Description:

The lattice Boltzmann method (LBM) is a modern numerical method allowing the solution of non-stationary partial
differential equations by solving the Boltzmann transport equation for unknown densities of the particle probability
distribution function. The course introduces the basics of the LBM theory, derived equivalent partial differential
equations for an advection-diffusion problem and for the incompressible Newtonian flluid flow, and the basic
properties of the numerical scheme are derived. The exercises are then devoted to the practical implementation and
computations of LBM using the computational infrastructure at FNSPE CTU in Prague, especially with the focus on
GPU computing.

Contents:

1. Presentation of the lattice Boltzmann method: introduction, history, brief algorithm, basic properties and modern
applications, dimensionless and characteristic quantities.
2. Boltzmann transport equation, space discretization, equilibrium distribution function approximation
3. General LBM algorithm, overview of modern LBM variants (SRT, MRT, CLBM, CuLBM, KBC, ELBM, etc.)
4. Derivation of equivalent partial differential equation, order of accuracy
5. LBM boundary conditions
6. Selected methods involving LBM: Phasefield equation, transport equation, immersed boundary method for fluid
interaction with solid or elastic body

Seminar contents:

1. Analysis of the numerical scheme - derivation of the equivalent partial differential equation
2. Implementation of basic LBM algorithm in C ++ for serial and parallel CPU computing.
3. Implementation of basic LBM algorithm in C ++ and CUDA for parallel computing on GPU.
4. Boundary conditions for LBM
5. Verification of the LBM numerical solution using analytical or exact solutions

Recommended literature:

Key references:
[1] Krüger, T., et al. The lattice Boltzmann method. Springer International Publishing 10 (2017): 978-3.
[2] Guo, Z. and Chang S. Lattice Boltzmann method and its applications in engineering. Vol. 3. World Scientific, 2013.
[3] Huang H, Sukop M and Lu X. Multiphase lattice Boltzmann methods: Theory and application. John Wiley & Sons;
2015.

Recommended references:
[4] Succi, S., The lattice Boltzmann equation: for fluid dynamics and beyond. Oxford University Press, 2001.
[5] Mohamad, A.A., Lattice Boltzmann method: fundamentals and engineering applications with computer codes.
Springer Science & Business Media, 2011.

Keywords:

Lattice Boltzmann method, numerical solution of partial differential equations

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar