T. Grafke and R. Grauer, Procedia IUTAM 9 (2013) 32.
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.