A family of single-node second-order boundary schemes for the lattice Boltzmann method

TL;DR

This paper introduces a universal family of second-order boundary schemes for the lattice Boltzmann method that are simple, stable, and applicable to various models, validated through numerical experiments.

Contribution

A new, simple, and universal family of second-order boundary schemes for the lattice Boltzmann method that do not depend on specific models and ensure stability.

Findings

Schemes achieve second-order accuracy with bounce-back rule

Numerical validation confirms stability and accuracy in 2D and 3D models

Applicable to multiple-relaxation-time lattice Boltzmann models

Abstract

In this work, we propose a family of single-node second-order boundary schemes for the lattice Boltzmann method with general collision terms. The construction of the schemes is quite universal and simple, it does not involve concrete lattice Boltzmann models and uses the half-way bounce-back rule as a central step. The constructed schemes are all second-order accurate if so is the bounce-back rule. In addition, the proposed schemes have good stability thanks to convex combinations. The accuracy and stability of several specific schemes are numerically validated for multiple-relaxation-time models in both 2D and 3D.