High Order Vortex Methods With Deforming Elliptical Gaussian Blobs 1: Derivation and Validation
Date
2001
Authors
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Publisher
Department of Mathematical Sciences
Abstract
This manuscript introduces a new vortex method based on elliptical Gaussian basis
functions. Each basis function translates, nutates, elongates and spreads through the action of the
local flow field and fluid viscosity. By allowing elements to deform, the method captures the effects of
local flow deviations with a fourth order spatial accuracy. This method uses a fourth order asymptotic
approximation to the Biot-Savart integrals for elliptical Gaussian vorticity distributions to determine
velocity and velocity derivatives. A robust adaptive refinement procedure reconfigures elements that
spread beyond the specified resolution. The high order convergence rate is verified by comparing
calculations with the vortex method to exact solutions in a variety of controlled experiments.
Description
Keywords
vortex methods, vorticity dynamics, computational fl uid dynamics, convergence theory