A Discrete Boltzmann Method (DBM) with a Maxwell-type boundary condition is constructed to investigate the influence of rarefaction on laminar Shock Wave/Boundary Layer Interaction (SWBLI). Due to the complexity of compressible flow, a Knudsen number vector Kn, whose components include the local Knudsen numbers such as Kn_ρ and Kn_U, is introduced to characterize the local structures, where Kn_ρ and Kn_U are Knudsen numbers defined in terms of the density and velocity interfaces, respectively. Since first focusing on the steady state of SWBLI, the DBM considers up to the second-order Kn_ρ (rarefaction/non-equilibrium) effects. The model is validated using Mach number 2 SWBLI and the necessity of using DBM with sufficient physical accuracy is confirmed by the shock collision problem. Key findings include the following: the leading-edge shock wave increases the local density Knudsen number Kn_ρ and eventually leads to the failure of linear constitutive relations in the Navier-Stokes (N-S) model and surely also in the lower-order DBM; the non-equilibrium effect differences in regions behind the leading-edge shock wave are primarily correlated with Kn_ρ, while in the separation region are primarily correlated with Kn_U; the non-equilibrium quantities D₂ and D_4,2, as well as the viscous entropy production rate Ṡ_NOMF can be used to identify the separation zone. The findings clarify various effects and main mechanisms in different regions associated with SWBLI, which are concealed in N-S model.

The understanding of flow behavior in rough fractures is essential for many engineering activities. When the aperture of a rough fracture approaches the mean free path of fluid molecules, the microflow effect, sometimes also referred to relative rarefaction effect, relative discrete effect or non-equilibrium effect, becomes pronounced. It was found often to enhance the flow rate. However, the surface roughness shows completely contrary influence. In order to clarify the influences of the two factors, a computer simulation work accompanied with theoretical analyses is conducted. Previous empirical models for hydraulic aperture which already containing roughness effect are modified with consideration of the microflow effect. Direct simulation using the lattice Boltzmann method is conducted on artificially created 2D fractures with random roughness following Gaussian distribution to reveal the competitive relationship of two effects. The simulation results also verify modified models. Among them, the one based on Rasouli and Hosseinian's model agrees with the simulation on the relationship between hydraulic aperture and mechanical aperture for both cases with very rough fractures and relatively smooth fractures. Further investigation confirms that, under various roughness, the ratio of hydraulic aperture over mechanical aperture shows quantitatively different trends as mechanical aperture decreases. This phenomenon exists on a relatively wide scale. An equilibrium point of two effects is also found through analysis of the relationship. The results reveal the mechanism of microflow in 2D rough fractures and also provide a reference for engineering problems like the transport of natural gas through microfractures.