Wall Orientation and Shear Stress in the Lattice Boltzmann Model

TL;DR

This paper introduces a simple, accurate method for calculating wall shear stress in lattice Boltzmann simulations, improving boundary normal estimation and demonstrating its application in medical artery flow analysis.

Contribution

It presents a new formula for wall shear stress calculation and a weighted mean approach for wall normal estimation, enhancing accuracy near boundaries in lattice Boltzmann models.

Findings

Improved accuracy of wall normal vectors in 2D and 3D.

Minor influence of normal vector errors on shear stress accuracy.

Successful application to human abdominal aorta flow simulation.

Abstract

The wall shear stress is a quantity of profound importance for clinical diagnosis of artery diseases. The lattice Boltzmann is an easily parallelizable numerical method of solving the flow problems, but it suffers from errors of the velocity field near the boundaries which leads to errors in the wall shear stress and normal vectors computed from the velocity. In this work we present a simple formula to calculate the wall shear stress in the lattice Boltzmann model and propose to compute wall normals, which are necessary to compute the wall shear stress, by taking the weighted mean over boundary facets lying in a vicinity of a wall element. We carry out several tests and observe an increase of accuracy of computed normal vectors over other methods in two and three dimensions. Using the scheme we compute the wall shear stress in an inclined and bent channel fluid flow and show a minor influence of the normal on the numerical error, implying that that the main error arises due to a corrupted velocity field near the staircase boundary. Finally, we calculate the wall shear stress in the human abdominal aorta in steady conditions using our method and compare the results with a standard finite volume solver and experimental data available in the literature. Applications of our ideas in a simplified protocol for data preprocessing in medical applications are discussed.