Biorthogonal Series Solution of Stokes Flow Problems in Sectorial Regions
Biorthogonal Series Solution of Stokes Flow Problems in Sectorial Regions
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DOI：
10.1137/0156002
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发表时间：
1996-02
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影响因子：
--
通讯作者：
S. Khuri
中科院分区：
文献类型：
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作者：
S. Khuri
在本文中，我们开发了一种特征函数展开方法来解决流体动力学中出现的扇形腔中的斯托克斯流动问题。该方法导致开发了一组本征函数、伴随本征函数、双正交条件以及用于计算本征函数展开系数的算法。然后通过截断来求解所得的无限线性方程组。这些双正交条件是本征函数和伴随本征函数满足的属性，用于计算本征函数展开解的系数。双正交条件是针对一类具有变量系数的四阶边值问题推导出来的，这些变量系数是由控制斯托克斯方程的分离变量引起的。该方法适用于二维扇形腔内缓慢、稳定的流动；通过盖板或带的均匀平移使流体运动。
In this paper we develop an eigenfunction expansion method for solving Stokes flow problems in sectorial cavities that arise in fluid dynamics. The method leads to the development of a set of eigenfunctions, adjoint eigenfunctions, biorthogonality conditions, and an algorithm for the computation of the coefficients of the eigenfunction expansion. The resulting infinite system of linear equations is then solved by truncation. These biorthogonality conditions are properties satisfied by the eigenfunctions and adjoint eigenfunctions, which are used to compute the coefficients of the eigenfunction expansion solution. The biorthogonality conditions are derived for a class of fourth-order boundary value problems with variable coefficients that arise from separating variables of the governing Stokes equation. The method is applied to the slow, steady flow in a two-dimensional sectorial cavity; the fluid is set into motion by the uniform translation of a covering plate or belt.