Vol. 1, No. 1, 2006

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Estimating hydrodynamic quantities in the presence of microscopic fluctuations

Alejandro L. Garcia

Vol. 1 (2006), No. 1, 53–78

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.

fluctuations, molecular simulations, hydrodynamics
Mathematical Subject Classification 2000
Primary: 82C80
Secondary: 76M28
Received: 19 June 2005
Revised: 12 January 2006
Accepted: 17 January 2006
Published: 8 May 2007
Alejandro L. Garcia
Department of Physics
San José State University
San José, CA 95192-0106
United States