An Eulerian approach for vortex motion using a level set regularization procedure
type: Item
instance of: scholarly article
title: An Eulerian approach for vortex motion using a level set regularization procedure
zbMATH Open document ID: 0859.76052
author: Eduard Harabetian
author: Chi-Wang Shu
author: Stanley Osher
published in: Journal of Computational Physics
publication date: 1997-04-09T00:00:00Z
review text: We present an Eulerian, fixed grid, approach to solve the motion of an incompressible fluid, in two and three dimensions, in which the vorticity is concentrated on a lower dimensional set. Our approach uses a decomposition of the vorticity of the form \(\xi=P(\varphi)\eta\), in which both \(\varphi\) (the level set function) and \(\eta\) (the vorticity strength vector) are smooth. We derive coupled equations for \(\varphi\) and \(\eta\) which give a regularization of the problem. The regularization is topological and is automatically accomplished through the use of numerical schemes whose viscosity shrinks to zero with grid size. The method also has the advantage of automatically allowing topological changes such as merging of surfaces. Numerical exmaples, including two- and three-dimensional vortex sheets, two-dimensional vortex dipole sheets, and point vortices, are given.
Mathematics Subject Classification ID: 76M25
Mathematics Subject Classification ID: 76B47
zbMATH DE Number: 938005
zbMATH Keywords: decomposition of vorticity
zbMATH Keywords: topological changes
zbMATH Keywords: two- and three-dimensional vortex sheets
zbMATH Keywords: two-dimensional vortex dipole sheets
zbMATH Keywords: point vortices
MaRDI profile type: Publication
full work available at URL: jcph.1996.0155
OpenAlex ID: W2045933559
DOI: 10.1006/JCPH.1996.0155
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description: scientific article; zbMATH DE number 938005