A study on the measurement of mean velocity and its convergence in molecular dynamics simulations

• Published in: International journal for numerical methods in fluids Vol. 67; no. 12; pp. 2130 - 2140
• Main Authors: Karimian, S. M. H., Izadi, S., Farimani, A. Barati
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 30.12.2011; Wiley
• Subjects: Computational methods in fluid dynamics; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); molecular dynamics; numerical simulation; periodic boundary condition; Physics; sampling and averaging; solution convergence; velocity measurement; Computational fluid dynamics; sampling and averaging; Digital simulation; Molecular dynamics method; Boundary conditions; Mean value; molecular dynamics; solution convergence; periodic boundary condition; Flow velocity; Modelling; Velocity measurement; numerical simulation
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.2487

In many particle‐based simulations, measurement of local mean flow velocity and other continuum‐based properties are of utmost importance. Macroscopic quantities, such as mean flow velocity, temperature, and density, can be estimated by averaging the corresponding microscopic behavior of the particles. The two main subjects that should be considered in the averaging over the particles in a specific problem are spatial and temporal behaviors of them. In this paper, we study the latter. Because of the chaotic nature of the collisions among the molecules and consequently their random path, extracted macroscopic values fluctuate about their average values causing statistical errors. In this paper, an averaging method called SAM‐Modified‐CAM (SMC) will be proposed for the measurement of mean velocity that reduces statistical errors in its calculation. This proposal is based on the study conducted here on the implementations of two common averaging methods, sample‐averaged measurement (SAM) and cumulative average measurement (CAM) in molecular dynamics. In addition, convergence of mean flow velocity measurement is thoroughly discussed, and a convergence criterion is proposed for this purpose. Implementation of the proposed method in different test cases has approved its reliable performance. Copyright © 2010 John Wiley & Sons, Ltd.