The Darcy-Forchheimer-Brinkman system is one mathematical model that describes the motion of a viscous fluid located in a porous domain. Recently, many papers have established the existence of a unique solution for this system depending on the boundary condition imposed. In this paper we investigate numerically a special Dirichlet-Robin boundary value problem associated with the nonlinear Darcy-Forchheimer-Brinkman system, i.e., the lid-driven cavity flow problem, by using the dual reciprocity boundary element method (DRBEM). The physical properties of such a flow are discussed by the geometry of the streamlines of the fluid flow for different Reynolds and Darcy numbers. Moreover, an additional sliding parameter is imposed on the moving wall, and its importance is highlighted by segmenting the upper lid into two opposite moving parts.

中文翻译：

---

达西-前叉-布林克曼系统相关的线性驱动问题的边界元方法

Darcy-Forchheimer-Brinkman系统是一种数学模型，用于描述位于多孔域中的粘性流体的运动。最近，许多论文根据所施加的边界条件，为该系统建立了独特的解决方案。在本文中，我们使用双重互易性边界元方法（DRBEM）对与非线性Darcy-Forchheimer-Brinkman系统相关的特殊Dirichlet-Robin边值问题，即盖驱动腔流动问题进行了数值研究。对于不同的雷诺数和达西数，通过流体流的流线的几何形状讨论了这种流的物理特性。此外，附加的滑动参数被施加到移动壁上，并且其重要性通过将上盖分成两个相对的移动部分而突出显示。