Finite Volume Incompressible Lattice Boltzmann Framework for Non-Newtonian Flow Simulations in Complex Geometries

Akshay Dongre (), John Ryan Murdock and Song-Lin Yang
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Akshay Dongre: Department of Mechanical Engineering-Engineering Mechanics, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931, USA
John Ryan Murdock: Department of Mechanical Engineering-Engineering Mechanics, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931, USA
Song-Lin Yang: Department of Mechanical Engineering-Engineering Mechanics, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931, USA

Mathematics, 2025, vol. 13, issue 10, 1-43

Abstract: Arterial diseases are a leading cause of morbidity worldwide, necessitating the development of robust simulation tools to understand their progression mechanisms. In this study, we present a finite volume solver based on the incompressible lattice Boltzmann method (iLBM) to model complex cardiovascular flows. Standard LBM suffers from compressibility errors and is constrained to uniform Cartesian meshes, limiting its applicability to realistic vascular geometries. To address these issues, we developed an incompressible LBM scheme that recovers the incompressible Navier–Stokes equations (NSEs) and integrated it into a finite volume (FV) framework to handle unstructured meshes while retaining the simplicity of the LBM algorithm. The FV-iLBM model with linear reconstruction (LR) scheme was then validated against benchmark cases, including Taylor–Green vortex flow, shear wave attenuation, Womersley flow, and lid-driven cavity flow, demonstrating improved accuracy in reducing compressibility errors. In simulating flow over National Advisory Committee for Aeronautics (NACA) 0012 airfoil, the FV-iLBM model accurately captured vortex shedding and aerodynamic forces. After validating the FV-iLBM solver for simulating non-Newtonian flows, pulsatile blood flow through an artery afflicted with multiple stenoses was simulated, accurately predicting wall shear stress and flow separation. The results establish FV-iLBM as an efficient and accurate method for modeling cardiovascular flows.

Keywords: lattice Boltzmann method; incompressible flows; computational fluid dynamics; cardiovascular flows; non-Newtonian flows (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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