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首页> 外文期刊>Engineering Mathematics >Application of Analytical Methods About Equations of Stokes for Transient Condition in Flow Over Oscillating Plane and Oscillating Flow Over Stationary Plane
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Application of Analytical Methods About Equations of Stokes for Transient Condition in Flow Over Oscillating Plane and Oscillating Flow Over Stationary Plane

机译：分析方法在静态平面上流动时瞬态条件的瞬态条件的应用及静止平面上的振动

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In this study, two highly accurate and simple analytical methods (known as semi exact solutions), the variational iteration method (VIM) and Adomian's decomposition method (ADM) are applied for illustrating transient condition of viscous fluid flow over oscillating plane and also oscillating viscous fluid flow over stationary plane. The flow of an incompressible viscous fluid, caused by the oscillation of a flat wall and also the flow of an oscillating fluid flow over stationary wall are considered by Navier-Stokes equations and are subjected to the behavior of fluid flow in boundary layer at transient condition. The main purpose of this article is to solve transient Navier-Stokes first and second equations in new mathematical solving method which is called semi exact solutions where in each case, the velocity of viscous fluid is determined as a function of time and also vertical distance from plane in boundary layer at transient condition. Results reveal the boundary layer thickness and also the transient fluid flow velocity in boundary layer and even more it shows that the (VIM) and (ADM) methods are very effective and accurate in comparison with the exact solution results. The results demonstrate the velocity of fluid in boundary layer as a function of displacement and time and it is shown that in different time, the value of velocity obtained by "VIM" and "ADM" solving methods is almost equal to velocity which is derived from exact or numerical solutions. So the main background and reason of applying the mentioned methods is to verify the accuracy of "VIM" and "ADM" in solving different fluid mechanics equations especially Navier-Stokes equations.
机译：在这项研究中，两个高度准确和简单的分析方法（称为半精确解决方案），变分迭代法（Vim）和Adomian的分解方法（ADM）用于说明振荡平面上的粘性流体流动的瞬态条件，以及振荡粘性流体流过固定平面。由扁平壁的振荡引起的不可压缩粘性流体的流动由Navier-Stokes方程考虑了固定壁上的振荡流体流动的流动，并且经受瞬态状态下边界层中的流体流动的行为。本文的主要目的是解决新的数学求解方法的瞬态Navier-Stokes第一和第二方程被称为半精确解决方案，其中在每种情况下，粘性流体的速度被确定为时间的函数和垂直距离瞬态条件下边界层的平面。结果揭示了边界层厚度以及边界层的瞬态流体流速，甚至更有表明（Vim）和（ADM）方法与精确的溶液结果相比非常有效和准确。结果证明了作为位移和时间的函数的边界层中流体的速度，并且显示在不同的时间，通过“Vim”和“ADM”求解方法获得的速度值几乎等于来自的速度精确或数值解决方案。因此，应用提到的方法的主要背景和原因是验证“Vim”和“ADM”在求解不同的流体力学方程中特别是Navier-Stokes方程的准确性。

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