Abstract:
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This research project presents an overview of the Lattice Boltzmann Method (LBM),
an alternative numerical approach to conventional CFD. LBM has increased in
popularity among the scientific community in recent years, due to its promising
abilities. Namely, it claims to achieve the same level of accuracy as that of traditional
CFD, while offering new benefits such as easy parallelization and the possibility of
implementing complex and multiscale flows. Unlike conventional CFD which focuses
on the numerical solution of the Navier Stokes Equations, the Lattice Boltzmann
Method focuses on microscopic particle interactions to represent the macroscopic
behaviour of the fluid.
The aim of this project is to appraise the ability of the Lattice Boltzmann Method to
accurately simulate incompressible flows and to analyse its accuracy performance
and stability. This report presents the theoretical basis of this novel method, as well
as a verification of its convergence results through some examples. These examples
are implemented through an open-source code (Palabos). This project not only
focuses on matching the LBM solutions with analytical or existing solutions, but it
also focuses on studying the effect that the parameters of the model have on the
results provided, on stability and on computational cost.
The results and their analysis show that LBM is an accurate method for representing
incompressible flows. The report also describes how to implement the Lattice
Boltzmann Method and suggests some ways to continue the work further. |