Progress in Lattice Boltzmann Schemes: Mesh Adaptation, High-Order Accuracy, Numerical Analysis, and Boundary Conditions

Speaker: Thomas Bellotti, Université Paris-Saclay
January 22, 2026

Presentation

Abstract

In this talk, I will cover several selected topics related to recent advances in lattice Boltzmann (LBM) schemes that I have achieved over the past few years, from both practical and theoretical perspectives. Lattice Boltzmann methods are widely used—particularly in computational fluid dynamics—because of their computational efficiency, excellent parallelizability, and ease of implementation for complex problems. I will begin by discussing dynamic mesh adaptation for LBM schemes, which are traditionally implemented on fixed Cartesian meshes and are known for their significant memory footprint. Using adaptive multiresolution techniques, we obtain effective control of the approximation error while substantially reducing memory requirements. A second main topic concerns the construction of fourth-order accurate LBM schemes for hyperbolic systems of conservation laws. These schemes build on symmetry properties of the underlying second-order method, which can be exploited through operator composition to achieve higher-order accuracy. The second part of the talk takes a more theoretical direction. In particular, I will explain how we established a connection between LBM schemes and multistep finite difference methods, thereby enabling the use of a broad range of classical analytical tools developed for the latter in the analysis of the former. I will conclude by discussing challenges related to the stability of boundary conditions for LBM schemes, analyzed from the perspective of the well-established GKS (Gustafsson–Kreiss–Sundström) framework. This analysis reveals several distinctive features when compared with standard finite difference schemes.

Biography

Thomas Bellotti is a CNRS junior tenured researcher in mathematics at the EM2C laboratory, CentraleSupélec (Université Paris-Saclay). He completed his Ph.D. in Applied Mathematics at Institut Polytechnique de Paris / École polytechnique under the supervision of M. Massot, B. Graille and L. Gouarin, focusing on the numerical analysis of lattice Boltzmann schemes and adaptive multiresolution methods. Before joining CNRS, he held a post-doctoral position at the University of Strasbourg under the supervision of P. Helluy. His research interests include adaptive multi-resolution strategies for lattice Boltzmann solvers, high-order kinetic schemes, and the theoretical foundations of numerical methods for fluid dynamics and PDEs.

Seminar Participation

Attending In Person

For select seminars, you may wish to attend in-person if you are in the vicinity of NASA Ames Research Center. These AMS seminars are held in Building N258 in Room 127, just off the front lobby. Sessions available to attend in-person will be indicated in the announcement information. In-person participants without NASA badges will need a valid visitor badge (US citizenship or permanent residency is required) to enter the facility.

Join Us Online

To attend an AMS seminar, click on the Microsoft Teams link in the seminar description. You can connect through the desktop Teams App if you have it, or you can select "Watch on the Web Instead" to enter the meeting as a guest. Please ensure that you've muted your microphone in Teams before you select "Join Now" to enter the meeting lobby.