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This article is cited in 1 scientific paper (total in 1 paper)
Describing the asymptotic behavior of a low-viscosity fluid in an elliptical plane with a moving boundary
Yu. V. Pivovarov Lavrentyev Institute of Hydrodynamics of Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090, Russia
Abstract:
A problem of plane-parallel steady motion of a low-viscosity incompressible fluid inside an elliptical cavity with a wall moving along its contour is under consideration. A slip condition with a constant or piecewise-constant slip function is set at the cavity boundary. This problem is solved using the method of merging asymptotic expansions. When the Reynolds number is of the order of $\operatorname{Re}=1500$ and there are no corner points in the flow region, the calculation time decreases by hundreds of times compared with the case where the finite difference method is applied. The flow region is divided into an inviscid core in which vorticity is constant and a “weak” boundary layer. The equation of the “weak” boundary layer by changing variables is reduced to a heat equation whose solution is constructed in the form of a series.
Keywords:
slip condition, boundary layer, heat equation, vorticity, current function.
Received: 07.03.2019 Revised: 18.06.2019 Accepted: 26.08.2019
Citation:
Yu. V. Pivovarov, “Describing the asymptotic behavior of a low-viscosity fluid in an elliptical plane with a moving boundary”, Prikl. Mekh. Tekh. Fiz., 61:1 (2020), 30–42; J. Appl. Mech. Tech. Phys., 61:1 (2020), 25–36
Linking options:
https://www.mathnet.ru/eng/pmtf354 https://www.mathnet.ru/eng/pmtf/v61/i1/p30
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