Convergence of locally self-similar solutions to exact numerical solutions of boundary layer equations for a plate | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2021. № 71. DOI: 10.17223/19988621/71/5

Convergence of locally self-similar solutions to exact numerical solutions of boundary layer equations for a plate

This paper considers a possibility of using locally self-similar solutions for a stationary boundary layer in linear stability problems. The solutions, obtained at various boundary conditions for a vibrationally excited gas, are compared with finite-difference calculations of the corresponding flows. An initial system of equations for a plane boundary layer of the vibrationally excited gas is derived from complete equations of two-temperature relaxation aerodynamics. Relaxation of vibrational modes of gas molecules is described in the framework of the Landau - Teller equation. Transfer coefficients depend on the static flow temperature. In a complete problem statement, the flows are calculated using the Crank - Nicolson finite-difference scheme. In all the considered cases, it is shown that the locally self-similar velocity and temperature profiles converge to the corresponding profiles for a fully developed boundary-layer flow calculated in a finite-difference formulation. The obtained results justify the use of locally self-similar solutions in problems of the linear stability theory for boundary-layer flows of a vibrationally excited gas.

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Keywords

boundary layer, stability, vibrationally excited gas, locally self-similar solutions, finite-difference calculations

Authors

Name	Organization	E-mail
Grigoriev Yuriy N.	Institute of Computational Technologies SB RAS	grigor@ict.nsc.ru
Gorobchuk Aleksey G.	Institute of Computational Technologies SB RAS	alg@eml.ru
Ershov Igor V.	Novosibirsk State Agrarian University	i_ershov@ngs.ru

Всего: 3

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