No abstract

The Enskog-Vlasov equation provides a consistent description of the microscopic molecular interactions for real fluids based on the kinetic and mean-field theories. The present fluid flows in nano-channels are investigated by the Enskog-Vlasov-BGK model, which simplifies the complicated Enskog-Vlasov collision operator and enables large-scale engineering design simulations. The density distributions of real fluids are found to exhibit inhomogeneities across the nano-channel, particularly at large densities, as a direct consequence of the inhomogeneous force distributions caused by the real fluid effects including the fluid molecules' volume exclusion and the long-range molecular attraction. In contrast to the Navier-Stokes equation with the slip boundary condition, which fails to describe nano-scale flows due to the coexistence of confinement, non-equilibrium, and real fluid effects, the Enskog-Vlasov-BGK model is found to capture these effects accurately as confirmed by the corresponding molecular dynamics simulations for low and moderate fluid densities.

In this work, a discrete unified gas kinetic scheme (DUGKS) is developed for multi-species flow in all flow regimes based on the Andries-Aoki-Perthame (AAP) kinetic model. Although the species collision operator in the AAP model conserves fully the mass, momentum, and energy for the mixture, it does not conserve the momentum and energy for each species due to the inter-species collisions. In this work, the species collision operator is decomposed into two parts, one part is fully conservative for the species and the other represents the excess part. With this decomposition, the kinetic equation is solved following the Strang-splitting procedure, in which the excess part of the collision operator is treated as a source, while the kinetic equation with the species conservative part is solved by the standard DUGKS. Particularly, the time integration of the source term is realized by either explicit or implicit Euler scheme. By this means, it is easy to extend the scheme to gas mixtures composed of Maxwell or hard-sphere molecules, while the previous DUGKS [Y. Zhang et al., Phys. Rev. E 97, 053306 (2018)] of binary gases was only designed for Maxwell molecules. Several tests are performed to valid the scheme, including the shock structure and plane Couette flow. Excellent agreement is observed between the solutions of the present method and the previous DUGKS and the unified gas kinetic scheme. The results also show that the present DUGKS with implicit source discretization is preferable for gas mixture flow problems involving different flow regimes.