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A robust fully mixed finite element model for flow and transport in unsaturated fractured porous media
Advances in Water Resources ( IF 4.7 ) Pub Date : 2022-06-25 , DOI: 10.1016/j.advwatres.2022.104259
Anis Younes , Hussein Hoteit , Rainer Helmig , Marwan Fahs

A fully mixed finite element (MFE) model is developed for nonlinear flow and transport in unsaturated fractured porous media with matrix-fracture and fracture-fracture fluid and mass exchanges. The model is based on the discrete fracture matrix (DFM) approach and assumes cross-flow equilibrium in the fractures. The MFE method is employed for the spatial discretization of both flow and transport on the 2D-matrix elements as well as on the 1D-fracture elements. An upwind scheme is employed to avoid unphysical oscillations in the case of advection dominant transport. The temporal discretization is performed using high-order time integration methods and efficient automatic time-stepping schemes via the MOL.

Two test problems dealing with flow and mass transport in saturated and unsaturated fractured porous media are simulated to show the validity of the new model by comparison against (i) a 1D-2D Comsol finite element model and (ii) a 2D-2D Discontinuous Galerkin (DG) model where both fractures and matrix continua are discretized with small 2D mesh elements. The robustness and efficiency of the developed 1D-2D MFE model are then investigated for a challenging problem dealing with infiltration of contaminated water into an initially dry soil involving a fracture network.

The new model yields stable results for advection-dominated and advection-dispersion transport configurations. Further, the results of the 1D-2D MFE model are in very good agreement with those of the 2D-2D DG model for both configurations. The simulation of infiltration of contaminated water into a dry fractured soil shows that the 1D-2D MFE model is within 15 times more efficient than the 2D-2D DG model, which confirms the high benefit of using robust and efficient DFM models for the simulation of flow and transport in fractured porous media.



中文翻译:

不饱和破裂多孔介质中流动和输运的稳健全混合有限元模型

开发了一个完全混合的有限元 (MFE) 模型,用于具有基质-裂缝和裂缝-裂缝流体和质量交换的非饱和裂缝多孔介质中的非线性流动和传输。该模型基于离散裂缝矩阵 (DFM) 方法并假设裂缝中的横流平衡。MFE 方法用于二维矩阵单元和一维断裂单元上流动和传输的空间离散化。在平流主导传输的情况下,采用逆风方案以避免非物理振荡。时间离散化是通过 MOL 使用高阶时间积分方法和高效的自动时间步长方案来执行的。

通过与 ( i ) 1D-2D Comsol 有限元模型和 ( ii ) 2D-2D 不连续 Galerkin模型进行比较,模拟了处理饱和和非饱和破裂多孔介质中的流动和质量传输的两个测试问题,以证明新模型的有效性。(DG) 模型,其中裂缝和基体连续体均使用小的 2D 网格元素进行离散化。然后研究开发的 1D-2D MFE 模型的稳健性和效率,以解决处理污染水渗透到涉及裂缝网络的初始干燥土壤中的挑战性问题。

新模型为平流主导和平流分散传输配置产生了稳定的结果。此外,对于两种配置,1D-2D MFE 模型的结果与 2D-2D DG 模型的结果非常一致。受污染的水渗入干裂土壤的模拟表明,1D-2D MFE 模型的效率是 2D-2D DG 模型的 15 倍以内,这证实了使用稳健高效的 DFM 模型模拟裂隙多孔介质中的流动和输运。

更新日期:2022-06-25
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