Geodesic
Convergence of locally self-similar solutions to exact numerical solutions of boundary layer equations for a plate
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 71 (2021), pp. 49-62

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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.
Keywords: boundary layer, stability, vibrationally excited gas, locally self-similar solutions, finite-difference calculations. 
@article{VTGU_2021_71_a4,
     author = {Yu. N. Grigoriev and A. G. Gorobchuk and I. V. Ershov},
     title = {Convergence of locally self-similar solutions to exact numerical solutions of boundary layer equations for a plate},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {49--62},
     publisher = {mathdoc},
     number = {71},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2021_71_a4/}
}
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Yu. N. Grigoriev; A. G. Gorobchuk; I. V. Ershov. Convergence of locally self-similar solutions to exact numerical solutions of boundary layer equations for a plate. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 71 (2021), pp. 49-62. http://geodesic.mathdoc.fr/item/VTGU_2021_71_a4/