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
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), "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