论文标题
关于骨折的多孔介质中单相Darcy流的无固体网格的杂交不连续的Galerkin方法
A hybridizable discontinuous Galerkin method on unfitted meshes for single-phase Darcy flow in fractured porous media
论文作者
论文摘要
我们提出了一种新型的杂交不连续的盖尔金（HDG）方法，该方法是在断裂的多孔培养基中单相Darcy流的未固定网格。特别是，我们将HDG方法应用于最近引入的重新解释的离散断裂模型（RDFM）[Xu＆Yang，2021提交]，该方法使用Dirac- $δ$函数来对导电和阻断骨折进行建模。由于裂缝使用dirac- $δ$函数方法，我们的数值方案自然允许对裂缝的未固定网格，这是提议方案的主要新颖性。此外，该计划是当地的保守派，并且与现有工作相比，相对容易实施。特别是，我们的方案是通过添加以下两个组件来简单地修改了现有的常规DARCY流量求解器：（i）在背景网格中找到一个co-dimension一个骨折，并将与这些裂缝相关的适当表面积分添加到刚度矩阵中，（II）通过导电和封闭的细胞对细胞进行调整（II）调节细胞（II））。 尽管提出的方案很简单，但在两维和三维的各种基准测试案例中，它的表现非常出色。这是第一次将真正的未有限元方案应用于3D中的复杂断裂的多孔培养基流问题，而封闭和导电性骨折都没有对网格的任何限制。
We present a novel hybridizable discontinuous Galerkin (HDG) method on unfitted meshes for single-phase Darcy flow in a fractured porous media. In particular we apply the HDG methodology to the recently introduced reinterpreted discrete fracture model (RDFM) [Xu & Yang, 2021 submitted] that use Dirac-$δ$ functions to model both conductive and blocking fractures. Due to the use of Dirac-$δ$ function approach for the fractures, our numerical scheme naturally allows for unfitted meshes with respect to the fractures, which is the major novelty of the proposed scheme. Moreover, the scheme is locally mass conservative and is relatively easy to implement comparing with existing work on the subject. In particular, our scheme is a simple modification of an existing regular Darcy flow HDG solver by adding the following two components: (i) locate the co-dimension one fractures in the background mesh and adding the appropriate surface integrals associated with these fractures into the stiffness matrix, (ii) adjust the penalty parameters on cells cut through conductive and blocking fractures (fractured cells). Despite the simplicity of the proposed scheme, it performs extremely well for various benchmark test cases in both two- and three-dimensions. This is the first time that a truly unfitted finite element scheme been applied to complex fractured porous media flow problems in 3D with both blocking and conductive fractures without any restrictions on the meshes.
