Numerical methodologies for investigation of moderate-velocity flow using a hybrid computational fluid dynamics — molecular dynamics simulation approach

Numerical approaches are presented to minimize the statistical errors inherently present due to finite sampling and the presence of thermal fluctuations in the molecular region of a hybrid computational fluid dynamics (CFD) — molecular dynamics (MD) flow solution. Near the fluid-solid interface the hybrid CFD-MD simulation approach provides a more accurate solution, especially in the presence of significant molecular-level phenomena, than the traditional continuum-based simulation techniques. It also involves less computational cost than the pure particle-based MD. Despite these advantages the hybrid CFD-MD methodology has been applied mostly in flow studies at high velocities, mainly because of the higher statistical errors associated with low velocities. As an alternative to the costly increase of the size of the MD region to decrease statistical errors, we investigate a few numerical approaches that reduce sampling noise of the solution at moderate-velocities. These methods are based on sampling of multiple simulation replicas and linear regression of multiple spatial/temporal samples. We discuss the advantages and disadvantages of each technique in the perspective of solution accuracy and computational cost.