title: Choice of boundary condition for lattice-Boltzmann simulation of moderate-Reynolds-number flow in complex domains.
abstract: Modeling blood flow in larger vessels using lattice-Boltzmann methods comes with a challenging set of constraints: a complex geometry with walls and inlets and outlets at arbitrary orientations with respect to the lattice, intermediate Reynolds (Re) 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 14, 2007 (2002); Bouzidi, Firdaouss, and Lallemand, Phys. Fluids 13, 3452 (2001); Junk and Yang, Phys. Rev. E 72, 066701 (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 Re number (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 (BFL) and Guo-Zheng-Shi (GZS) 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 Re 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.
authors.affiliation: Centre for Computational Science, Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, United Kingdom.
authors.forename: Rupert W
authors.initials: RW
authors.lastname: Nash
authors.affiliation: Centre for Computational Science, Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, United Kingdom and CoMPLEX, University College London, Physics Building, Gower Street, London, WC1E 6BT, United Kingdom.
authors.forename: Hywel B
authors.initials: HB
authors.lastname: Carver
authors.affiliation: Centre for Computational Science, Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, United Kingdom and CoMPLEX, University College London, Physics Building, Gower Street, London, WC1E 6BT, United Kingdom.
authors.forename: Miguel O
authors.initials: MO
authors.lastname: Bernabeu
authors.affiliation: Centre for Computational Science, Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, United Kingdom and Research Software Development Team, Research Computing and Facilitating Services, University College London, Podium Building - 1st Floor, Gower Street, London, WC1E 6BT, United Kingdom.
authors.forename: James
authors.initials: J
authors.lastname: Hetherington
authors.affiliation: Centre for Computational Science, Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, United Kingdom.
authors.forename: Derek
authors.initials: D
authors.lastname: Groen
authors.affiliation: Centre for Computational Science, Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, United Kingdom and Institute for Materials and Processes, School of Engineering, University of Edinburgh, King's Buildings, Mayfield Road, Edinburgh, EH9 3JL, United Kingdom.
authors.forename: Timm
authors.initials: T
authors.lastname: Krüger
authors.affiliation: Centre for Computational Science, Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, United Kingdom.
authors.forename: Peter V
authors.initials: PV
authors.lastname: Coveney
mesh_terms: D000465:Algorithms; D000818:Animals; D001783:Blood Flow Velocity / Q000502:physiology*; D001808:Blood Vessels / Q000502:physiology*; D001809:Blood Viscosity / Q000502:physiology; D003198:Computer Simulation; D006801:Humans; D008955:Models, Cardiovascular; D009716:Numerical Analysis, Computer-Assisted; D012212:Rheology / Q000379:methods*