PhD Thesis

Finite-time Euler Singularities: A Lagrangian perspective

Abstract

This work presents numerical evidence against the formation of a finite-time singularity for the vortex dodecapole initial condition. It uses data obtained from high resolution adaptively refined numerical simulations to test the assumptions demanded by analytic blowup criteria connecting vortex line geometry to velocity increase. In the course of this work, a numerical framework has been extended to allow the integration of the incompressible three-dimensional Euler equations on adaptively refined grids, which supports the diagnostics of geometrical and Lagrangian criteria and scales close to optimal on massively parallel machines.


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