论文标题
自适应交错的DG方法用于骨折的多孔介质中的达西流动
Adaptive staggered DG method for Darcy flows in fractured porous media
论文作者
论文摘要
破裂的多孔培养基中的对流动在应用中很重要。数值模拟中的一个主要挑战是该流量受裂缝的强烈影响，因此解决方案通常包含复杂的特征，这些特征需要高计算网格分辨率。不需要使用均匀的细网，而是需要更高效的自适应精制网格。在本文中，我们设计和分析了一种新型的残留型后验误差估计器，用于在断裂的多孔介质中的Darcy流的一般多边形网格上的交错DG方法。该方法可以处理相当通用的网格，并且可以简单地将悬挂的节点纳入该方法的构造中，这对于自适应网格的细化而言是高度赞赏的。证明了误解器的可靠性和效率。可靠性的推导取决于原始公式中连续设置的稳定性。定义了一个在每个批量域内连续的构型对应物，以促进可靠性的推导。最后，进行了几项数值实验，包括多个非相互裂缝，以确认所提出的理论。
Modeling flows in fractured porous media is important in applications. One main challenge in numerical simulation is that the flow is strongly influenced by the fractures, so that the solutions typically contain complex features, which require high computational grid resolutions. Instead of using uniformly fine mesh, a more computationally efficient adaptively refined mesh is desirable. In this paper we design and analyze a novel residual-type a posteriori error estimator for staggered DG methods on general polygonal meshes for Darcy flows in fractured porous media. The method can handle fairly general meshes and hanging nodes can be simply incorporated into the construction of the method, which is highly appreciated for adaptive mesh refinement. The reliability and efficiency of the error estmator are proved. The derivation of the reliability hinges on the stability of the continuous setting in the primal formulation. A conforming counterpart that is continuous within each bulk domain for the discrete bulk pressure is defined to facilitate the derivation of the reliability. Finally, several numerical experiments including multiple non-intersecting fractures are carried out to confirm the proposed theories.
