Statistical error in particle simulations of hydrodynamic phenomena

by: Nicolas G Hadjiconstantinou, Alejandro L Garcia, Martin Z Bazant, Gang He

Journal of Computational Physics, Vol. 187, No. 1. (1 May 2003), pp. 274-297.

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Abstract

We present predictions for the statistical error due to finite sampling in the presence of thermal fluctuations in molecular simulation algorithms. Specifically, we establish how these errors depend on Mach number, Knudsen number, number of particles, etc. Expressions for the common hydrodynamic variables of interest such as flow velocity, temperature, density, pressure, shear stress, and heat flux are derived using equilibrium statistical mechanics. Both volume-averaged and surface-averaged quantities are considered. Comparisons between theory and computations using direct simulation Monte Carlo for dilute gases, and molecular dynamics for dense fluids, show that the use of equilibrium theory provides accurate results.

@article{Hadjiconstantinou2003, abstract = {We present predictions for the statistical error due to finite sampling in the presence of thermal fluctuations in molecular simulation algorithms. Specifically, we establish how these errors depend on Mach number, Knudsen number, number of particles, etc. Expressions for the common hydrodynamic variables of interest such as flow velocity, temperature, density, pressure, shear stress, and heat flux are derived using equilibrium statistical mechanics. Both volume-averaged and surface-averaged quantities are considered. Comparisons between theory and computations using direct simulation Monte Carlo for dilute gases, and molecular dynamics for dense fluids, show that the use of equilibrium theory provides accurate results.}, author = {Hadjiconstantinou, Nicolas G. and Garcia, Alejandro L. and Bazant, Martin Z. and He, Gang }, citeulike-article-id = {2835180}, doi = {10.1016/S0021-9991(03)00099-8}, journal = {Journal of Computational Physics}, keywords = {fluid, molecular, simulation}, month = {May}, number = {1}, pages = {274--297}, posted-at = {2008-05-26 17:44:35}, priority = {2}, title = {Statistical error in particle simulations of hydrodynamic phenomena}, url = {http://dx.doi.org/10.1016/S0021-9991(03)00099-8}, volume = {187}, year = {2003} }

RIS record

TY - JOUR ID - Hadjiconstantinou2003 L3 - citeulike-article-id:2835180 TI - Statistical error in particle simulations of hydrodynamic phenomena JF - Journal of Computational Physics VL - 187 IS - 1 SP - 274 EP - 297 N2 - We present predictions for the statistical error due to finite sampling in the presence of thermal fluctuations in molecular simulation algorithms. Specifically, we establish how these errors depend on Mach number, Knudsen number, number of particles, etc. Expressions for the common hydrodynamic variables of interest such as flow velocity, temperature, density, pressure, shear stress, and heat flux are derived using equilibrium statistical mechanics. Both volume-averaged and surface-averaged quantities are considered. Comparisons between theory and computations using direct simulation Monte Carlo for dilute gases, and molecular dynamics for dense fluids, show that the use of equilibrium theory provides accurate results. KW - fluid KW - molecular KW - simulation AU - Hadjiconstantinou, Nicolas AU - Garcia, Alejandro AU - Bazant, Martin AU - He, Gang PY - 2003/05/01/ UR - http://dx.doi.org/10.1016/S0021-9991(03)00099-8 ER -

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