Lattice Boltzmann Method

Garant předmětu:

Radek Fučík

Lecturer:

Radek Fučík

Tutor:

Pavel Eichler, Radek Fučík

Supervisor:

Department of Mathematics

Synopsis:

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.

Requirements:

Syllabus of lectures:

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

Syllabus of tutorials:

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

Study Objective:

Study materials:

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.

Note:

Time-table for winter semester 2023/2024:

Time-table is not available yet

Time-table for summer semester 2023/2024:

Time-table is not available yet

The course is a part of the following study plans:

• Matematické inženýrství (compulsory elective course)