A trial-free-boundary method for computing Batchelor flows
type: Item
instance of: scholarly article
title: A trial-free-boundary method for computing Batchelor flows
zbMATH Open document ID: 0881.76019
DOI: 10.1016/S0377-0427(96)00152-5
author: Andrew Acker
author: Ercan Kadakal
author: Kenneth Miller
published in: Journal of Computational and Applied Mathematics
publication date: 1997-07-15T00:00:00Z
review text: Batchelor (or Prandtl-Batchelor) flows are steady inviscid flows in which a bounded domain of constant vorticity \(\omega\) is separated from an external irrotational flow by a vortex sheet. In two-dimensional case, these flows are described by the following free-boundary problem: determine a curve \(\Gamma\) and a function \(u\) such that \(\Delta u=-\omega\) inside \(\Gamma\), \(\Delta u=0\) outside \(\Gamma\), and there is a constant jump in \(|\nabla u|^2\) across \(\Gamma\). Here a family \(T_\varepsilon\) of extended operator methods (called by the authors trial-free-boundary method) is employed to solve the problem approximately, giving for \(\varepsilon\to 0\) the exact solution. For every fixed \(\varepsilon>0\), the authors establish the convexity and monotonicity of the operator \(T_\varepsilon\), and prove the existence of the approximate solution \(u_\varepsilon\). The convergence \(u_\varepsilon\to u\) is demonstrated, however, only numerically in some examples.
Mathematics Subject Classification ID: 76B47
Mathematics Subject Classification ID: 76M25
Mathematics Subject Classification ID: 35R35
zbMATH DE Number: 1034165
zbMATH Keywords: family of extended operator methods
zbMATH Keywords: domain of constant vorticity
zbMATH Keywords: vortex sheet
zbMATH Keywords: convexity
zbMATH Keywords: monotonicity
zbMATH Keywords: existence
zbMATH Keywords: convergence
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1034165