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

TL;DR

This work tackles the computational bottleneck of simulating nano-confined, strongly inhomogeneous fluids by developing an efficient discrete unified gas kinetic scheme (DUGKS) for the Enskog-Vlasov–based kinetic model. It introduces three key improvements: (i) coarse sampling for the mean-field potential to reduce the integral workload, (ii) adaptive volume-averaging (AVAM) for the average density to maintain accuracy near walls, and (iii) a finite-difference-based nonlocal gradient evaluation that lowers complexity to $O(N)$. The proposed method demonstrates accurate static structure results and force-driven/nanoconfined flow predictions in 2D (and scalable to 3D) with substantial speedups over the original DUGKS, validating its potential for large-scale nanoscale simulations. The findings indicate that pressure-driven and force-driven flows are not generally equivalent at the nanoscale due to nonlinear density distributions, and that density-adjacent adsorption layers and corner effects strongly influence flow behavior, offering practical insights for nano-engineered systems.

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 $O(NN_σ)$ associated with direct computation of integrals, where $N$ is the number of cells in the flow field and $N_σ$ is the number of cells in a cube with a side length equal to the molecular diameter $σ$. 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.

Figures (14)

• Figure 1: Schematic of fluid molecules confined between two parallel solid walls.
• Figure 2: Density distributions of LJ fluids at different widths and average densities. (a) $H=2.5\sigma$, $n_0=0.335\sigma^{-3}$; (b) $H=3.6\sigma$, $n_0=0.476\sigma^{-3}$; (c) $H=7.5\sigma$, $n_0=0.561\sigma^{-3}$. Monte Carlo results are taken from Ref. snook1980solvation.
• Figure 3: Density profiles of LJ fluids obtained from the present DUGKS. Effects of $(a)$ temperature $(5\text{nm},\ 40\text{MPa})$; $(b)$ pressure $(5\text{nm},\ 350\text{K})$; $(c)$ channel width $(350\text{K},\ 40\text{MPa})$ on the density distribution. The MD results are given in Ref. nan2020slip. Only half domain is shown due to the symmetry.
• Figure 4: Density $(a)$ and velocity $(b)$ profiles of force-driven flow in organic nanopores obtained from the present DUGKS and the original DUGKS. The MD results can be found in Ref. chen2017channel.
• Figure 5: Density $(a)$ and velocity $(b)$ profiles of force-driven flow in inorganic nanopores obtained from the present DUGKS and the original DUGKS. The results of MD simulations are given in Ref. wang2016breakdown.