Geodesic
Computation of evolution of Tollmein-Schlichten waves based on the global stability analysis
Matematičeskoe modelirovanie, Tome 35 (2023) no. 9, pp. 45-60

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A computational methodology is presented for calculating spatial evolution of Tollmien-Schlichting waves and their amplitude growth-rate factor in substantially non-parallel compressible flows, based on a global stability analysis of stationary solutions of the full Navier-Stokes equations. Three stages of this methodology (obtaining a stationary solution, carrying out a global stability analysis and post-processing) are described, and results are presented of its validation based on the comparison of the results of calculating the characteristics of Tollmien-Schlichting waves on a flat plate with the corresponding results of the classical stability theory in the parallel approximation. An example of calculating the flow around a plate with a rectangular cavity is presented to illustrate the possibility of applying the proposed methodology to non-parallel flows.
Keywords: Tollmien-Schlichting waves, non-parallel flows, global stability analysis, full Navier-Stokes equations, amplification factor
Mots-clés : laminar-turbulent transition. 
@article{MM_2023_35_9_a3,
     author = {K. Belyaev and A. Garbaruk and V. Golubkov and M. Strelets},
     title = {Computation of evolution of {Tollmein-Schlichten} waves based on the global stability analysis},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {45--60},
     publisher = {mathdoc},
     volume = {35},
     number = {9},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2023_35_9_a3/}
}
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K. Belyaev; A. Garbaruk; V. Golubkov; M. Strelets. Computation of evolution of Tollmein-Schlichten waves based on the global stability analysis. Matematičeskoe modelirovanie, Tome 35 (2023) no. 9, pp. 45-60. http://geodesic.mathdoc.fr/item/MM_2023_35_9_a3/