RETRACTED: Lagrange crisis and generalized variational principle for 3D unsteady flow
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 26 September 2019
Issue publication date: 2 March 2020
Retraction statement
The publishers of International Journal of Numerical Methods for Heat & Fluid Flow wish to retract the article He, J.-H. (2020), “Lagrange crisis and generalized variational principle for 3D unsteady flow”, International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 30 No. 3, pp. 1189-1196. https://doi.org/10.1108/HFF-07-2019-0577.
An internal investigation into a series of submissions has uncovered evidence that the peer review process was compromised. As a result of these concerns, the findings of the article cannot be relied upon. This decision has been taken in accordance with Emerald's publishing ethics and the COPE guidelines on retractions.
The author of this paper would like to note that they do not agree with the content of this notice.
The publishers of the journal sincerely apologize to the readers.
The retracted article is available at: https://doi.org/10.1108/HFF-07-2019-0577
Abstract
Purpose
A three-dimensional (3D) unsteady potential flow might admit a variational principle. The purpose of this paper is to adopt a semi-inverse method to search for the variational formulation from the governing equations.
Design/methodology/approach
A suitable trial functional with a possible unknown function is constructed, and the identification of the unknown function is given in detail. The Lagrange multiplier method is used to establish a generalized variational principle, but in vain.
Findings
Some new variational principles are obtained, and the semi-inverse method can easily overcome the Lagrange crisis.
Practical implications
The semi-inverse method sheds a promising light on variational theory, and it can replace the Lagrange multiplier method for the establishment of a generalized variational principle. It can be used for the establishment of a variational principle for fractal and fractional calculus.
Originality/value
This paper establishes some new variational principles for the 3D unsteady flow and suggests an effective method to eliminate the Lagrange crisis.
Keywords
Citation
He, J.-H. (2020), "RETRACTED: Lagrange crisis and generalized variational principle for 3D unsteady flow", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 30 No. 3, pp. 1189-1196. https://doi.org/10.1108/HFF-07-2019-0577
Publisher
:Emerald Publishing Limited
Copyright © 2019, Emerald Publishing Limited