Equilibrium distribution functions for lattice model D3Q15 are proposed in the framework of lattice Boltzmann method in free energy model. Bubble merging process is studied. It shows that bubble merging not only depends on initial bubble distance, but also depends on surface tension. The greater the surface tension is, the greater the critical distance for bubble merging. Furthermore, influence of initial bubble distance, surface tension and viscosity on merging velocity are investigated.

Turbulence in the presence of rotation is numerically investigated with MRT-lattice Bohzmann method. Influence of rotation (Rossby number and Ekman number) on turbulence is studied in detail. Numerical results include turbulence energy, dissipation rate, iso-surface of velocity, vortex structure, dissipation length and integral length and so on. It shows that rotation slows down turbulence energy decaying rate. Moreover, the initial homogeneity of turbulence is broken down in the presence of rotation. Vortices rotating in opposite direction of the system are suppressed gradually and columnar vortices appear rotating in the same direction of the system eventually. In addition, it was found that Kolmogorov length decreases as rotation increases while integral length increases.

A fluctuating-lattice Boltzmann method is used for direct numerical simulations of Brownian motion of non-spherical particles. Numerical results include mean-square velocities and velocity autocorrelation functions of elliptical and rectangular particles. It showns that equi-partition theorem applies to non-spherical particles as well and energy of each degree of freedom depends on corresponding mean-square velocity or rotational velocity. Furthermore, translational temperature of Brownian particle is identical to its rotational temperature. Finally, velocity autocorrelation function of Brownian particle decays at relative long times as~ct^-1, where coefficlent c is independent of particle shape.

A compressible lattice-Boltzmann model coupled with non-equilibrium extrapolation method are adopted to simulate gas flow in microchannels at slip regime (Kn≤0.1).Numerical results,including velocity profiles at outlet,pressure distributions and mass flowrates,agree well with analytical solutions and experimental results.In addition,gas flow in a 180 degree curved channel is numerically simulated.It shows that boundary layer separation is suppressed by slip velocity at the wall.In addition,mass flowrate of a curved channel is smaller than that of a straight one.

An LB-DF/FD method,combined with lattice Boltzmann method (LBM) and direct-forcing/fictitious domain (DF/FD) scheme,is set up for fluid-solid interaction problems.The LB-DF/FD method uses two unrelated meshes to avoid re-meshing procedure.They are Eulerian mesh for the flow domain and Lagrangian mesh for the solid domain.LB-DF/FD method overcomes fluctuations in computation of forces on solid particle in conventional LBM.The method is validated with simulation of flow past a fixed circular cylinder,a circular cylinder moving in an infinite channel or rotating in an infinite field.Flow around two circular cylinders in tandem at low Reynolds numbers is simulated by using LB-DF/FD method.Effects of spacing gap between cylinders (g^*) and Renolds number (Re) are investigated.Numerical results including streamlines,lift and drag force and torque exerted on the cylinder,at Re=0.001,0.1 and 10,0.2≤g^*≤8.0 are presented.g^* shows remarkable effect on lift and drag force and torque exerted on cylinders.Stokes cell number and drag force exerted on cylinders depend on Re.

A unified method is proposed to treat 3D moving boundaries at arbitrary velocity as an extension of kinetic format and bounce-back format. Velocities at inlet and on solid wall are special cases of the model. A simplified expression is given in a three dimensional 15-velocity model. Numerical simulation for a diagonally lid-driven three-dimensional cavity flow is performed to verify this scheme. Compared with finite difference method (FDM), the proposed method proves reasonable.