  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.
