论文标题
混合虚拟元素方法在地下流的复杂网格上的性能
Performances of the mixed virtual element method on complex grids for underground flow
论文作者
论文摘要
地下物理过程的数值模拟经常需要与几何和/或数据相关的挑战。前者主要是由于沉积层的形状以及裂缝和断层的存在，而后者则连接到岩石基质的性质，这些岩石基质可能在太空中突然变化。近似方案的发展最近集中在克服此类困难上，目的是获得具有良好近似特性的数值方案。在这项工作中，我们对混合虚拟元素方法（MVEM）的性能进行数值研究，以解决断裂多孔介质中单相流模型的解决方案。该方法能够处理多面体类型的网格细胞并处理混合尺寸问题。事实证明，它相对于渗透性场的变化和元素的形状是有力的。我们的数值实验集中于两个涵盖上述临界几个方面的测试用例。
The numerical simulation of physical processes in the underground frequently entails challenges related to the geometry and/or data. The former are mainly due to the shape of sedimentary layers and the presence of fractures and faults, while the latter are connected to the properties of the rock matrix which might vary abruptly in space. The development of approximation schemes has recently focused on the overcoming of such difficulties with the objective of obtaining numerical schemes with good approximation properties. In this work we carry out a numerical study on the performances of the Mixed Virtual Element Method (MVEM) for the solution of a single-phase flow model in fractured porous media. This method is able to handle grid cells of polytopal type and treat hybrid dimensional problems. It has been proven to be robust with respect to the variation of the permeability field and of the shape of the elements. Our numerical experiments focus on two test cases that cover several of the aforementioned critical aspects.
