On bifurcations and traction forces on an obstacle in incompressible flow
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917151750750208 |
|---|---|
| author | Cach, Jakub Tůma, Karel Blechta, Jan Schwarzacher, Sebastian |
| author_facet | Cach, Jakub Tůma, Karel Blechta, Jan Schwarzacher, Sebastian |
| contents | We present a systematic numerical investigation of bifurcations in the two-dimensional incompressible Navier-Stokes flow past a confined circular cylinder. The results indicate that there is a qualitative correspondence between changes in the traction profiles of the steady Navier-Stokes equations and bifurcations of the long-time behavior of the unsteady Navier-Stokes equations. The bifurcations include the appearance of symmetry breaking, oscillations, and multiple steady solutions. The well-known planar Schäfer-Turek benchmark is considered with Reynolds numbers up to 1000. For the analysis of bifurcations and traction profiles, several numerical strategies are applied, including a duality method for computing traction profiles, deflation methods, and linear stability analysis. Long-time flow behavior is often explored through direct numerical simulation of the unsteady equations; an approach that is computationally demanding. The relations presented here indicate the possibility of a computationally inexpensive strategy to detect critical Reynolds numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15424 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On bifurcations and traction forces on an obstacle in incompressible flow Cach, Jakub Tůma, Karel Blechta, Jan Schwarzacher, Sebastian Fluid Dynamics Numerical Analysis We present a systematic numerical investigation of bifurcations in the two-dimensional incompressible Navier-Stokes flow past a confined circular cylinder. The results indicate that there is a qualitative correspondence between changes in the traction profiles of the steady Navier-Stokes equations and bifurcations of the long-time behavior of the unsteady Navier-Stokes equations. The bifurcations include the appearance of symmetry breaking, oscillations, and multiple steady solutions. The well-known planar Schäfer-Turek benchmark is considered with Reynolds numbers up to 1000. For the analysis of bifurcations and traction profiles, several numerical strategies are applied, including a duality method for computing traction profiles, deflation methods, and linear stability analysis. Long-time flow behavior is often explored through direct numerical simulation of the unsteady equations; an approach that is computationally demanding. The relations presented here indicate the possibility of a computationally inexpensive strategy to detect critical Reynolds numbers. |
| title | On bifurcations and traction forces on an obstacle in incompressible flow |
| topic | Fluid Dynamics Numerical Analysis |
| url | https://arxiv.org/abs/2512.15424 |