Raoyang Zhang

Pore scale study of flow in porous media: Scale dependency, REV, and statistical REV

Flow in porous media is studied at the pore-scale with lattice Boltzmann simulations on pore geometries reconstructed from computed microtomographic images. Pore scale results are analyzed to give quantities such as permeability, porosity and specific surface area at various scales and at various locations. With this, some fundamental issues such as scale dependency and medium variability can be assessed quantitatively. More specifically, the existence and size of the well known concept, representative elementary volume (REV), can be quantified. It is found that the size of an REV varies spatially and depends on the quantity being represented. For heterogeneous media, a better measure may be the so called “statistical REV”, which has weaker requirements than does the deterministic REV.

Direct numerical simulations of the Navier-Stokes alpha model

Abstract We explore the utility of the recently proposed alpha equations in providing a subgrid model for fluid turbulence. Our principal results are comparisons of direct numerical simulations of fluid turbulence using several values of the parameter alpha, including the limiting case where the Navier–Stokes equations are recovered. Our studies show that the large scale features, including statistics and structures, are preserved by the alpha models, even at coarser resolutions where the fine scales are not fully resolved. We also describe the differences that appear in simulations. We provide a summary of the principal features of the alpha equations, and offer some explanation of the effectiveness of these equations used as a subgrid model for three-dimensional fluid turbulence.

On the three-dimensional Rayleigh–Taylor instability

The three-dimensional Rayleigh–Taylor instability is studied using a lattice Boltzmann scheme for multiphase flow in the nearly incompressible limit. This study focuses on the evolution of the three-dimensional structure of the interface. In addition to the bubble and spike fronts, a saddle point is found to be another important landmark on the interface. Two layers of heavy-fluid roll-ups, one at the spike tip and the other at the saddle point, were observed. The secondary instability in the horizontal planes entangles the already complicated structure of the interface. Parallel computations are utilized to accommodate the massive computational requirements of the simulations.

Lattice Boltzmann method for simulations of liquid-vapor thermal flows.

We present a lattice Boltzmann method that has the capability of simulating thermodynamic multiphase flows. This approach is fully thermodynamically consistent at the macroscopic level. Using this method, the liquid-vapor boiling process, including liquid-vapor formation and coalescence together with a full coupling of temperature, is simulated.

Efficient kinetic method for fluid simulation beyond the Navier-Stokes equation

We present a further theoretical extension to the kinetic-theory-based formulation of the lattice Boltzmann method of Shan [J. Fluid Mech. 550, 413 (2006)]. In addition to the higher-order projection of the equilibrium distribution function and a sufficiently accurate Gauss-Hermite quadrature in the original formulation, a regularization procedure is introduced in this paper. This procedure ensures a consistent order of accuracy control over the nonequilibrium contributions in the Galerkin sense. Using this formulation, we construct a specific lattice Boltzmann model that accurately incorporates up to third-order hydrodynamic moments. Numerical evidence demonstrates that the extended model overcomes some major defects existing in conventionally known lattice Boltzmann models, so that fluid flows at finite Knudsen number Kn can be more quantitatively simulated. Results from force-driven Poiseuille flow simulations predict the Knudsens minimum and the asymptotic behavior of flow flux at large Kn.

Interface and surface tension in incompressible lattice Boltzmann multiphase model

This paper studies the interfacial dynamics and surface tension in an incompressible lattice Boltzmann multiphase model proposed recently by He et al. [J. Comput. Phys. 152 (1999) 642]. The model tracks different phases and the interface between them using an index fluid with molecular interaction. When the molecular interaction is strong enough, the index fluid automatically segregates into two different phases. The surface tension is implemented in the model using a term as a function of the gradient of the index fluid density. The strength of the surface tension depends on the molecular interaction, and can be adjusted conveniently by a free parameter. Numerical simulations for a variety of flow conditions with surface tension are carried out to demonstrate the capability of the model.

Surface tension effects on two-dimensional two-phase Kelvin–Helmholtz instabilities

Abstract The two-dimensional Kelvin–Helmholtz instability is studied using a lattice Boltzmann multi-phase model in the nearly incompressible limit. This study focuses on the effects of surface tension on the evolution of vortex pairing in a two-dimensional mixing layer. Several types of interface pinch-off are observed and the corresponding mechanisms are discussed. The contribution of surface tension to the flow kinetic energy is mainly negative. Part of this kinetic energy can be transformed to potential energy stored in the surface tension. The contribution of surface tension to the flow enstrophy is positive and small vortices are generated near interfaces. Broken interfaces and small vortices near interfaces dominate the late stage of flow fields with strong surface tension.

A new fourth order finite difference scheme for the heat equation

Abstract We propose and investigate a new simple fourth order finite difference scheme for the heat equation. Numerical simulations do confirm theoretical analysis of accuracy and stability condition.