Measurement bias of fluid velocity in molecular simulations

In molecular simulations of fluid flow, the measurement of mean fluid velocity is considered to be a straightforward computation, yet there is some ambiguity in its definition. We show that in systems far from equilibrium, such as those with large temperature or velocity gradients, two commonly used definitions give slightly different results. Specifically, a bias can arise when computing the mean fluid velocity by measuring the mean particle velocity in a cell and averaging this mean over samples. We show that this bias comes from the correlation of momentum and density fluctuations in non-equilibrium fluids, obtain an analytical expression for predicting it, and discuss what system characteristics (e.g., number of particles per cell, temperature gradients) reduce or magnify the error. The bias has a physical origin so although we demonstrate it by direct simulation Monte Carlo (DSMC) computations, the same effect will be observed with other particle-based simulation methods, such as molecular dynamics and lattice gases.