期刊
COMPUTERS & FLUIDS
卷 66, 期 -, 页码 215-230出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.compfluid.2012.06.008
关键词
Stokes flow; Boundary integral method; Stokeslet; Quadrature; Singular integrals; Nystrom's method; Toeplitz matrix
Fluid flow phenomena in the Stokesian regime abounds in nature as well as in microfluidic applications. Discretizations based on boundary integral formulations for such flow problems allow for a reduction in dimensionality but have to deal with dense matrices and the numerical evaluation of integrals with singular kernels. The focus of this paper is the discretization of wall confinements, and specifically the numerical treatment of flat solid boundaries (walls), for which a set of high-order quadrature rules that accurately integrate the singular kernel of the Stokes equations are developed. Discretizing by Nystrom's method, the accuracy of the numerical integration determines the accuracy of the solution of the boundary integral equations, and a higher order quadrature method yields a large gain in accuracy at negligible cost. The structure of the resulting submatrix associated with each wall is exploited in order to substantially reduce the memory usage. The expected convergence of the quadrature rules is validated through numerical tests, and this boundary treatment is further applied to the classical problem of a sedimenting sphere in the vicinity of solid walls. (C) 2012 Elsevier Ltd. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据