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Fluid Dynamics with the Lattice Boltzmann Method
Last Updated: 2026-06-03 00:07:39
Abstract
The course provides an introduction to theoretical foundations and practical usage of the Lattice Boltzmann Method for fluid dynamics simulations.
Objective
Methods like molecular dynamics, DSMC, lattice Boltzmann etc are being increasingly used by engineers all over and these methods require knowledge of kinetic theory and statistical mechanics which are traditionally not taught at engineering departments. The goal of this course is to give an introduction to ideas of kinetic theory and non-equilibrium thermodynamics with a focus on developing simulation algorithms and their realizations. During the course, students will be able to develop a lattice Boltzmann code on their own. Practical issues about implementation and performance on parallel machines will be demonstrated hands on. Central element of the course is the completion of a lattice Boltzmann code (using the framework specifically designed for this course). The course will also include a review of topics of current interest in various fields of fluid dynamics, such as multiphase flows, reactive flows, microflows among others. Optionally, we offer an opportunity to complete a project of student's choice as an alternative to the oral exam. Samples of projects completed by previous students will be made available.
Content
The course builds upon three parts: I Elementary kinetic theory and lattice Boltzmann simulations introduced on simple examples. II Theoretical basis of statistical mechanics and kinetic equations. III Lattice Boltzmann method for real-world applications. The content of the course includes: 1. Background: Elements of statistical mechanics and kinetic theory: Particle's distribution function, Liouville equation, entropy, ensembles; Kinetic theory: Boltzmann equation for rarefied gas, H-theorem, hydrodynamic limit and derivation of Navier-Stokes equations, Chapman-Enskog method, Grad method, boundary conditions; mean-field interactions, Vlasov equation; Kinetic models: BGK model, generalized BGK model for mixtures, chemical reactions and other fluids. 2. Basics of the Lattice Boltzmann Method and Simulations: Minimal kinetic models: lattice Boltzmann method for single-component fluid, discretization of velocity space, time-space discretization, boundary conditions, forcing, thermal models, mixtures. 3. Hands on: Development of the basic lattice Boltzmann code and its validation on standard benchmarks (Taylor-Green vortex, lid-driven cavity flow etc). 4. Practical issues of LBM for fluid dynamics simulations: Lattice Boltzmann simulations of turbulent flows; numerical stability and accuracy. 5. Microflow: Rarefaction effects in moderately dilute gases; Boundary conditions, exact solutions to Couette and Poiseuille flows; micro-channel simulations. 6. Advanced lattice Boltzmann methods: Entropic lattice Boltzmann scheme, subgrid simulations at high Reynolds numbers; Boundary conditions for complex geometries. 7. Introduction to LB models beyond hydrodynamics: Relativistic fluid dynamics; flows with phase transitions.
Resources
Lecture Notes
Lecture notes on the theoretical parts of the course will be made available.Selected original and review papers are provided for some of the lectures on advanced topics.Handouts and basic code framework for implementation of the lattice Boltzmann models will be provided.
General Information
- Language
- English
- Levels
- BSC , DR , MSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- oral 30 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture with exercise | Fluid Dynamics with the Lattice Boltzmann Method | No time listed | 3 h weekly |
Offered In
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Core Courses (The Core Courses in the Master’s program Mechanical Engineering listed below are indicative and include courses designed by the Department at the Master's level. With the approval of the tutor, students may also select Master's-level courses offered by other departments at ETH. These courses will be marked as non-regular in the LAG, but their categorization as Core Courses is possible if included in the approved LAG.)
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Fluid Dynamics (One of the course units 151-0103-00L Fluid Dynamics II 151-0109-00L Turbulent Flows is compulsory. Students able to follow courses in German are advised to choose 151-0103-00L Fluid Dynamics II.)
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General Electives (Students may choose General Electives from the entire course programme of ETH Zurich - with the following restrictions: courses that belong to the first or second year of a Bachelor curriculum at ETH Zurich as well as courses from GESS "Science in Perspective" are not eligible here. The following courses are explicitly recommended to physics students by their lecturers. (Courses in this list may be assigned to the category "General Electives" directly in myStudies. For the category assignment of other eligible courses keep the choice "no category" and take contact with the Study Administration ( ) after having received the credits.))
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Doctorate Materials Science (Further information at: )
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Deep Track Courses (At least 20 credits must be completed within the deep track courses. Surplus credit points can be counted towards the electives.)
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Elective Courses Aerospace Engineering (These subjects can only be credited as electives.)
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