Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Numerical Mathematics

Editor-in-Chief: Hoppe, Ronald H. W. / Kuznetsov, Yuri

Managing Editor: Olshanskii, Maxim

Editorial Board Member: Benzi, Michele / Brenner, Susanne C. / Carstensen, Carsten / Dryja, M. / Feistauer, Miloslav / Glowinski, R. / Lazarov, Raytcho / Nataf, Frédéric / Neittaanmaki, P. / Bonito, Andrea / Quarteroni, Alfio / Guzman, Johnny / Rannacher, Rolf / Repin, Sergey I. / Shi, Zhong-ci / Tyrtyshnikov, Eugene E. / Zou, Jun / Simoncini, Valeria / Reusken, Arnold

4 Issues per year


IMPACT FACTOR 2016: 0.405
5-year IMPACT FACTOR: 2.212

CiteScore 2016: 0.47

SCImago Journal Rank (SJR) 2016: 0.378
Source Normalized Impact per Paper (SNIP) 2016: 0.502

Mathematical Citation Quotient (MCQ) 2016: 1.02

Online
ISSN
1569-3953
See all formats and pricing
More options …
Volume 20, Issue 3-4 (Dec 2012)

Issues

A finite element BFGS algorithm for the reconstruction of the flow field generated by vortex rings

Y. Zhang
  • Laboratoire de Math´ematiques Rapha¨el Salem, Universit´e de Rouen, F-76801 Saint-Étienne-du-Rouvray, France
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ I. Danaila
  • Laboratoire de Math´ematiques Rapha¨el Salem, Universit´e de Rouen, F-76801 Saint-Étienne-du-Rouvray, France
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2013-03-30 | DOI: https://doi.org/10.1515/jnum-2012-0017

Abstract

- Vortex rings are generated in numerous practical applications (biological propulsion, internal combustion engines) by the sudden injection of a fluid. Measurements of such flows often provide partial information, generally limited to the exterior of the vortex ring. We propose in this paper a new algorithm for the reconstruction of the stream function inside a bounded domain, where a vortex ring is supposed to form.We derive a quasi-Newton Broyden- Fletcher-Goldfarb-Shanno (BFGS) algorithm for this problem, using a cost function that describes the matching between the reconstructed field and given values of normal derivatives on the boundary of the domain. The algorithm computes the best parameters of the vortex model that is used to describe the vorticity distribution inside the vortex ring. Several vortex models are considered. The method is implemented in freefem++ using a P1 finite-element spatial discretization. Validation tests using analytical models (Hill’s spherical vortex) and Navier-Stokes direct numerical simulation data show good agreement between reconstructed and reference fields.

Keywords: vortex ring models; finite element methods; reconstruction; BFGS; freefem++

About the article

Published Online: 2013-03-30

Published in Print: 2012-12-01


Citation Information: Journal of Numerical Mathematics, ISSN (Online) 1569-3953, ISSN (Print) 1570-2820, DOI: https://doi.org/10.1515/jnum-2012-0017.

Export Citation

© 2013 by Walter de Gruyter GmbH & Co.. Copyright Clearance Center

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Ionut Danaila and Bartosz Protas
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 2015, Volume 471, Number 2180, Page 20150323

Comments (0)

Please log in or register to comment.
Log in