The impact of groundwater velocity fields on streamlines in an aquifer system with a discontinuous aquitard (Inner Mongolia, China)

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Abstract

Many numerical methods that simulate groundwater flow, particularly the continuous Galerkin finite element method, do not produce velocity information directly. Many algorithms have been proposed to improve the accuracy of velocity fields computed from hydraulic potentials. The differences in the streamlines generated from velocity fields obtained using different algorithms are presented in this report. The superconvergence method employed by FEFLOW, a popular commercial code, and some dual-mesh methods proposed in recent years are selected for comparison. The applications to depict hydrogeologic conditions using streamlines are used, and errors in streamlines are shown to lead to notable errors in boundary conditions, the locations of material interfaces, fluxes and conductivities. Furthermore, the effects of the procedures used in these two types of methods, including velocity integration and local conservation, are analyzed. The method of interpolating velocities across edges using fluxes is shown to be able to eliminate errors associated with refraction points that are not located along material interfaces and streamline ends at no-flow boundaries. Local conservation is shown to be a crucial property of velocity fields and can result in more accurate streamline densities. A case study involving both three-dimensional and two-dimensional cross-sectional models of a coal mine in Inner Mongolia, China, are used to support the conclusions presented.

Keywords

Groundwater flow Numerical modeling Mining Streamline Local conservation 

L’impact des champs de vitesse de l’eau souterraine sur les lignes de courant dans un système aquifère avec un semi-perméable discontinu (Mongolie intérieure, Chine)

Résumé

De nombreuses méthodes numériques qui simulent l’écoulement d’eau souterraine, particulièrement la méthode aux éléments finis continus de Galerkine, ne produisent pas directement l’information sur la vitesse. De nombreux algorithmes ont été proposés pour améliorer la précision des champs de vitesse calculés à partir des potentiels hydrauliques. Dans cet article, sont présentées les différences entre les lignes de courant générées à partir de champs de vitesse obtenus en utilisant différents algorithmes. La méthode de superconvergence employée dans FEFLOW, un code du commerce très utilisé, et certaines méthodes à double maillage proposées ces dernières années ont été sélectionnées pour effectuer les comparaisons. Les applications destinées à représenter des conditions hydrogéologiques utilisant des lignes de courant sont utilisées ; il est montré que les erreurs sur les lignes de courant conduisent à des erreurs notables sur les conditions aux limites, la localisation des interfaces matérielles, les flux et les conductivités hydrauliques. De plus, les effets des procédures utilisées dans ces deux types de méthodes, notamment l’intégration de la vitesse et la conservation locale, sont analysés. Il est montré que la méthode d’interpolation des vitesses de l’autre côté des bords utilisant les flux est capable d’éliminer les erreurs associées à des points de réfraction qui ne se situent pas le long des interfaces matérielles et aux extrémités des lignes de courant au niveau des limites à flux nul. Il en ressort que la conservation locale est une propriété cruciale des champs de vitesse et que cette méthode peut conduire à des densités de lignes de courant plus précises. Un cas d’étude utilisant à la fois des modèles tridimensionnels et en coupe 2D d’une mine de charbon en Mongolie intérieure, Chine, est utilisé pour appuyer les conclusions de l’étude.

El impacto de los campos de velocidad del agua subterránea en las líneas de flujo en un sistema acuífero con un acuitardo discontinuo (Mongolia Interior, China)

Resumen

Muchos métodos numéricos que simulan el flujo de agua subterránea, particularmente el método de elemento finito de Galerkin continuo, no producen directamente información de velocidad. Se han propuesto muchos algoritmos para mejorar la precisión de los campos de velocidad calculados a partir de potenciales hidráulicos. Las diferencias en las líneas de flujo generadas a partir de los campos de velocidad obtenidos utilizando diferentes algoritmos se presentan en este trabajo. El método de superconvergencia empleado por FEFLOW, un código comercial popular, y algunos métodos de doble malla propuestos en los últimos años son seleccionados para la comparación. Se utilizan las aplicaciones para representar las condiciones hidrogeológicas utilizando líneas de flujo y se muestra que los errores en las líneas de flujo conducen a errores notables en las condiciones de contorno, en las ubicaciones de las interfaces materiales, en los flujos y en las conductividades. Además, se analizan los efectos de los procedimientos utilizados en estos dos tipos de métodos, incluida la integración de la velocidad y la conservación local. Se muestra que el método de interpolación de velocidades a través de los bordes utilizando flujos permite eliminar los errores asociados con los puntos de refracción que no se encuentran a lo largo de las interfaces de los materiales y los extremos aerodinámicos en los límites de no flujo. La conservación local se muestra como una propiedad crucial de los campos de velocidad y puede dar lugar a densidades aerodinámicas más precisas. Se utiliza un estudio de caso que involucra modelos transversales tridimensionales y bidimensionales de una mina de carbón en Mongolia Interior, China, para sustentar las conclusiones presentadas.

地下水流速场对流线的影响: 以中国内蒙古某含有不完整弱透水层的含水系统为例

摘要

许多地下水数值模拟方法不直接计算流速, 如连续迦辽金有限单元法。为提高基于水头的流速场计算精度,前人提出了大量算法。本文对比了利用商业软件FEFLOW中的超收敛算法和近几年提出的双重网格算法计算流速场得到的流线的区别。在利用流线刻画水文地质条件的过程中,流线误差会导致边界条件、介质边界、流量和渗透系数方面的显著误差。本文深入分析了流速场计算方法中流速插值和局部均衡的作用,发现:基于边界流量插值计算流速的方法能够消除流线折射点不在介质边界和流线在隔水边界终止等流线误差;局部均衡可以提高流线计算精度,是流速场的重要性质。以中国内蒙古某煤矿地下水三维模型和二维剖面模型为例进行研究,得到了对比研究结果。

O impacto dos campos de velocidades da água subterrânea nas linhas de fluxo em um sistema aquífero com um aquitardo descontínuo (interior da Mongólia, China)

Resumo

Muitos métodos numéricos que simulam o fluxo das águas subterrâneas, particularmente o método de elementos finitos contínuos de Galerkin, não produzem diretamente informações de velocidades. Muitos algoritmos já foram propostos para melhorar a precisão dos campos de velocidades a partir de potenciais hidráulicos. São apresentadas neste artigo as diferenças nas linhas de fluxo geradas a partir dos campos de velocidades obtidas usando diferentes algoritmos. O método de superconvergência empregado pelo FEFLOW, um código comercial popular, e alguns métodos de dupla malha propostos nos últimos anos são selecionados para comparação. São usadas aplicações para descrever condições hidrogeológicas usando linhas de fluxo, bem como mostrados os erros nessas linhas de fluxo para levar a erros notáveis nas condições de contorno, nos locais de interfaces de materiais, fluxos e condutividades. Além disso, são analisados os efeitos dos procedimentos utilizados nesses dois tipos de métodos, incluindo integração de velocidade e conservação local. O método de interpolação das velocidades entre as bordas usando fluxos mostra-se capaz de eliminar erros associados a pontos de refração que não estão localizados ao longo de interfaces de materiais e linhas de fluxo finais em limites sem fluxo. A conservação local mostra ser uma propriedade crucial dos campos de velocidades e pode resultar em densidades de linhas de fluxo mais precisas. É utilizado um estudo de caso envolvendo modelos transversais tridimensionais e bidimensionais de uma mina de carvão no interior da Mongólia, China, para apoiar as conclusões apresentadas.

Notes

Acknowledgements

All the related data can be obtained from the corresponding author, Yingwang Zhao. The authors would like to thank the editor and the reviewers for their constructive suggestions.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Geoscience and Surveying EngineeringChina University of Mining & Technology, BeijingBeijingChina
  2. 2.National Engineering Research Center of Coal Mine Water Hazard ControllingBeijingChina
  3. 3.Information Engineering CollegeBeijing Institute of Petrochemical TechnologyBeijingChina

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