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arXiv · 1212.0573

Lagrangian and geometric analysis of finite-time Euler singularities

Tobias Grafke·Rainer Grauer
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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 8192^3 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.

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Tobias Grafke, Rainer Grauer. 2012-12-03. Lagrangian and geometric analysis of finite-time Euler singularities. https://arxiv.org/abs/1212.0573

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