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.

中文翻译：

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描述具有移动边界的椭圆平面中低粘度流体的渐近行为

一个椭圆腔内的低粘度不可压缩流体的平面平行稳定运动问题正在考虑中，其中壁沿其轮廓移动。在型腔边界处设置具有恒定或分段恒定滑动函数的滑动条件。这个问题是用合并渐近展开式的方法解决的。当雷诺数为 Re = 1500 量级且流动区域无角点时，计算时间比采用有限差分法的情况减少数百倍。流动区域被划分为一个涡量恒定的无粘性核心和一个“弱”边界层。通过改变变量将“弱”边界层方程简化为热方程，其解以级数的形式构建。