3d Pulsatile Flow With the Lattice Boltzmann BGK Method

Abstract

We present detailed analysis of the accuracy of the lattice Boltzmann BGK method in simulating pulsatile flow in a 2D channel and a 3D tube. For the 2D oscillatory flow, we have observed a half time-steps shift between the theory and the simulation, that enhances the accuracy at least one order of magnitude. For 3D tube flow, we have tested the accuracy of the lattice Boltzmann BGK method in recovering the Womersley solution for pulsatile flow in a rigid tube with a sinusoidal pressure gradient. The obtained flow parameters have been compared to the analytical solutions. The influence of different boundary conditions such as the bounce-back and inlet-outlet boundary conditions on the accuracy was studied. Relative errors of the order of 0.001 in 2D with the bounce back on the nodes have been achieved. For the 3D simulations, it has been possible to reduce the error from 15% with the simple bounce-back to less than 5% with a curved boundary condition.

Mesoscopic simulations of systolic flow in the human abdominal aorta

“…It is a discretization of the Boltzmann equation that describes the evolution of particles in kinetic theory. Due to its simple implementation, straightforward parallelization and easy grid generation, the capability of the lattice Boltzmann method has been demonstrated in various complex applications including Newtonian blood flow simulations (Krafczyk et al, 1998;Artoli et al, 2002), nonNewtonian and suspension flows (e.g. Ladd, 1994), and complex geometry (e.g.…”

“…Secondly, the pressure is simply a linear function in the speed of sound (p ¼ rc 2 s ) while the NS solvers need to solve the Poisson equation. Finally and most important for the field of hemodynamics, is that the stress tensor can be directly obtained from the non-equilibrium parts of the distribution functions f ð1Þ i through the following relation (Ladd, 1994;Artoli et al, 2002) …”

“…All these advantages make the lattice Boltzmann method a promising candidate for simulating time-dependent blood flow in arteries. The lattice Boltzmann method can easily be adapted to simulate time-dependent flows such as the flow driven by a cardiac pressure cycle in a tube (Artoli et al, 2002). Since it is a linear function in the pressure, timedependent density gradients can easily be implemented to represent a systolic flow rate.…”

Unsteady flow in a 2D elastic tube with the LBGK method

“…In particular, we focus on modeling blood flow in the large arteries of the human body. We recently showed that LBGK is in principle capable of simulating such flows within the range of Reynolds and Womersley numbers that exist in the large arteries [1]. As a proof of concept we applied LBGK to simulate flow in the lower abdominal aorta, including the bifurcation to the left and right illiac arteries (supplying the legs with blood) [2,3].…”

Accuracy versus Performance in Lattice Boltzmann BGK Simulations of Systolic Flows

“…Suitability and accuracy of the newly established lattice Boltzmann method in simulating time dependent fluid flows is demonstrated in the literature [1,2,3]. It is shown that use of curved boundary conditions noticeably enhances the accuracy as compared to using the simple bounce-back on the links [4,5].…”