Journal
INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW
Volume 26, Issue 3-4, Pages 694-697Publisher
EMERALD GROUP PUBLISHING LTD
DOI: 10.1108/HFF-09-2015-0368
Keywords
Variational theory; Navier-Stokes equation; Semi-inverse method; Viscous flow
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Purpose - The purpose of this paper is to point out a paradox in variational theory for viscous flows. Chien (1984) claimed that a variational principle of maximum power loses for viscous fluids was established, however, it violated the well-known Helmholtz's principle. Design/methodology/approach - Restricted variables are introduced in the derivation, the first order and the second order of variation of the restricted variables are zero. Findings - An approximate variational principle of minimum power loses is established, which agrees with the Helmholtz's principle, and the paradox is solved. Research limitations/implications - This paper focusses on incompressible viscose flows, and the theory can be extended to compressible one and other viscose flows. It is still difficult to obtain a variational formulation for Navier-Stokes equations. Practical implications - The variational principle of minimum power loses can be directly used for numerical methods and analytical analysis. Originality/value - It is proved that Chien's variational principle is a minimum principle.
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