Most of the existing lattice Boltzmann BGK models (LBGK) can be viewed as compressible schemes to simulate incompressible fluid flows. The compressible effect might lead to some undesirable errors in numerical simulations. In this paper a LBGK model without compressible effect is designed for simulating incompressible flows. The incompressible Navier-Stokes equations are exactly recovered from this incompressible LBGK model. Numerical simulations of the plane Poiseuille flow, the unsteady 2-D shear decaying flow, the driven cavity flow, and the flow around a circular cylinder are performed. The results agree well with the analytic solutions and the results of previous studies.

A second-order moment (SOM) model for gas-phase turbulence, combined with a Langevin-based probability density function (PDF) transport model for particle-phase turbulence, named SOM-PDF model for gas-particle turbulence, is proposed here. The SOM is solved by the well-known finite-volume method (FVM), while the PDF is solved by directly calculate the Langevin equation for both particle velocity and fluid velocities seen by particles, as proposed by Simonin (1996), using pseudo time-dependent Monte-Carlo method (MC). A time-averaged method is used to reduce the amount of stochastic-particle needed. The DSM-PDF model was applied to simulate a gas-particle turbulent flow in a pipe with expansion. The prediction results are compared with PDPA measured results and those predicted using the PDF derived ensemble-averaged stress model (ESM). The comparison shows that both models can well predict the averaged flow field of particle phase, while the DSM-PDF model got a better distribution of particle time-averaged velocity and fluctuation velocity at the area where shear is dominant. The difference may arise from several aspects: the merits of MC technology of no numerical diffusion, and most important, the capability of taken into account the effect of non-Gaussian distribution of particle velocities at shear dominant area, while Gaussian distribution is pre-assumed for ESM.

A second-order moment (SOM) gas-phase turbulence model, combined with a Monte-Carlo (MC) simulation of stochastic particle motion using Langevin equation to simulate the gas velocity seen by particles, is called an SOM-MC two-phase turbulence model. The SOM-MC model was applied to simulate swirling gas-particle flows with a swirl number of 0.47. The prediction results are compared with the PDPA measurement data and those predicted using the Langevin-closed unified second-order moment (LUSM) model. The comparison shows that both models give the predicted time-averaged flow field of particle phase in general agreement with those measured, and there is only slight difference between the prediction results using these two models. In the near-inlet region, the SOM-MC model gives a more reasonable distribution of particle axial velocity with reverse flows due to free of particle numerical diffusion, but it needs much longer computation time. Both models underpredict the gas and particle fluctuation velocities, compared with those measured. This is possibly caused by the particle-wall and particle-particle interaction in the near-wall region, and the effect of particles on dissipation of gas turbulence, which is not taken into account in both models.

Two type of structures-Turing patterns and spiral waves-are obtained in chloride-iodide-malonic acid (CIMA) reaction-diusion model by using lattice Bhatnagar-Gross-Krook (LBGK) method.

A boundary treatment for curved walls in lattice Boltzmann method is proposed. The distribution frmction at a wall node who has a link across the physical boundary is decomposed into its equilibrium and nonequilibrium parts. The equilibrium part is then approximated with a fictitious one where the boundary condition is enforced, and the nonequilibrium part is approximated using a first-order extrapolation based on the nonequilibrium part of the distribution on the neighboring fluid node. Numerical results show that the present treatment is of second-order accuracy, and has well-behaved stability characteristics.