A framework is developed for a robust and highly accurate numerical solution of the coupled Stokes-Darcy system in three dimensions. The domain decomposition method is based on a Dirichlet-Neumann type splitting of the interface conditions and solving separate Stokes and Darcy problems iteratively. Second kind boundary integral equations are formulated for each problem. The integral equations use a smoothing of the kernels that achieves high accuracy on the boundary, and a straightforward quadrature to discretize the integrals. Numerical results demonstrate the convergence, accuracy, and dependence on parameter values of the iterative solution for a problem of viscous flow around a porous sphere with a known analytical solution, as well as more general surfaces.
翻译:开发了一个框架,以便从三个方面为斯托克斯-达西混合系统开发一个稳健和高度精确的数字解决方案; 域分解方法基于对界面条件的Drichlet-Neumann型分割,并迭接地解决单独的斯托克斯和达西问题; 为每个问题设计了二类边界整体方程式; 集成方程式使用在边界上达到高度精确度的内核平滑和直截了当的二次方程式来分离整体体。 数值结果显示迭代方程式的趋同性、准确性和对迭代方法参数值的依赖性,以已知的分析解决方案以及更普通的表面,解决在多孔领域周围流动的粘性问题。