A hybridizable discontinuous Galerkin method on unfitted meshes for single-phase Darcy flow in fractured porous media

A hybridizable discontinuous Galerkin method on unfitted meshes for single-phase Darcy flow in fractured porous media
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DOI：
10.1016/j.advwatres.2023.104390
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发表时间：
2022-09
期刊：
ArXiv
影响因子：
--
通讯作者：
G. Fu;Yang Yang-Yang
G. Fu;Yang Yang-Yang
中科院分区：
其他
文献类型：
--
作者：
G. Fu;Yang Yang-Yang

文献摘要

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我们提出了一种针对裂缝多孔介质中单相达西流的未拟合网格的新型可杂交间断伽辽金（HDG）方法。特别是，我们将 HDG 方法应用于最近引入的重新解释的离散裂缝模型 (RDFM)，该模型使用 Dirac-δ 函数来模拟传导裂缝和阻塞裂缝。由于对裂缝使用 Dirac-δ 函数方法，我们的数值方案自然允许与裂缝相关的不拟合网格，这是该方案的主要新颖之处。此外，该计划在当地群众中是保守的。特别是，我们的方案有一个简单的形式，它是对现有常规达西流 HDG 求解器的新颖修改，添加了以下两个组件：（i）在背景网格中定位同维一裂缝，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）调整穿过传导和阻塞裂缝（裂缝单元）的单元的罚参数。尽管所提出的方案很简单，但它对于二维和三维的各种基准测试用例都表现良好。据我们所知，这是第一次将不拟合的有限元方案应用于 3D 中复杂的裂缝多孔介质流动问题，其中包括阻塞裂缝和传导裂缝，且对网格没有任何限制。
We present a novel hybridizable discontinuous Galerkin (HDG) method on unfitted meshes for single-phase Darcy flow in a fractured porous medium. In particular we apply the HDG methodology to the recently introduced reinterpreted discrete fracture model (RDFM) 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. In particular, our scheme has a simple form, which is a novel 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 add 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 quite well for various benchmark test cases in both two and three dimensions. To the best of our knowledge, this is the first time that an 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.