An improved boundary condition at a low grid resolution and Reynolds number

TL;DR

This paper proposes an improved boundary condition method for lattice Boltzmann simulations that enhances accuracy at low grid resolutions and Reynolds numbers, especially around complex geometries and concave corners.

Contribution

It introduces an extrapolation technique using inverse distance weighting to improve momentum conservation and achieve second-order accuracy at lower grid resolutions.

Findings

Enhanced accuracy at low grid resolution and Reynolds number.

Improved momentum conservation at concave corners.

Reduced computational cost due to lower grid resolution.

Abstract

Complex geometries can be easily treated using the well-known full-way and half-way bounce-back rules. However, the accuracy of the full-way bounce-back rule is one order lower than the half-way bounce-back rule. Moreover, when the walls are not aligned with the lattices, the errors increase. Including the collision operator on the walls with the full-way bounce-back rule leads to an improvement of the accuracy of the pressure-drop, but, a loss of momentum is observed on concave corners. We propose to improve the momentum conservation by adding an extrapolation of the density by the inverse distance weighting at concave corners. The technique is shown to give a second-order accuracy at a lower grid resolution, thus, the computational cost can be reduced.