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Russian Journal of Nonlinear Dynamics, 2022, том 18, номер 3, страницы 441–464
(Mi nd804)
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Nonlinear physics and mechanics
Construction of Inhomogeneous Velocity Fields
Using Expansions in Terms of Eigenfunctions
of the Laplace Operator
E. V. Vetchanin, E. A. Portnov Ural Mathematical Center, Udmurt State University,
ul. Universitetskaya 1, Izhevsk, 426034 Russia
Аннотация:
In this paper we present a method for constructing inhomogeneous velocity fields of an incompressible fluid using expansions in terms of eigenfunctions of the Laplace operator whose
weight coefficients are determined from the problem of minimizing the integral of the squared
divergence. A number of examples of constructing the velocity fields of plane-parallel and axisymmetric flows are considered. It is shown that the problem of minimizing the integral value
of divergence is incorrect and requires regularization. In particular, we apply Tikhonov’s regularization method. The method proposed in this paper can be used to generate different initial
conditions in investigating the nonuniqueness of the solution to the Navier – Stokes equations.
Ключевые слова:
inhomogeneous velocity field, expansion in terms of eigenfunctions, ill-conditioned
system of linear algebraic equations.
Поступила в редакцию: 04.08.2022 Принята в печать: 22.09.2022
Образец цитирования:
E. V. Vetchanin, E. A. Portnov, “Construction of Inhomogeneous Velocity Fields
Using Expansions in Terms of Eigenfunctions
of the Laplace Operator”, Rus. J. Nonlin. Dyn., 18:3 (2022), 441–464
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/nd804 https://www.mathnet.ru/rus/nd/v18/i3/p441
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