Analytical and numerical studies have shown that multipolar vortices can emerge in two-dimensional flow due to azimuthal normal mode perturbations of shielded vortices. It has been found that mode 2 and 3 perturbations can lead to the formation of stable tripoles and quadrapoles, respectively, while higher order modes result in more complex unstable compound vortices. We have used the lattice Boltzmann method to simulate the effect of azimuthal perturbations on shielded vortices at moderate Reynolds numbers. We have found that azimuthal normal mode perturbations result in the formation of multipoles, which decay due to viscous dissipation. We could also observe that the outcome of such simulations is very sensitive to the displacement of perturbations above wavenumber-3 excitations, in spite of the significant viscosity we used.

We review recent developments in lattice Boltzmann method for reacting flows in porous media.  We present the lattice Boltzmann approaches for incompressible flow, solute transport and chemical reactions in both the pore space and at the fluid/solid interfaces. We discuss in detail the methods to update solid phase when significant mass transfer between solids and fluids is involved due to dissolution and/or precipitation. Applications in different areas are presented and perspectives of applying this method to a few important fields are discussed.

The problem of forced convection heat transfer of supercritical CO₂ in a horizontal channel is investigated numerically by a lattice Boltzmann method. This study is stimulated by our recent experimental findings on solar collectors using supercritical CO₂ as a working fluid, which can achieve the collector efficiency high up to 70%. To deeply understand the heat transfer characteristics of supercritical CO₂ and provide a theoretical guidance for improving our current experimental system, in present study several typical experimental flow conditions are simulated. In particular, the work focuses on the convective heat transfer characteristics of supercritical CO₂ flowing in a horizontal channel with mediate Reynolds numbers ranging from 210 to 840 and constant heat fluxes from 400.0 to 800.0 W/m$^2$. The simulations show that the heat transfer increases with heat flux and decreases with Reynolds number. Furthermore, the mechanisms of heat transfer enhancement of supercritical CO₂ fluid are identified.

A 2D lattice Boltzmann model for inviscid compressible flows was proposed in this paper. Finite volume method was implemented on 2D curvilinear structural grids to solve the lattice BGK-Boltzmann equations. MUSCL scheme was used to perform interpolation. The obtained results agree excellently well with experimental and previous numerical results.

Over the past two decades, there have been enormous advances in lattice Boltzmann (LB) numerical simulation and modelling. The lattice Boltzmann method has become a practical and promising tool for many fluid problems. A majority of recent studies have relied on numerical computations of isothermal flows. However, much less efforts have been devoted to complex thermal flows, such as flows in porous media subjected to external magnetic force, flows with temperature-dependent properties. In this paper, an overview is made based on some accomplishments in these numerical endeavours. Along with the paper's sections, the state-of-the-art trend and the LBM advances in modelling and in computational aspects for specific classes of problems of major interest will be fully touched on. Concluding remarks are given and the axis of our future studies will be traced.

The widely used micro-flow wall-boundary conditions for lattice Boltzmann method (LBM) are evaluated in a force driven combined nanochannel flow. The flow field consists of a two-dimensional nanochannel (mother channel) of an infinite length having flat plates of a finite length inside. The flat plate is set above the bottom wall of the nanochannel with a narrow gap. The flow, thus, develops through this narrow gap (narrower channel) and the other side of the plate (wide gap). The Knudsen number based on the mother channel height is Kn=0.14 whereas the characteristic Knudsen number in the narrower channel is 1.1. To obtain the reference data, the molecular dynamics (MD) simulation is performed with a fully diffusive wall condition. The LBMs are based on the lattice BGK model and with the bounce-back/specular reflection (BSBC) and the diffuse scattering (DSBC) wall boundary conditions. The relaxation time is modified to include sensitivity to Kn. The DSBC shows generally satisfactory results in the test flow cases including fully developed force driven Poiseuille flows, where the BSBC performs worse at Kn>0.5 with a fixed bridge coefficient of $b=0.7$. This results in its overprediction of the flow rate in the narrower channel region since the characteristic Knudsen number there is 1.1. The MD simulation suggests that the flow develops gradually through the narrower channel region though all the LBM predictions show almost instant flow development. This fact suggests that the relaxation time model needs to have more sensitivity to the locally defined Kn. Further discussions of the BSBC with a different set of models suggest that the regularization process is required for predicting complex nanoscale flows.

A semiclassical lattice Boltzmann method is presented for axisymmetric flows of gas of particles of arbitrary statistics. The method is first derived by directly projecting the Uehling-Uhlenbeck Boltzmann-BGK equations in two-dimensional rectangular coordinates onto the tensor Hermite polynomials using moment expansion method and then the forcing strategy of Halliday et al. (Phys. Rev. E., 64 (2001), 011208) is adopted and forcing term is added into the resulting microdynamic evolution equation.  The determination of the forcing terms is dictated by yielding the emergent macroscopic equations toward a particular target form. The correct macroscopic equations of the incompressible axisymmetric viscous flows are recovered through the Chapman-Enskog expansion. Computations of uniform flow over a sphere to verify the method are included. The results also indicate distinct characteristics of the effects of quantum statistics.

We investigate a two-relaxation-time (TRT) lattice Boltzmann algorithm with the asymptotic analysis technique. The results are used to analyze invariance properties of the method. In particular, we focus on time dependent Stokes and Navier-Stokes problems.

To understand lattice Boltzmann model capability for capturing non-equilibrium effects, the model with first-order expansion of the equilibrium distribution function is analytically investigated. In particular, the velocity profile of Couette flows is exactly obtained for the D2Q9 model, which shows retaining the first order expansion can capture rarefaction effects in the incompressible limit. Meanwhile, it clearly demonstrates that the D2Q9 model is not able to reflect flow characteristics in the Knudsen layer.

In this paper, we apply a recently proposed thermal axisymmetric lattice Boltzmann model to the thermocapillary driven flow in a cylindrical container. The temperature profiles and isothermal lines at the free surface with Prandtl (Pr) number fixed at 0.01 and Marangoni (Ma) number varying from 10 to 500 are measured and compared with the previous numerical results. In addition, we also give the numerical results for different Ma numbers at Pr=1.0. It is shown that present results agree well with those reported in previous studies.

Lattice-Boltzmann (LB) simulations are a common tool to numerically estimate the permeability of porous media. For valuable results, the porous structure has to be well resolved resulting in a large computational effort as well as high memory demands. In order to estimate the permeability of realistic samples, it is of importance to not only implement very efficient codes, but also to choose the most appropriate simulation setup to achieve accurate results. With the focus on accuracy and computational effort, we present a comparison between different methods to apply an effective pressure gradient, efficient boundary conditions, as well as two LB implementations based on pore-matrix and pore-list data structures.