Journal of Numerical Mathematics
Editor-in-Chief: Hoppe, Ronald H. W. / Kuznetsov, Yuri
Managing Editor: Olshanskii, Maxim
Editorial Board: 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
A finite element BFGS algorithm for the reconstruction of the flow field generated by vortex rings
- 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.
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.