Lagrange crisis and generalized variational principle for 3D unsteady flow

By Ji-Huan He. International journal of numerical methods for heat & fluid flow, 2019

144 citations recorded by the source corpus.

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.

Subfields: Modeling and Simulation, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4f0b48e5b993102d62c3bf2c07f770a2973545c5

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Citations in the corpus

New promises and future challenges of fractal calculus: From two-scale thermodynamics to fractal variational principle (2020, methodology): “When  =1, the above problem was widely studied and its various variational formulations were established[91-95].”
The simplest approach to nonlinear oscillators (2019, unknown): “From the SelectedWorks of Ji-Huan He 2019 results-in-physics.pdf Ji-Huan He Available at: https://works.bepress.com/ji_huan_he/105/ Contents lists available at ScienceDirect Results in Physics journal homepage: www.elsevier.com/locate/rinp Microarticle The simplest approach to nonlinear oscillators…”