Lagrange crisis and generalized variational principle for 3D unsteady flow

被引:156
|
作者
He, Ji-Huan [1 ,2 ]
机构
[1] Soochow Univ, Coll Text & Clothing Engn, Natl Engn Lab Modern Silk, Suzhou, Peoples R China
[2] Xian Univ Architecture & Technol, Xian, Peoples R China
关键词
Plasma; Variational theory; Semi-inverse method; Burger equation; ITERATION METHOD; UNKNOWN SHAPE; EQUATIONS; MODEL;
D O I
10.1108/HFF-07-2019-0577
中图分类号
O414.1 [热力学];
学科分类号
摘要
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. Originality/value This paper establishes some new variational principles for the 3D unsteady flow and suggests an effective method to eliminate the Lagrange crisis.
引用
收藏
页码:1189 / 1196
页数:8
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