Statistical Error in Particle Simulations of Low Mach Number Flows
Author(s)Hadjiconstantinou, Nicolas G.; Garcia, Alejandro L.
We present predictions for the statistical error due to finite sampling in the presence of thermal fluctuations in molecular simulation algorithms. Expressions for the fluid velocity, density and temperature are derived using equilibrium statistical mechanics. The results show that the number of samples needed to adequately resolve the flow-field scales as the inverse square of the Mach number. The theoretical results are verified for a dilute gas using direct Monte Carlo simulations. The agreement between theory and simulation verifies that the use of equilibrium theory is justified.
High Performance Computation for Engineered Systems (HPCES);
statistical error, molecular simulation algorithms, equilibrium statistical mechanics, thermal fluctuations