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.
Highlights
In the last two decades, lattice-Boltzmann methods (LBM) [1,2,3] have been widely studied and used for fluid flow problems
Simple bounce-back (SBB) gives the best computational performance in all cases while BFL requires between 20% and 60% more compute time; the extra time needed remains approximately constant across all collision operators and velocity sets, but reduces as a
The majority of benchmark problems reported in the latticeBoltzmann literature use lattice-aligned geometries, rather than the complex domains required by many applications
Summary
In the last two decades, lattice-Boltzmann methods (LBM) [1,2,3] have been widely studied and used for fluid flow problems. Accurate simulation of the flow of blood in an individual could have near-term clinical benefits for, inter alia, the treatment of aneurysms [4,5,6] or stenoses [7,8,9] Applications such as these have a number of challenges [retaining computational performance in a relatively sparse, three-dimensional (3D) fluid domain; capturing the complex rheology of a dense suspension of deformable particles; accounting for the compliance of vessel walls] but here we address the choice of boundary condition method in complex domains.
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