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).
2. G.W. He, G.D.
Jin and X. Zhao, Scalesimilarity model for Lagrangian time
correlations in isotropic and stationary turbulence, Phys Rrev. E 80
(6) 066313 (2009).
3. D.Li, X.Zhang and G.W.He, Temporal decorrelations in compressible
isotropic turbulence, Phys. Rev. E,88(2): 021001 (2013).

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).
2. G.W. He, M. Wang and S. K. Lele, On the computation
of spacetime correlations by largeeddy simulation, Phys. Fluids 16
(11): 38593867 (2004).
3. Y. Yang, G.W. He and L.P. Wang, Effects of subgridscale modeling on
Lagrangian statistics in large eddy simulation, J. Turbulence 9 (8):
124 (2008).
4. G.D. Jin, G.W. He and L.P. Wang, Largeeddy simulation of
turbulentcollision of heavy particles in isotropic turbulence, Phys.
Fluids 22 (5): 055106 (2010).

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).
2. Q. Li and G.W. He, An atomisticcontinuum hybrid
simulation of fluid flows over superhydrophobic surfaces,
Biomicrofluidics 3(2): 022409 (2009).

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,
J. Comp. Phys. 228 (20): 78217836 (2009).
