论文标题
耦合多维流量问题的任意订单混合虚拟元素公式
An arbitrary order Mixed Virtual Element formulation for coupled multi-dimensional flow problems
论文作者
论文摘要
离散断裂和矩阵（DFM）模型将断裂的多孔介质描述为嵌入在代表周围多孔介质的3D矩阵中的2D平面多边形的复杂集。 DFM中流量的数值模拟需要在三维矩阵，平面裂缝和一个维裂缝相交的三维矩阵上离散化偏微分方程，并且需要在不同维度的实体之间进行适当的耦合条件，需要在不同维度的实体之间添加各个相互之间的问题。目前的工作提出了用于此类多维问题的混合配方中虚拟元素方法的任意订单实施。讨论了有关网格生成的有效策略的详细信息，并解决了实施方面。提供了各种上下文中的几个数值结果，其中显示了该方法在复杂多维域中流动模拟的适用性。
Discrete Fracture and Matrix (DFM) models describe fractured porous media as complex sets of 2D planar polygons embedded in a 3D matrix representing the surrounding porous medium. The numerical simulation of the flow in a DFM requires the discretization of partial differential equations on the three dimensional matrix, the planar fractures and the one dimensional fracture intersections, and suitable coupling conditions between entities of different dimensionality need to be added at the various interfaces to close the problem. The present work proposes an arbitrary order implementation of the Virtual Element method in mixed formulation for such multidimensional problems. Details on effective strategies for mesh generation are discussed and implementation aspects are addressed. Several numerical results in various contexts are provided, which showcase the applicability of the method to flow simulations in complex multidimensional domains.
