针对小长度尺度上参数对比较大的断裂介质中的流动和传输问题的空间和时间方案对比研究

IF 2.1 3区 地球科学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Computational Geosciences Pub Date : 2024-05-13 DOI:10.1007/s10596-024-10293-y
Wansheng Gao, Insa Neuweiler, Thomas Wick
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引用次数: 0

摘要

在这项工作中,进一步开发并比较了用于裂隙介质传输问题的各种高精度数值方案。具体来说,要捕捉急剧的梯度和时间上的突然变化,低精度阶次的方案并不总是足够的。为此,研究人员制定了高达二阶的非连续 Galerkin、流线上风 Petrov-Galerkin 和有限差分。由此产生的方案使用稀疏直接数值求解器求解。此外,一阶和二阶时间非连续伽勒金方法分别采用局部细化网格上的空间有限元进行整体求解和解耦求解。我们的算法开发通过一个规则断裂网络和断裂介质中的几个进一步配置进行了验证,这些断裂介质在小长度尺度上具有较大的参数对比。其中,对数值方案和实施的评估主要集中在三个关键方面,即精度、单调性和计算成本。
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A comparison study of spatial and temporal schemes for flow and transport problems in fractured media with large parameter contrasts on small length scales

In this work, various high-accuracy numerical schemes for transport problems in fractured media are further developed and compared. Specifically, to capture sharp gradients and abrupt changes in time, schemes with low order of accuracy are not always sufficient. To this end, discontinuous Galerkin up to order two, Streamline Upwind Petrov-Galerkin, and finite differences, are formulated. The resulting schemes are solved with sparse direct numerical solvers. Moreover, time discontinuous Galerkin methods of order one and two are solved monolithically and in a decoupled fashion, respectively, employing finite elements in space on locally refined meshes. Our algorithmic developments are substantiated with one regular fracture network and several further configurations in fractured media with large parameter contrasts on small length scales. Therein, the evaluation of the numerical schemes and implementations focuses on three key aspects, namely accuracy, monotonicity, and computational costs.

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来源期刊
Computational Geosciences
Computational Geosciences 地学-地球科学综合
CiteScore
6.10
自引率
4.00%
发文量
63
审稿时长
6-12 weeks
期刊介绍: Computational Geosciences publishes high quality papers on mathematical modeling, simulation, numerical analysis, and other computational aspects of the geosciences. In particular the journal is focused on advanced numerical methods for the simulation of subsurface flow and transport, and associated aspects such as discretization, gridding, upscaling, optimization, data assimilation, uncertainty assessment, and high performance parallel and grid computing. Papers treating similar topics but with applications to other fields in the geosciences, such as geomechanics, geophysics, oceanography, or meteorology, will also be considered. The journal provides a platform for interaction and multidisciplinary collaboration among diverse scientific groups, from both academia and industry, which share an interest in developing mathematical models and efficient algorithms for solving them, such as mathematicians, engineers, chemists, physicists, and geoscientists.
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