Stabilized Lattice Boltzmann-Enskog method for compressible flows and its application to one and two-component fluids in nanochannels

TL;DR

This paper introduces a stable numerical method for solving the Boltzmann-Enskog equation for non-ideal fluids, effectively reducing errors and enabling detailed simulations of compressible flows in nanochannels.

Contribution

The paper presents a novel stabilized lattice Boltzmann-Enskog method incorporating a Lagrangian scheme and improved time integration to accurately simulate compressible, inhomogeneous fluid flows.

Findings

Significantly reduces numerical errors in single-component fluid simulations.

Successfully models two-component fluid flow in complex nanochannel geometries.

Demonstrates improved stability and accuracy over previous methods.

Abstract

A numerically stable method to solve the discretized Boltzmann-Enskog equation describing the behavior of non ideal fluids under inhomogeneous conditions is presented. The algorithm employed uses a Lagrangian finite-difference scheme for the treatment of the convective term and a forcing term to account for the molecular repulsion together with a Bhatnagar-Gross-Krook relaxation term. In order to eliminate the spurious currents induced by the numerical discretization procedure, we use a trapezoidal rule for the time integration together with a version of the two-distribution method of He et al. (J. Comp. Phys 152, 642 (1999)). Numerical tests show that, in the case of one component fluid in the presence of a spherical potential well, the proposed method reduces the numerical error by several orders of magnitude. We conduct another test by considering the flow of a two component fluid in a channel with a bottleneck and provide information about the density and velocity field in this structured geometry.