# Fourth-order analysis of a diffusive lattice Boltzmann method for barrier coatings

## TL;DR

This paper analyzes a diffusive lattice Boltzmann method for barrier coatings, identifying higher-order corrections and boundary condition issues, ultimately demonstrating high accuracy in simulations for most parameter ranges.

## Contribution

It provides a fourth-order analysis of the lattice Boltzmann method, improves boundary conditions, and assesses the method's accuracy for simulating fluid transport in barrier coatings.

## Key findings

- Higher-order corrections improve accuracy in certain parameter ranges.
- Standard boundary conditions cause significant errors, which can be mitigated.
- The method achieves below 0.1% error in most practical scenarios.

## Abstract

We examine the applicability of diffusive lattice Boltzmann methods to simulate the fluid transport through barrier coatings, finding excellent agreement between simulations and analytical predictions for standard parameter choices. To examine more interesting non-Fickian behavior and multiple layers of different coatings, it becomes necessary to explore a wider range of parameters. However, such a range of parameters exposes deficiencies in such an implementation. To investigate these discrepancies, we examine the form of higher-order terms in the hydrodynamic limit of our lattice Boltzmann method. We identify these corrections to fourth order and validate these predictions with high accuracy. However, it is observed that the validated correction terms do not fully explain the bulk of observed error. This error was instead caused by the standard finite boundary conditions for the contact of the coating with the imposed environment. We identify a self-consistent form of these boundary conditions for which these errors are dramatically reduced. The instantaneous switching used as a boundary condition for the barrier problem proves demanding enough that any higher-order corrections meaningfully contribute for a small range of parameters. There is a large parameter space where the agreement between simulations and analytical predictions even in the second-order form are below 0.1%, making further improvements to the algorithm unnecessary for such an application.