Consistency and stability of boundary conditions for a two-velocities lattice Boltzmann scheme
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910896936189952 |
|---|---|
| author | Bellotti, Thomas |
| author_facet | Bellotti, Thomas |
| contents | We theoretically explore boundary conditions for lattice Boltzmann methods, focusing on a toy two-velocities scheme to tackle a linear one-dimensional advection equation. 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{ö}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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_02009 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Consistency and stability of boundary conditions for a two-velocities lattice Boltzmann scheme Bellotti, Thomas Numerical Analysis We theoretically explore boundary conditions for lattice Boltzmann methods, focusing on a toy two-velocities scheme to tackle a linear one-dimensional advection equation. 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{ö}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. |
| title | Consistency and stability of boundary conditions for a two-velocities lattice Boltzmann scheme |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2407.02009 |