Document Type

Article

Publication Date

1-1-2006

Publication Title

Communications in Applied Mathematics and Computational Science

Volume

1

Issue Number

1

First Page

53

Last Page

78

DOI

10.2140/camcos.2006.1.53

Keywords

fluctuations, molecular simulations, hydrodynamics

Disciplines

Applied Mathematics | Other Astrophysics and Astronomy | Other Physics

Abstract

This paper discusses the evaluation of hydrodynamic variables in the presence of spontaneous fluctuations, such as in molecular simulations of fluid flows. The principal point is that hydrodynamic variables such as fluid velocity and temperature must be defined in terms of mechanical variables such as momentum and energy density). Because these relations are nonlinear and because fluctuations of mechanical variables are correlated, care must be taken to avoid introducing a bias when evaluating means, variances, and correlations of hydrodynamic variables. The unbiased estimates are formulated; some alternative, incorrect approaches are presented as cautionary warnings. The expressions are verified by numerical simulations, both at thermodynamic equilibrium and at a nonequilibrium steady state.

Comments

First published in Communications in Applied Mathematics and Computational Science in Vol. 1, No. 1, 2010, published by Mathematical Sciences Publishers.

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