Spacetime correlation and twotime, two point closure An important concept on turbulence is that smallscale eddies are progressively decorrelated in time. This decorrelation progress can be characterized by twotime, twopoint correlations of fluctuating velocities, or simply, spacetime correlations. Over the years, several spacetime correlation models have been developed to provide the necessary time scales for turbulence closure theory and used as the staple methods to analyze spatial and temporal data from experiments and numerical simulations, such as Taylor frozenflow model and Kraichnan random sweeping model. We are developing the spacetime correlation models for turbulent flows in both Eulerian and Lagrangian frames. 1. X. Zhao and G.W. He, Spacetime correlations of fluctuating velocities in turbulent shear flows, Phys. Rev. E 79 (4): 046316 (2009).

Timeaccurate largeeddy simulation (LES) The increasing applications of LES to compute sound sources and particleladen turbulence require that LES with a subgrid scale (SGS) model could accurately predict spacetime correlations. Most of currently existing SGS models are based on energybudget equations. Therefore, they are able to correctly predict energy spectra at large scales, but they may incorrectly predict spacetime correlations. We are investigating the effects of SGS models on spacetime correlations and developing timeaccurate SGS models. 1. G.W. He, R. Rubinstein and L.P. Wang, Effects of subgridscale modeling on time correlations in large eddy simulation, Phys. Fluids 14: 2186  2193 (2002).

A hybrid molecular and continuum simulation A description of fluids in microdevices is often involved in both continuum scales and molecular ones. Either continuum or molecular method alone is unable to characterize the fluids. The challenge is how to couple across scales. We are developing a dynamic coupling model for the hybrid method of the NavierStokes equations and molecular dynamics without adjust parameters. The hybrid simulation predicts the largest slip length among the available numerical simulations. 1. Y.C. Wang and G.W. He, A dynamic coupling model for hybrid atomisticcontinuum computation, Chem. Eng. Sci. 62 (13): 35743579 (2007).

A smoothing technique for immersed boundary method 1. X.L. Yang, X. Zhang, Z.L. Li and G.W. He, A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulation, 