A Lattice Boltzmann and Immersed Boundary Scheme for Model Blood Flow in Constricted Pipes: Part 1 – Steady Flow (Communications in Computational Physics, 2014)
Hemodynamics is a complex problem with several distinct characteristics;fluid is non-Newtonian, flow is pulsatile in nature, flow is three-dimensional due tocholesterol/plague built up, and blood vessel wall is elastic. In order to simulate thistype of flows accurately, any proposed numerical scheme has to be able to replicatethese characteristics correctly, efficiently, as well as individually and collectively. Sincethe equations of the finite difference lattice Boltzmann method (FDLBM) are hyperbolic, and can be solved using Cartesian grids locally, explicitly and efficiently on parallel computers, a program of study to develop a viable FDLBM numerical schemethat can mimic these characteristics individually in any model blood flow problemwas initiated. The present objective is to first develop a steady FDLBM with an immersed boundary (IB) method to model blood flow in stenoic artery over a range ofReynolds numbers. The resulting equations in the FDLBM/IB numerical scheme canstill be solved using Cartesian grids; thus, changing complex artery geometry can betreated without resorting to grid generation. The FDLBM/IB numerical scheme is validated against known data and is then used to study Newtonian and non-Newtonianfluid flow through constricted tubes. The investigation aims to gain insight into theconstricted flow behavior and the non-Newtonian fluid effect on this behavior.