地下水流建模的离散外部微积分方法

IF 2.7 3区 工程技术 Q3 ENGINEERING, CHEMICAL
Jin Xu, Wenfan Zhang, Zheng Chen
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引用次数: 0

摘要

本文从离散外演算原理出发,提出了一个模拟地下水流动的数值公式。本文首先利用微分形式及其算子,将非定常流场的控制方程转化为外微积分框架下的公式。外部微积分公式的空间离散化是基于简单复形及其双网格的概念,而时间导数项则是采用差分数值格式进行离散化。根据上述离散化方案,建立了以流量和压力为主要变量的混合数值公式。为了评估基于dec的方法在模拟地下水流动方面的有效性和准确性,进行了大量的数值研究。评估包括与解析解的比较,例如单井的Theis解,以及使用既定方法模拟多井泵送情景获得的数值结果。解与解析和数值结果均表现出高度的一致性。此外,研究结果表明,该方法适用于更复杂的环境,包括带有防水帷幕的矿井脱水和带有阻隔物的三维流动。结果表明DEC方法作为一种有效的地下水求解方法的潜力,其特点是具有良好的局部质量守恒性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Discrete Exterior Calculus Method for Groundwater Flow Modeling

Discrete Exterior Calculus Method for Groundwater Flow Modeling

A numerical formula for modeling groundwater flow is presented in this study, derived from the principles of discrete exterior calculus (DEC). The study begins with transforming the governing equations for unsteady flow into formulas in the framework of exterior calculus, utilizing differential forms and their operators. The spatial discretization of the exterior calculus formula is based on the conception of simplicial complex and its dual mesh, while the time derivative term is discretized using the difference numerical scheme. Following the above discretization scheme, a mixed numerical formulation was developed, with flux and pressure as primary variables. To evaluate the DEC-based method’s effectiveness and accuracy in modeling groundwater flow, an extensive numerical study is conducted. The assessment includes comparisons with analytical solutions, such as Theis’s solution for a single well, as well as numerical results obtained from simulating multi-well pumping scenarios using established methods. The solutions exhibit a high degree of consistency with both analytical and numerical results. Furthermore, the results demonstrate the applicability of the proposed approach in more complex settings, ranging from pit dewatering with a waterproof curtain to three-dimensional flow with cutoff barriers. The results illustrate the potential of the DEC method as an effective groundwater solver, distinguished by its excellent local mass conservation.

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来源期刊
Transport in Porous Media
Transport in Porous Media 工程技术-工程:化工
CiteScore
5.30
自引率
7.40%
发文量
155
审稿时长
4.2 months
期刊介绍: -Publishes original research on physical, chemical, and biological aspects of transport in porous media- Papers on porous media research may originate in various areas of physics, chemistry, biology, natural or materials science, and engineering (chemical, civil, agricultural, petroleum, environmental, electrical, and mechanical engineering)- Emphasizes theory, (numerical) modelling, laboratory work, and non-routine applications- Publishes work of a fundamental nature, of interest to a wide readership, that provides novel insight into porous media processes- Expanded in 2007 from 12 to 15 issues per year. Transport in Porous Media publishes original research on physical and chemical aspects of transport phenomena in rigid and deformable porous media. These phenomena, occurring in single and multiphase flow in porous domains, can be governed by extensive quantities such as mass of a fluid phase, mass of component of a phase, momentum, or energy. Moreover, porous medium deformations can be induced by the transport phenomena, by chemical and electro-chemical activities such as swelling, or by external loading through forces and displacements. These porous media phenomena may be studied by researchers from various areas of physics, chemistry, biology, natural or materials science, and engineering (chemical, civil, agricultural, petroleum, environmental, electrical, and mechanical engineering).
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