ارزیابی عملکرد روش‌های عددی در شبیه‌سازی جریان آب زیرزمینی (مطالعه موردی: آبخوان بیرجند)

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دکتری منابع آب، گروه علوم و مهندسی آب، دانشگاه بیرجند. بیرجند، ایران.

2 استاد گروه علوم و مهندسی آب، دانشگاه بیرجند، بیرجند، ایران.

3 دانشیار گروه علوم و مهندسی آب، دانشگاه بیرجند، بیرجند، ایران. گروه پژوهشی تغییر اقلیم و خشکسالی، دانشگاه بیرجند، بیرجند، ایران.

10.22034/hydro.2023.12330

چکیده

داشتن دانش و اطلاع دقیق از وضعیت منابع آب زیرزمینی جهت برنامه‌ریزی و توسعه پایدار در مناطق خشک و نیمه‌خشک اهمیت دوچندانی دارد. از طرفی به‌دلیل این‌که مدل‌سازی آب زیرزمینی در مطالعات میدانی دارای مشخصاتی نظیر مرزهای نامنظم، ناهمگنی و ناهمسانگردی و همچنین شرایط مرزی و مدل مفهومی پیچیده است، دشواری‌های زیادی در فرایند شبیه‌سازی وجود دارد. به‌دلیل قابلیت‌های مناسب و عملکرد قابل‌قبول روش‌های عددی، این پژوهش در نظر دارد تا یک چارچوب مناسب جهت شبیه‌سازی آب زیرزمینی در مناطق خشک را که مبتنی بر روش‌های تفاضل محدود (FD)، اجزای محدود (FE) و بدون شبکه (Mfree) است، ارائه کند. معادله جریان آب زیرزمینی براساس روش‌های FD، FE و Mfree گسسته شد و عملکرد آن‌ها در یک آبخوان فرضی و یک مطالعه میدانی مورد ارزیابی قرار گرفت. ارزیابی نتایج عددی به‌دست‌آمده در آبخوان فرضی و مقایسه با جواب تحلیلی، حاکی از آن است که عملکرد هر سه مدل‌ عددی قابل‌قبول است. به‌طوری‌که مقدار شاخص RMSE برای روش‌های Mfree، FE و FD به‌ترتیب 005/0، 016/0 و 018/0 متر به دست آمد. لکن با افزایش پیچیدگی‌های شبیه‌سازی در مطالعه میدانی، از دقت روش‌های عددی مبتنی بر مش (شبکه‌بندی) نظیر FD و FE کاسته شد. ارزیابی عملکرد روش FD نشان داد که این روش در مسائل با هندسه‌های منظم و شرایط مرزی ساده از عملکرد خوبی برخوردار است، لکن در مسائل واقعی و شرایط واقعی با هندسه‌های نامنظم که با ناهمسانگردی و ناهمگنی مواجه هستند از دقت آن به‌شدت کاسته می‌شود. به‌طوری‌که مقدار شاخص RMSE برای روش FD در آبخوان واقعی، حدود 77/1 متر به­دست آمد. نتیجه فوق البته با شدت کمتر برای روش FE نیز صادق است (مقدار RMSE برای FE و در آبخوان واقعی حدود 36/0 به­دست آمد). همچنین نتایج این مطالعه در خصوص روش Mfree ثابت کرد که این روش ضمن داشتن دقت بالاتر نسبت به روش‌های FD و FE از انعطاف‌پذیری بسیار بالایی در مواجه با هندسه‌های نامنظم و موضوعات ناهمسانگردی و ناهمگنی برخوردار است. مقدار شاخص RMSE برای روش Mfree در مطالعه میدانی، 26/0 متر به­دست آمد.

کلیدواژه‌ها

عنوان مقاله [English]

Performance Assessment of Numerical Solutions in Groundwater Simulation (case study: Birjand aquifer)

نویسندگان [English]

  • Ahmad Jafarzadeh 1
  • Abbas Khashei 2
  • Mohsen PurrezaBilondi 3
1 PhD Graduate of Water Resources, Department of Water Engineering, University of Birjand, Birjand, Iran.
2 Professor of Water Engineering, Department of Water Engineering, University of Birjand, Birjand, Iran.
3 Associated Professor of Water Engineering, Department of Water Engineering, University of Birjand, Birjand, Iran. Research Group of Drought and Climate change, University of Birjand, Birjand, Iran.
چکیده [English]

The extensive knowledge of groundwater resources' status has double importance for the planning of the sustainable future in the arid regions. Strictly, without an efficient model with accurate simulation, it is impossible to have a good understanding of groundwater behavior. Since groundwater modeling in real problems comprises irregular boundaries, heterogeneity, anisotropy, and conceptualization, there exist many challenges in the simulation process. Due to proper acceptable performance, this study aims to present a proper framework to simulate groundwater flow based on Finite Difference (FD), Finite Element (FE), and Meshfree (Mfree) methods. The governing equation of groundwater flow was discretized through FD, FE, and Mfree approximations, and their performance was examined in two case studies: hypothetical case and field study. The findings of this study revealed that the Mfree has more applicability than others because some noticeable challenges were found in the simulation process of the FD and FE. Comparison of analytical solutions and simulated values in the hypothetical aquifer indicated that all methods are compliant. In terms of the RMSE criterion, the Mfree, FE, and FD were evaluated respectively, 0.005, 0.016, and 0.018 m. However, the numerical methods' act, especially the mesh-based methods (FD and FE) in the field study, becomes less accurate. Performance assessment of the FD indicated that this method has good ability in a simple test case with regular geometry, while in an aquifer with irregular geometry associated with isotropy and heterogeneity, its accuracy is greatly diminished. So that, the RMSE for FD methods in field study was evaluated 1.77 m. The same results may be obtained from the FE method, such that its RMSE was obtained 0.36 m. Investigations of this study showed that the FE needs time-consuming preprocessing practices to implement in the different aquifer. The results of the Mfree application indicated that this method is more efficient than others due to its very high flexibility in irregular geometry with isotropy and heterogeneity issues. The RMSE for the Mfree in the field study obtained 0.26 m.

کلیدواژه‌ها [English]

  • Arid Region
  • Finite Element
  • Mesh Less
  • Structure Uncertainty Weighted Residuals

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هیدروژئولوژی
دوره 7، شماره 2
ناشر
اسفند 1401
صفحه 61-75

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