On the dynamics of the boundary vorticity for incompressible viscous flows
Fluid Dynamics
2023-08-28 v1 Numerical Analysis
Analysis of PDEs
Numerical Analysis
Probability
Abstract
The dynamical equation of the boundary vorticity has been obtained, which shows that the viscosity at a solid wall is doubled as if the fluid became more viscous at the boundary. For certain viscous flows the boundary vorticity can be determined via the dynamical equation up to bounded errors for all time, without the need of knowing the details of the main stream flows. We then validate the dynamical equation by carrying out stochastic direct numerical simulations (i.e. the random vortex method for wall-bounded incompressible viscous flows) by two different means of updating the boundary vorticity, one using mollifiers of the Biot-Savart singular integral kernel, another using the dynamical equations.
Keywords
Cite
@article{arxiv.2308.13055,
title = {On the dynamics of the boundary vorticity for incompressible viscous flows},
author = {V. Cherepanov and J. Liu and Z. Qian},
journal= {arXiv preprint arXiv:2308.13055},
year = {2023}
}
Comments
16 pages, 26 figures