The lattice Boltzmann method (LBM) has been widely used to simulate microgaseous flows in recent years. However, it is still a challenging task for LBM to model that kind of microscale flow involving complex geometries, owing to the use of uniform Cartesian lattices in space. In this work, a boundary condition for microflows in the slip regime is developed for LBM in which the shape of a solid wall is well considered. The proposed treatment is a combination of the Maxwellian diffuse reflection scheme and the simple bounce-back method. A portion of each part is determined by the relative position between the boundary node and curved walls, which is the key point that distinguishes this method from some previous schemes where the smooth curved surface was assumed to be zigzag lines. The present curved boundary condition is implemented with the multiple-relaxation-times model and verified for several established cases, including the plane microchannel flow (aligned and inclined), microcylindrical Couette flow, and the flow over an inclined microscale airfoil. The numerical results agree well with those predicted by the direct simulation Monte Carlo method.

We analyze the transport and deposition behavior of dilute microparticles in turbulent Rayleigh–Bénard convection. Two-dimensional direct numerical simulations were carried out for the Rayleigh number (Ra) of 10⁸ and the Prandtl number (Pr) of 0.71 (corresponding to the working fluids of air). The Lagrangian point particle model was used to describe the motion of microparticles in the turbulence. Our results show that the suspended particles are homogeneously distributed in the turbulence for the Stokes number (St) less than 10⁻³, and they tend to cluster into bands for 10⁻³ ≲ St ≲ 10⁻². At even larger St, the microparticles will quickly sediment in the convection. We also calculate the mean-square displacement (MSD) of the particle’s trajectories. At short time intervals, the MSD exhibits a ballistic regime, and it is isotropic in vertical and lateral directions; at longer time intervals, the MSD reflects a confined motion for the particles, and it is anisotropic in different directions. We further obtained a phase diagram of the particle deposition positions on the wall, and we identified three deposition states depending on the particle’s density and diameter. An interesting finding is that the dispersed particles preferred to deposit on the vertical wall where the hot plumes arise, which is verified by tilting the cell and altering the rotation direction of the large-scale circulation.

Microscale gas flow attracts significant research interest in recent years since it is concerned with a wide range of engineering applications. It is noted that the Navier–Stokes equations-based scheme and the standard lattice Boltzmann method both encounter a great challenge in the simulation of such flows. The newly developed discrete unified gas kinetic scheme (DUGKS) has been demonstrated to be capable of modeling microflows, but presently it is mainly limited to the problems with straight boundaries. In this study, the ghost-cell (GC) immersed boundary method is introduced to the DUGKS for handling curved boundaries. The most attractive feature of the GC method is to set a ghost point inside the solid domain, at which the information is unknown and will be extrapolated linearly from the corresponding wall and image nodes. As for the two latter points, the distribution functions are first evaluated by the inverse distance weighted (IDW) method and then should be corrected according to the impenetrability condition and Maxwellian diffuse-scattering rule. Three typical test cases, including the plane Poiseuille flow, cylindrical Couette flow and flow through porous media are simulated to validate the present IDW-GC-DUGKS. The results demonstrate the accuracy and feasibility of the method for the gaseous microflows.