Space-time correlation and two-time, two point closure

An important concept on turbulence is that small-scale eddies are progressively decorrelated in time. This decorrelation progress can be characterized by two-time, two-point correlations of fluctuating velocities, or simply, space-time correlations. Over the years, several space-time 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 frozen-flow model and Kraichnan random sweeping model. We are developing the space-time correlation models for turbulent flows in both Eulerian and Lagrangian frames.

1. X. Zhao and G.W. He, Space-time 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, Scale-similarity 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).

Time-accurate large-eddy simulation (LES)

The increasing applications of LES to compute sound sources and particle-laden turbulence require that LES with a sub-grid scale (SGS) model could accurately predict space-time correlations. Most of currently existing SGS models are based on energy-budget equations. Therefore, they are able to correctly predict energy spectra at large scales, but they may incorrectly predict space-time correlations. We are investigating the effects of SGS models on space-time correlations and developing time-accurate SGS models.

1. G.W. He, R. Rubinstein and L.P. Wang, Effects of subgrid-scale 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 space-time correlations by large-eddy simulation, Phys. Fluids 16 (11): 3859-3867 (2004).
3. Y. Yang, G.W. He and L.P. Wang, Effects of subgrid-scale modeling on Lagrangian statistics in large eddy simulation, J. Turbulence 9 (8): 1-24 (2008).
4. G.D. Jin, G.W. He and L.P. Wang, Large-eddy simulation of turbulent-collision of heavy particles in isotropic turbulence, Phys. Fluids 22 (5): 055106 (2010).

A hybrid molecular and continuum simulation

A description of fluids in micro-devices 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 Navier-Stokes 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 atomistic-continuum computation, Chem. Eng. Sci. 62 (13): 3574-3579 (2007).
2. Q. Li and G.W. He, An atomistic-continuum 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): 7821-7836 (2009).