Geodesic
Parallel implementation of the 16th-order multioperator scheme: application to problems of instability of vortices and boundary layers
Matematičeskoe modelirovanie, Tome 34 (2022) no. 8, pp. 3-18

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A family of schemes for the Euler and Navier-Stokes equations is considered based on multioperator approximations of derivatives with inversion of two-point operators and allowing for very high orders. The general idea of MPI-parallelization of the type of algorithms under consideration as well as the evaluation of parallel efficiency is described. The results of direct numerical simulation of the occurrence and development of instability of two types are presented, i.e. the instability of a Gaussian-type vortex in a subsonic flow and the Tollmien-Schlichting instability in a subsonic boundary layer. A common feature of these calculations was the absence of any artificial excitations. The "exciters" of instability were small differences between numerical solutions and exact ones, the broadband spectra of which may indicate some analogy with the natural turbulent background in real flows.
Keywords: schemes with multioperators approximations, parallel efficiency, Euler and Navier-Stokes equations, instability of vortices and boundary layers. 
@article{MM_2022_34_8_a0,
     author = {M. V. Lipavskii and A. I. Tolstykh and D. A. Shirobokov},
     title = {Parallel implementation of the 16th-order multioperator scheme: application to problems of instability of vortices and boundary layers},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--18},
     publisher = {mathdoc},
     volume = {34},
     number = {8},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2022_34_8_a0/}
}
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M. V. Lipavskii; A. I. Tolstykh; D. A. Shirobokov. Parallel implementation of the 16th-order multioperator scheme: application to problems of instability of vortices and boundary layers. Matematičeskoe modelirovanie, Tome 34 (2022) no. 8, pp. 3-18. http://geodesic.mathdoc.fr/item/MM_2022_34_8_a0/