论文标题
耦合的stokes-darcy问题与darcy问题的强大预处理以原始形式
Robust preconditioning for coupled Stokes-Darcy problems with the Darcy problem in primal form
论文作者
论文摘要
耦合的Darcy-Stokes问题广泛用于在由多孔零件和自由零件组成的物理系统中建模流体传输。在这项工作中，我们考虑了耦合的达西 - 斯托克斯问题的单醇溶液算法的预处理，其中达西问题是原始形式。我们采用操作员的预处理框架，并在问题之间的界面处使用分数求解器，以获得相对于材料参数（即渗透率，粘度和海狸-Joseph-Saffman参数）的订单最佳方案。我们的方法类似于我们早期的工作，但是由于达西问题是原始的形式，因此界面上的大众保护引入了一些挑战。这些挑战将在本文中具体解决。提供了说明性能的数值实验。预处理在非标准的Sobolev空间中构成，可能被视为其在应用中使用的障碍。但是，我们详细介绍了实施性方面，并表明预科人员在实践中实现非常可行。
The coupled Darcy-Stokes problem is widely used for modeling fluid transport in physical systems consisting of a porous part and a free part. In this work we consider preconditioners for monolitic solution algorithms of the coupled Darcy-Stokes problem, where the Darcy problem is in primal form. We employ the operator preconditioning framework and utilize a fractional solver at the interface between the problems to obtain order optimal schemes that are robust with respect to the material parameters, i.e. the permeability, viscosity and Beavers-Joseph-Saffman parameter. Our approach is similar to our earlier work, but since the Darcy problem is in primal form, the mass conservation at the interface introduces some challenges. These challenges will be specifically addressed in this paper. Numerical experiments illustrating the performance are provided. The preconditioner is posed in non-standard Sobolev spaces which may be perceived as an obstacle for its use in applications. However, we detail the implementational aspects and show that the preconditioner is quite feasible to realize in practice.
