Lattice Boltzmann method with artificial bulk viscosity using a neural collision operator
- The lattice Boltzmann method (LBM) stands apart from conventional macroscopic approaches due to its low numerical dissipation and reduced computational cost, attributed to a simple streaming and local collision step. While this property makes the method particularly attractive for applications such as direct noise computation, it also renders the method highly susceptible to instabilities. A vast body of literature exists on stability-enhancing techniques, which can be categorized into selective filtering, regularized LBM, and multi-relaxation time (MRT) models. Although each technique bolsters stability by adding numerical dissipation, they act on different modes. Consequently, there is not a universal scheme optimally suited for a wide range of different flows. The reason for this lies in the static nature of these methods; they cannot adapt to local or global flow features. Still, adaptive filtering using a shear sensor constitutes an exception to this. For this reason, we developed a novel collision operator that uses space- and time-variant collision rates associated with the bulk viscosity. These rates are optimized by a physically informed neural net. In this study, the training data consists of a time series of different instances of a 2D barotropic vortex solution, obtained from a high-order Navier–Stokes solver that embodies desirable numerical features. For this specific text case our results demonstrate that the relaxation times adapt to the local flow and show a dependence on the velocity field. Furthermore, the novel collision operator demonstrates a better stability-to-precision ratio and outperforms conventional techniques that use an empirical constant for the bulk viscosity.
Document Type: | Article |
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Language: | English |
Author: | Jan Tobias Horstmann, Mario Christopher Bedrunka, Holger Foysi |
Parent Title (English): | Computers & Fluids |
Volume: | 272 |
Article Number: | 106191 |
Number of pages: | 13 |
ISSN: | 0045-7930 |
URN: | urn:nbn:de:hbz:1044-opus-77818 |
DOI: | https://doi.org/10.1016/j.compfluid.2024.106191 |
Publisher: | Elsevier |
Publishing Institution: | Hochschule Bonn-Rhein-Sieg |
Date of first publication: | 2024/02/02 |
Copyright: | © 2024 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license. |
Keyword: | Artificial bulk viscosity; MRT-LBM; Neural collision operator; Numerical stability |
Departments, institutes and facilities: | Fachbereich Ingenieurwissenschaften und Kommunikation |
Institut für Technik, Ressourcenschonung und Energieeffizienz (TREE) | |
Dewey Decimal Classification (DDC): | 6 Technik, Medizin, angewandte Wissenschaften / 62 Ingenieurwissenschaften / 620 Ingenieurwissenschaften und zugeordnete Tätigkeiten |
Entry in this database: | 2024/02/09 |
Licence (German): | Creative Commons - CC BY - Namensnennung 4.0 International |