-1105},
publisher = {EDP Sciences},
title = {Computational fluctuating fluid dynamics},
url = {http://eudml.org/doc/250763},
volume = {44},
year = {2010},
}

TY - JOUR
AU - Bell, John B.
AU - Garcia, Alejandro L.
AU - Williams, Sarah A.
TI - Computational fluctuating fluid dynamics
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/8//
PB - EDP Sciences
VL - 44
IS - 5
SP - 1085
EP - 1105
AB - 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.
LA - eng
KW - Fluctuating hydrodynamics; Landau-Lifshitz-Navier-Stokes equations; stochastic partial differential equations; finite difference methods; binary gas mixtures; fluctuating hydrodynamics
UR - http://eudml.org/doc/250763
ER -

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