An efficient discrete unified gas kinetic scheme for strongly inhomogeneous fluids at the nanoscale

Abstract

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 have mainly focused on one-dimensional cases, partly due to the significant computational cost $O(NN_{\sigma})$ associated with direct computation of integrals, where $N$ is the number of cells in the flow field and $N_\sigma$ is the number of cells in a cube with a side length equal to the molecular diameter $\sigma$. In this study, we propose a discrete unified gas kinetic scheme (DUGKS) with efficient numerical strategies for integrals to overcome the inefficiency of the direct method, reducing the computational cost to $O(N)$. Both accuracy and efficiency of the proposed DUGKS are assessed through several test cases, including static fluid structures and force-driven flow dynamics in parallel plate channels. As example applications, pressure-driven flow between two flat plates and force-driven flow in a square duct are investigated to highlight distinctive phenomena at the nanoscale.