À la Une

Soutenance de thèse Francesco Marson


M. Francesco Marson soutiendra en anglais, en vue de l'obtention du grade de docteur ès sciences, mention informatique, sa thèse intitulée:

Directional Lattice Boltzmann Boundary Conditions

Date: Lundi 31 janvier 2022 à 14h00

Lieu: Battelle A, auditoire rez-de-chaussée (Covid: 2G) ou en ligne, sur Zoom (inscription ici).


Jury :

  • Prof. Bastien Chopard (UNIGE, directeur de thèse)
  • Prof. Jonas Latt (UNIGE, co-directeur de thèse)


The main goal of the present thesis is the proposition of highly accurate curved boundary conditions aiming to reduce the need for grid refinement or non-Cartesian grids, meanwhile maintaining a highly favorable profile for massively parallel implementation on CPU or GPU systems. This investigation is the nonunique outcome of a broad work of analysis, unification, and improvement of the directional boundary conditions of the lattice Boltzmann method (LBM).

Directional or link-wise boundary conditions (DBC) constitute one of the three principal families of boundary conditions, and they have the characteristic to apply independently along with the different lattice directions. The others are, namely, the node-based and the immersed boundaries. The present dissertation will demonstrate how to describe the DBC family as a unified method, reducing, in this way, the confusion among the zoo of possible schemes for the LBM. Also, it will show how this group can be tuned to produce local single-node methods with parabolic exactness, previously an exclusive feature of advanced multi-reflections schemes that requires access to information in multiple nodes to operate. The other families generally need access to information outside the boundary nodes, still leading to non-parabolic exactness (with few specific exceptions).

Three decades after its birth, the LBM has proven to be a robust numerical approach. It is currently a widespread tool, not only in the academic context but also in industrial applications. Its regular Cartesian computational grid is equally one of its main assets and one of its main limitations. On the one hand, it guarantees a simple implementation and effective domain decomposition for parallel computing. On the other hand, it limits its geometrical flexibility and accuracy when dealing with complex geometries. Therefore, the challenge is to increase the LBM geometrical flexibility without affecting its overall accuracy and its excellent amenability to parallel computing. To meet this hurdle beyond the techniques available in the literature, we followed three policies: increase accuracy, reduce communication, preserve simplicity and uniformity.

The first matter comprises three distinct subtopics: convergence order, accuracy at under-resolved scales, and parametrization. An efficacious curved boundary condition firstly preserves the order of convergence of the bulk to avoid costly grid-refinement procedures before their time: one should avoid using first-order methods. Additionally, it should provide high accuracy at the coarsest scales. It means securing the same level of exactness of the LBM bulk, also in the boundaries. If, for example, the bulk can exactly reproduce at steady state a linear velocity profile, the boundary condition must not spoil this characteristic. Finally, a desirable characteristic is a parametric behavior. Roughly speaking, if we consider the steady-state solution, the accuracy should only depend upon the spatial resolution and the non-dimensional number characterizing the type of flow.

The second policy concerns maintaining the parallel performances of LBM. If a boundary condition is accurate, it is often at the cost of nonlocal computations that spoil the favorable compute to communication ratio of the LBM. Then, it is desirable to construct boundary schemes that can be applied locally in a single node without accessing further information outside the time step and boundary node where they act. It is an infrequent characteristic; for example, immersed boundary methods need large kernels, node-oriented methods based on macroscopic interpolation ( through multiscale expansions) are also nonlocal.

The third twofold theme is the simplicity and uniformity of the boundary scheme. The first aspect rates with the preservation of the user-friendliness of the numerical method. The second regards the suitability of the boundary schemes to the singlethread-multiple-data GPU paradigm. Furthermore, simplicity and uniformity facilitate the load balancing procedure in parallel computing systems.

To summarize, following our main three goals, we propose a novel family of directional boundaries, named ELI (for Enhanced Local Interpolation, or Enhanced Linear scheme), and a set of new corrections to DBC. These corrections grant advanced accuracy,

especially in low Reynolds number flows (a common condition in the proximity of boundaries). The development followed two successive steps. In the first one, a generalized geometrical understanding of the interpolated "bounce-back" rule, allowed revealing the existence of ELI, a family of schemes that use ghost populations located at the wall. In the second, the numerical analysis of ail existing directional schemes unveiled the standardized ELI formulation leading to a generic class that encloses ail existing DBC into a unique expression supported by new accuracy improvements. In detail, one of the newly introduced corrections provides parabolic accuracy to many families of DBC: it allows for exact modeling of a Stokes Poiseuille flow in an arbitrary inclined channel. Theoretical analysis and numerical investigations in elementary and complex flows support these assertions. Therefore, the ELI schemes in their improved corrected version can sometimes be a cheap alternative to the more expensive grid refinement or body-fitted meshes approaches. Further, they are local both from the algorithmic and the physical viewpoint: they do not need to recover information outside the boundary node and can model narrow gaps where only a single computational node is present.

To conclude, we expect that the newly proposed schemes will provide a valuable tool to improve accuracy and scalability, especially in large-scale biological simulations, the main inspiration for this research.