The kinetic model with multiple integral terms based on the Enskog-Vlasov(EV) equation is widely employed to describe the inhomogeneous fluids at the nanoscale. However, previous studies based on the kinetic model have mainly focused on the one-dimensional cases. This is partly due to the fact that the direct computation of integrals leads to a significant computational cost O(NNσ), where N and Nσ are the number of cells in the entire flow field and a cube with a side length equal to the molecular diameter σ, respectively. In this study, a discrete unified gas kinetic scheme (DUGKS) with efficient numerical strategies for integrals is proposed to overcome the inefficiency of the direct method, reducing the computational cost to O(N). The accuracy and efficiency of the proposed DUGKS are assessed by comparing our numerical results for both static fluid structures and dynamic flow behaviors with those from direct method, molecular dynamics (MD) and Monte Carlo simulations. We present speedups for two-dimensional pressure-driven flows with varying Nσ to further demonstrate the efficiency of the proposed DUGKS. The results show that CPU time is reduced by up to two orders of magnitude compared to the direct method, and the speedup is proportional to Nσ. Overall, proposed DUGKS can serve as a potential numerical tool for two- and three-dimensional simulations of various fluid-solid systems at the nanoscale

Strongly inhomogeneous fluids, Kinetic model, Discrete unified gas kinetic scheme, Nano-confined flows