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A highly adaptive three dimensional hybrid vortex method for inviscid flows

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Multiscale Numerics for the Atmosphere and Ocean

Motivated by outstanding problems surrounding vortex stretching, a new numerical method to solve the inviscid Euler equations for a three-dimensional, incompressible fluid is presented. Special emphasis on spatial adaptivity is given to resolve as broad a range of scales as possible in a completely self-similar fashion. We present a hybrid vortex method whereby we discretise the vorticity in Lagrangian filaments and perform an inversion to compute velocity on an adapted finite-volume grid. This allows for a two-fold adaptivity strategy. First, although naturally spatially adaptive by definition, the vorticity filaments undergo `renoding’. We redistribute nodes along the filament to concentrate their density in regions of high curvature. Secondly the Eulerian mesh is adapted to follow high strain by increasing resolution based on local filament dimensions. These features allow vortex stretching and folding to be resolved in a completely automatic and self-similar way. The method is validated via well known vortex rings and newly discovered helical vortex equilibria are also used to test the method.

This talk is part of the Isaac Newton Institute Seminar Series series.

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