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Filtration of Viscous Fluid in Homogeneous Domain with Mixed Boundary Condition
Lobachevskii Journal of Mathematics Pub Date : 2021-07-06 , DOI: 10.1134/s1995080221060305
R. M. Tretiakova 1, 2
Affiliation  

Abstract

A three-dimensional problem of viscous fluid filtration in domain containing homogeneous porous medium is considered. Filtration flow is described by Darcy–Brinkman law. The boundary of the medium is divided into parts with either impermeability condition or condition on velocity vector flux or pressure. Integral representation for velocity and pressure of fluid is constructed with methods of potential theory. System of integral equations satisfying boundary conditions is solved numerically with piecewise-constant approximation and collocation method. The numerical scheme is tested on problems with different boundary conditions. The effect of viscousity on the flow is also studied. The tests demonstrate high accuracy of numerical method.



中文翻译:

混合边界条件下均质域中粘性流体的过滤

摘要

考虑了含有均质多孔介质的域中粘性流体过滤的三维问题。过滤流由达西-布林克曼定律描述。介质的边界被分成具有不渗透性条件或速度矢量通量或压力条件的部分。流体的速度和压力的积分表示是用势论的方法构造的。采用分段常数逼近和搭配方法对满足边界条件的积分方程组进行数值求解。该数值方案在具有不同边界条件的问题上进行了测试。还研究了粘度对流动的影响。试验证明了数值方法的高精度。

更新日期:2021-07-07
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