Describing the Asymptotic Behavior of a Low-Viscosity Fluid in an Elliptical Plane with a Moving Boundary
Yu. V. Pivovarov
Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: условие проскальзывания, пограничный слой, уравнение теплопроводности, завихренность, функция тока}, slip condition, boundary layer, heat equation, vorticity, current function
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 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.
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