On bifurcations and traction forces on an obstacle in incompressible flow

Fuente: arXiv
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Main Authors: Cach, Jakub, Tůma, Karel, Blechta, Jan, Schwarzacher, Sebastian
Format: Preprint
Published: 2025
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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