Report
Consistency and stability of boundary conditions for a two-velocities lattice Boltzmann scheme
| العنوان: | Consistency and stability of boundary conditions for a two-velocities lattice Boltzmann scheme |
|---|---|
| المؤلفون: | Bellotti, Thomas |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis |
| الوصف: | We theoretically explore boundary conditions for lattice Boltzmann methods, focusing on a toy two-velocities scheme. By mapping lattice Boltzmann schemes to Finite Difference schemes, we facilitate rigorous consistency and stability analyses. We develop kinetic boundary conditions for inflows and outflows, highlighting the trade-off between accuracy and stability, which we successfully overcome. Consistency analysis relies on modified equations, whereas stability is assessed using GKS (Gustafsson, Kreiss, and Sundstr{\"o}m) theory and -- when this approach fails on coarse meshes -- spectral and pseudo-spectral analyses of the scheme's matrix that explain effects germane to low resolutions. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.02009 |
| رقم الانضمام: | edsarx.2407.02009 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |