Abstract
A family of schemes for the Euler and Navier–Stokes equations is considered based on multioperator approximations of derivatives with the inversion of two-point operators and that permit very high orders. The general idea of the MPI-parallelization of the type of algorithms considered and the evaluation of parallel efficiency are described. The results of direct numerical simulations of the occurrence and development of two types of instability are presented: 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 is the absence of any artificial excitations. The “exciters” of instability were small differences between numerical solutions and exact ones, whose broadband spectra may indicate some analogy with the natural turbulent background in real flows.
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ACKNOWLEDGMENTS
The results presented in this paper were obtained using the supercomputers Joint Supercomputer Center, Russian Academy of Sciences, a branch of the Federal Scientific Center Research Institute for System Research, Russian Academy of Sciences.
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Lipavskii, M.V., Tolstykh, A.I. & Shirobokov, D.A. Parallel Implementation of the 16th-Order Multioperator Scheme: Application to Problems of the Instability of Vortices and Boundary Layers. Math Models Comput Simul 15, 167–176 (2023). https://doi.org/10.1134/S2070048223020114
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DOI: https://doi.org/10.1134/S2070048223020114