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Lagrange crisis and generalized variational principle for 3D unsteady flow

Ji-Huan He (National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, Suzhou, China and School of Science, Xi'an University of Architecture and Technology, Xi’an, China)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 26 September 2019

Issue publication date: 2 March 2020

228

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

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