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An assessment of lattice Boltzmann method for swallowing simulations Mazhari, Seyed Babak

Abstract

Lattice Boltzmann is a fixed grid particle based method originated from molecular dynamics which uses a kinetic-based approach to simulate fluid flows. The fixed grid nature and simplicity of lattice Boltzmann algorithm makes it an appealing approach for preliminary swallowing simulations. However, the issues of compressibility effect and boundary/initial condition implementation can be the source of instability and inaccuracy especially at high Reynolds simulations. The current work is an assessment of the lattice Boltzmann method with respect to high Reynolds number flow simulations, compressibility effect of the method, and the issue of boundary and initial condition implementation. Here we investigate the stability range of the lattice Boltzmann single relaxation and multi relaxation time models as well as the issue of consistent boundary/initial condition implementation. The superior stability of multi relaxation time (MRT) model is shown on the lid-driven cavity flow benchmark as a function of Reynolds number. The computational time required for the SRT model to simulate the li-driven cavity flow at Re=3200 is about 14 times higher than the MRT model and it’s shown that computational time is related to the third power of lattice resolution. It is suggested that single relaxation time model is inefficient for simulations with moderately high Reynolds number Re>1000 and the use of multi relaxation time model becomes necessary. Compressibility effect is the next topic of study where the incompressible lattice Boltzmann method is introduced. The compressibility error of the method surpasses the spatial discretization error and becomes the dominant source of error as the flow Reynolds number increases. It is shown on a 2D Womersley flow benchmark that the physical time step required for LBM is about 300 times larger than the physical time step of the finite volume implicit solver while generating results with the same order of accuracy at Re=2000. Due to the compressibility error inherent to the method, lattice Boltzmann is not recommended for preliminary swallowing simulations with high Reynolds number, since implicit time advancement methods can generate results with the same order of accuracy in noticeably less computational time.

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