Choice of boundary condition for lattice-Boltzmann simulation of moderate Reynolds number flow in complex domains

TL;DR

This study compares different boundary conditions for lattice-Boltzmann simulations of blood flow in complex geometries, finding that Bouzidi-Firdaouss-Lallemand and Guo-Zheng-Shi methods offer higher accuracy and efficiency.

Contribution

It implements and evaluates three boundary condition methods in an open-source lattice-Boltzmann code for complex, physiologically relevant blood flow simulations.

Findings

Bouzidi-Firdaouss-Lallemand and Guo-Zheng-Shi methods achieve second-order spatial convergence.

Simple bounce-back degrades to first-order accuracy.

BFL method performs better in unsteady flows and is computationally less expensive.

Abstract

Modeling blood flow in larger vessels using lattice-Boltzmann methods comes with a challenging set of constraints: a complex geometry with walls and inlet/outlets at arbitrary orientations with respect to the lattice, intermediate Reynolds number, and unsteady flow. Simple bounce-back is one of the most commonly used, simplest, and most computationally efficient boundary conditions, but many others have been proposed. We implement three other methods applicable to complex geometries (Guo, Zheng and Shi, Phys Fluids (2002); Bouzdi, Firdaouss and Lallemand, Phys. Fluids (2001); Junk and Yang Phys. Rev. E (2005)) in our open-source application \HemeLB{}. We use these to simulate Poiseuille and Womersley flows in a cylindrical pipe with an arbitrary orientation at physiologically relevant Reynolds (1--300) and Womersley (4--12) numbers and steady flow in a curved pipe at relevant Dean number (100--200) and compare the accuracy to analytical solutions. We find that both the Bouzidi-Firdaouss-Lallemand and Guo-Zheng-Shi methods give second-order convergence in space while simple bounce-back degrades to first order. The BFL method appears to perform better than GZS in unsteady flows and is significantly less computationally expensive. The Junk-Yang method shows poor stability at larger Reynolds number and so cannot be recommended here. The choice of collision operator (lattice Bhatnagar-Gross-Krook vs.\ multiple relaxation time) and velocity set (D3Q15 vs.\ D3Q19 vs.\ D3Q27) does not significantly affect the accuracy in the problems studied.