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首页> 外文期刊>Journal of teoretical and applied mechanics >ON SOME GENERAL SOLUTIONS OF TRANSIENT STOKES AND BRINKMAN EQUATIONS
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ON SOME GENERAL SOLUTIONS OF TRANSIENT STOKES AND BRINKMAN EQUATIONS

机译：关于暂态Stokes和Brinkman方程的一些一般解

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摘要

General solution representations for velocity and pressure fields describing transient flows at small Reynolds numbers (Stokes flows) and flows obeying Brinkman models are presented. The geometry dependent vector representations emerge from the incompressibility condition and are expressed in terms of just two scalar functions similar to the Papkovich-Neuber and Boussinesq-Galerkin solution type. We provide new formulae connecting our differential representations and other solutions describing unsteady Stokes flow including Lamb's (1932) general infinite series solution. The unified approach presented here further demonstrates an important link between oscillatory flows and flow through porous media using Brinkman models. It is shown that the solutions of boundary value problems in the latter can be obtained in a straightforward fashion, from the results of the former. This simple but surprising analogy is further explained using the properties (mathematical as well as physical) that are shared by the two different models. The construction of certain physical quantities is also illustrated for spherical and spheroidal inclusions. It is believed that the general solutions presented here will be useful in the computation of multi-particle interactions in transient and Brinkman flows and also in linear elasticity.
机译：提出了速度和压力场的一般解决方案表示，描述了小雷诺数（斯托克斯流）下的瞬态流和服从Brinkman模型的流。依赖于几何的矢量表示法是从不可压缩条件出现的，仅用两个标量函数表示，类似于Papkovich-Neuber和Boussinesq-Galerkin解类型。我们提供了连接微分表示法和其他描述不稳定Stokes流的解决方案的新公式，包括Lamb（1932）的一般无限级数解。本文介绍的统一方法进一步证明了使用Brinkman模型在振荡流和通过多孔介质的流之间的重要联系。从前者的结果可以看出，后者的边值问题的解决方案可以直接获得。使用两个不同模型共享的属性（数学的和物理的）进一步解释了这种简单但令人惊讶的类比。还说明了球形和球形夹杂物的某些物理量的构造。可以相信，这里介绍的一般解决方案将对瞬态和Brinkman流以及线性弹性中的多粒子相互作用的计算有用。

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