论文标题
具有不合格时间网格的减少断裂模型的快速准确域分解方法
Fast and accurate domain decomposition methods for reduced fracture models with nonconforming time grids
论文作者
论文摘要
本文与断裂的多孔培养基中可压缩流体流的数值解有关。断裂表示快速途径（即具有高渗透性），并将其建模为嵌入在多孔培养基中的超表面。我们旨在为这种减少的断裂模型开发快速和准确的全球时间域分解（DD）方法，其中裂缝中较小的时间步长可以与子域中的较大时间步长结合。使用压力连续性方程和断裂接口中的切向PDE作为传输条件，得出了三种不同的DD公式。每种方法都会导致时空界面问题，该问题在迭代和全球范围内均可及时解决。有效的预调节器旨在加速迭代方法的收敛性，同时使用不合格的网格及时保留准确性。提出了针对非抑制和部分浸泡裂缝的二维问题的数值结果，以显示提出的方法的改善性能。
This paper is concerned with the numerical solution of compressible fluid flow in a fractured porous medium. The fracture represents a fast pathway (i.e., with high permeability) and is modeled as a hypersurface embedded in the porous medium. We aim to develop fast-convergent and accurate global-in-time domain decomposition (DD) methods for such a reduced fracture model, in which smaller time step sizes in the fracture can be coupled with larger time step sizes in the subdomains. Using the pressure continuity equation and the tangential PDEs in the fracture-interface as transmission conditions, three different DD formulations are derived; each method leads to a space-time interface problem which is solved iteratively and globally in time. Efficient preconditioners are designed to accelerate the convergence of the iterative methods while preserving the accuracy in time with nonconforming grids. Numerical results for two-dimensional problems with non-immersed and partially immersed fractures are presented to show the improved performance of the proposed methods.
