2018/02/23 by Adam Larios, Yuan Pei, Larios, Adam +3 · 1 citation
Engineering · Mathematics · #35A01 #35B44 #35B65 #35Q30 #35Q35 #76D03 #76D05 #76D17 #76N10 #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.1802.08766
openalex publication_date 2018/02/23 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
The velocity-vorticity formulation of the 3D Navier-Stokes equations was\nrecently found to give excellent numerical results for flows with strong\nrotation. In this work, we propose a new regularization of the 3D Navier-Stokes\nequations, which we call the 3D velocity-vorticity-Voigt (VVV) model, with a\nVoigt regularization term added to momentum equation in velocity-vorticity\nform, but with no regularizing term in the vorticity equation. We prove global\nwell-posedness and regularity of this model under periodic boundary conditions.\nWe prove convergence of the model's velocity and vorticity to their\ncounterparts in the 3D Navier-Stokes equations as the Voigt modeling parameter\ntends to zero. We prove that the curl of the model's velocity converges to the\nmodel vorticity (which is solved for directly), as the Voigt modeling parameter\ntends to zero. Finally, we provide a criterion for finite-time blow-up of the\n3D Navier-Stokes equations based on this inviscid regularization.\n