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COS 530: Computational Fluid Dynamics - The Lattice Boltzmann Method

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COS 530: Computational Fluid Dynamics - The Lattice Boltzmann Method

Course Title	Computational Fluid Dynamics - The Lattice Boltzmann Method
Course Code	COS 530
Course Type	Elective
Level	PhD
Instructor’s Name	Asst. Prof. Nikos Savva (Lead Instructor)
ECTS	5
Lectures / week	1 (90 min. each)
Laboratories / week	1 (90 min. each)
Course Purpose and Objectives	The Lattice Boltzmann method (LBM) is rapidly evolving as one of the popular numerical approaches for modelling complex fluid flows. One of its key advantages is that it is naturally massively parallel compared to more traditional methodologies and it has proved to be rather successful at modelling flows in complex geometries, multiphase flows and interfacial dynamics. The course aims to provide a concise overview of the theoretical foundations of the method, as well as expose students to the practical implementation aspects of the method through a series of hands-on laboratory sessions where they be able to develop their own LBM; practical issues about implementation and performance will also be discussed.
Learning Outcomes	By the end of the course students will: (i) understand the origins of the method and assess its relevance for a given application; benefits and limitations compared to simulations of the Navier-Stokes equation; (ii) learn practical skills adopt best practices in developing LBM codes; (iii) critically assess and evaluate the numerical and physical accuracy of the method
Prerequisites	None
Background Requirements	Knowledge of: fundamentals of statistical mechanics; a programming language e.g. C, C++, Matlab.
Course Content	Week 1: Description of fluid dynamics and different scales and overview of kinetic theory (distribution function and its moments, the Boltzmann equation and the collision operator; macroscopic conservation equations). Week 2: The Lattice Boltzmann equation. Implementation aspects; discretization in velocity space; discretization in space and time. Week 3: Analysis of the Lattice Boltzmann equation: Chapman-Enskog analysis, stability and accuracy considerations. Initial and boundary conditions (periodic conditions, wall conditions, symmetry and free-slip; momentum exchange at solid boundaries) Week 4: LBM with forces and how these influence the initial and boundary conditions; LBM for advection-diffusion problems. Week 5: Flows at moderate Reynolds numbers; Non-dimensionalization and choice of simulation parameters. Week 6: Multiphase and multicomponent flows, free-energy Lattice Boltzmann model, Shan-Chen pseudopotential method, limitations and extensions. Week 7: Improved Lattice Boltzmann models: MRT and TRT collision operators for improving accuracy; boundary conditions for fluid-structure interactions.
Teaching Methodology	- 7 x 1.5-hour lectures - 7 x 1.5-hour lab sessions - 2 journal clubs (includes preparation) - 4 marked assignments - project and presentation
Bibliography	- Krűger, T., Kusumaatmaja H., Kuzmin, A, Shardt O., Silva, G. and Viggen, E. M.Krűger, T., Kusumaatmaja H., Kuzmin, A, Shardt O., Silva, G. and Viggen, E. M.(2017) The Lattice Boltzmann Method: Principles and Practice. Springer. - Guo, Z. and Shu, C. (2013) Lattice Boltzmann Method and its Applications inEngineering, Advances in Computational Fluid Dynamics Vol-3. World Scientific Publishing. - Succi, Sauro (2001). The Lattice Boltzmann Equation for Fluid Dynamics andBeyond. Oxford University Press.
Assessment	Project assignments
Language	English