# Computational Fluid Dynamics using the Lattice Boltzmann Method

## Tianyu Raymond Li

### Bachelor of Mathematics Advanced (Honours) Project

### 2013

### Abstract

Computational fluid dynamics is a subset of fluid mechanics that analyses and
incorporates numerical method and algorithms to solve fluid flow problems. It
is an increasingly important discipline as there exists many natural phenomena
that cannot be formulated with an analytical solution. The Lattice Boltzmann
method is a newer class of computational fluid dynamics schemes that simulates
fluid flow by solving a discretised Boltzmann equation in conjunction with
particle collision models. This thesis shall present a full derivation of the
Navier-Stokes equations (the governing equations of fluid flow) under
prescribed assumptions, the history and development of the Lattice
Boltzmann Method, the Lattice Boltzmann algorithm and verification against
benchmark scenarios. The physical problems used as comparison are Poiseuille
flow and fluid flow in a lid driven cavity. Additionally, Navier-Stokes
equations can be recovered from the discretised Boltzmann equation via the
Chapman-Enskog expansion; a complete derivation and justification will also
be included.

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Page Created: 28th June 2015.

Last Updated: 28th June 2015.