THERMAL SCIENCE

International Scientific Journal

Yue WuORCID

,

Guang-Qing Feng

VARIATIONAL PRINCIPLE FOR AN INCOMPRESSIBLE FLOW

ABSTRACT
This paper gives a general approach to the inverse problem of calculus of variations. The 2-D Euler equations of incompressible flow are used as an example to show how to derive a variational formulation. The paper begins with ideal Laplace equation for its potential flow without vorticity, which admits the Kelvin 1849 variational principle. The next step is to assume a small vorticity to obtain an approximate variational formulation, which is then amended by adding an additional unknown term for further determined, this process leads to the well-known semi-inverse method. Lagrange crisis is also introduced, and some methods to solve the crisis are discussed
KEYWORDS
Kelvin’s variational principle, semi-inverse method, Euler-Lagrange equation
PAPER SUBMITTED: 2022-03-01
PAPER REVISED: 2022-07-24
PAPER ACCEPTED: 2022-07-24
PUBLISHED ONLINE: 2023-06-11
DOI REFERENCE: https://doi.org/10.2298/TSCI2303039W
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE No. 3, PAGES [2039 - 2047]
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Variational principle for an incompressible flow

© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence