Title: DNS of thin shear instability by ninth-order multioperators-based schemes

Authors: A.I. Tolstykh, M.V. Lipavskii, E.N. Chigerev

Addresses: Department of Applied Mathematical Physics, Computing Center of Russian Academy of Sciences, Vavilov St. 40, 119333 Moscow, Russia. ' Department of Applied Mathematical Physics, Computing Center of Russian Academy of Sciences, Vavilov St. 40, 119333 Moscow, Russia. ' Department of Applied Mathematical Physics, Computing Center of Russian Academy of Sciences, Vavilov St. 40, 119333 Moscow, Russia

Abstract: The multioperators principle of constructing arbitrary-order approximations and schemes is outlined. Its essence is forming linear combinations of basis operators from certain types of one-parameter operators families by fixing distinct values of the parameter. Highly accurate ninth-order multioperators based schemes for fluid dynamics are presented. Illustrative examples following by direct numerical simulations of thin incompressible 2D shear layers instability are presented. The Navier-Stokes calculations were carried out with complete resolution of turbulent scales. The results obtained for large time intervals show the full history of the flow development with rolling up, generation and decaying of turbulence.

Keywords: high-order finite difference schemes; upwind schemes; direct numerical simulation; DNS; Navier–Stokes equations; multioperators; thin shear instability; fluid dynamics; incompressibility; turbulence.

DOI: 10.1504/IJCSM.2007.016544

International Journal of Computing Science and Mathematics, 2007 Vol.1 No.2/3/4, pp.432 - 443

Available online: 07 Jan 2008 *

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