THERMAL SCIENCE

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Yue Wu

,

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 Issue 3, PAGES [2039 - 2047]
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Variational principle for an incompressible flow

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