论文标题
耦合非线性stokes和darcy流的全球时间域分解方法
A global-in-time domain decomposition method for the coupled nonlinear Stokes and Darcy flows
论文作者
论文摘要
我们研究了基于时间依赖性的非线性stokes-darcy模型的域分解的去耦迭代算法，其中可以在流动区域和多孔介质中使用不同的时间步骤。基于质量保护的接口条件，耦合系统被公式为时空接口问题。然后，通过嵌套迭代方法解决非线性界面问题，该方法在每个牛顿迭代中涉及线性化界面问题的解决方案，并且在每个Krylov迭代中，平行的解决方案是时间依赖性线性化的Stokes和Darcy问题。因此，可以使用时间（和空间中的）局部离散来处理在不同时间尺度上演变的耦合方程的多物理系统。提出了具有不合格时间网格的数值结果，以说明该方法的性能。
We study a decoupling iterative algorithm based on domain decomposition for the time-dependent nonlinear Stokes-Darcy model, in which different time steps can be used in the flow region and in the porous medium. The coupled system is formulated as a space-time interface problem based on the interface condition for mass conservation. The nonlinear interface problem is then solved by a nested iteration approach which involves, at each Newton iteration, the solution of a linearized interface problem and, at each Krylov iteration, parallel solution of time-dependent linearized Stokes and Darcy problems. Consequently, local discretizations in time (and in space) can be used to efficiently handle multiphysics systems of coupled equations evolving at different temporal scales. Numerical results with nonconforming time grids are presented to illustrate the performance of the proposed method.
