Lagrangian and geometric analysis of finite-time Euler singularities

2012/12/03 by Tobias Grafke, Rainer Grauer, Grafke, Tobias +1
Physics and Astronomy · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #physics.flu-dyn

paper · pdf · doi:10.48550/arxiv.1212.0573

arXiv admin note: text overlap with arXiv:1210.2534

arxiv created 2012/12/03 · arxiv updated 2012/12/05

Abstract

We present a numerical method of analyzing possibly singular incompressible 3D Euler flows using massively parallel high-resolution adaptively refined numerical simulations up to 8192³ mesh points. Geometrical properties of Lagrangian vortex line segments are used in combination with analytical non-blowup criteria by Deng et al [Commun. PDE 31 (2006)] to reliably distinguish between singular and near-singular flow evolution. We then apply the presented technique to a class of high-symmetry initial conditions and present numerical evidence against the formation of a finite-time singularity in this case.

Citations

• Finite-Time Euler singularities: A Lagrangian perspective

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