Neyshabur Plain Groundwater Flow Modelling Using Analytic Element and Point Collocation Mesh Free Methods

Document Type : Research Article


1 MSc. Graduate, Department of Civil Engineering and Geodesy, Graduate University of Advanced Technology, Kerman, Iran

2 Assistant Professor, Department of Civil Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, Kerman, Iran


In this paper, an effective approach using Analytic Element Method (AEM) is presented for large-scale groundwater flow modelling in two dimensional steady state condition. Hydrologic characteristics are exerted in the AEM by using Laplace equations and linear functions. In this algorithm, the potential discharge of each hydrologic characteristic is obtained and combined using the superposition principle and then added to the aquifer potential discharge. In order to compare AEM results, Point Collocation Method (PCM) has been used which is a free-mesh approach based on the finite element method. In PCM approach, some points are distributed on the computational domain and the shape functions are created in order to solve the governing equation. Proposed algorithm evaluation was done by Neyshabur plain data. The particle swarm optimization algorithm has been employed for model calibration. The Python object-oriented programming language was used in implementation of modelling. There is no need for interpolation in AEM. The AEM approach is not a complicated method and uses simple superposition principle. The comparison of results indicate that the results of AEM are more accurate than the results of PCM.


بانک اطلاعات معاونت مطالعات پایه منابع آب (1381). "آمار کمّی منابع آب زیرزمینی (چاه، چشمه و قنات) محدوده مطالعاتی نیشابور با کد 4738"، شرکت سهامی آب منطقه‌ای خراسان رضوی، ایران.
خاشعی سیوکی ع.، قهرمان ب. و کوچک‌زاده م. (1390). "ارزیابی پتانسیل استحصال آب از آبخوان با روش فرایند تحلیلی سلسله مراتبی فازی (مطالعه موردی: دشت نیشابور)"، مجله پژوهش آب ایران، دوره 5، شماره 9، ص.ص. 171-180.
خاشعی سیوکی ع.، قهرمان ب. و کوچک زاده م. (1392). "مقایسه مدل‌های شبکه عصبی مصنوعی، ANFIS و رگرسیونی در برآورد سطح ایستابی آبخوان دشت نیشابور"، نشریه آبیاری و زهکشی ایران، دوره، شماره 1، ص.ص. 10-22.
محمدی ا.، حسامی کرمانی م.ر. و قائینی حصاروئیه م. (1392). "مقایسه روش‌های بهینه‌سازی ترکیب‌شده با روش المان تحلیلی برای تصفیه آب‌های زیرزمینی"، مجموعه مقالات هفتمین کنگره ملی عمران، دانشگاه سیستان و بلوچستان، زاهدان، ایران.
ولایتی س. و توسلی س. (1370). منابع و مسائل آب خراسان، انتشارات آستان قدس رضوی، مشهد.
Badv, K. and Deriszadeh, M. (2005). "Wellhead protection area delineation using the analytic element method", Water, Air, and Soil Pollution, 161 (1), pp. 39-54.
Bakker, M., Anderson, E., Olsthoorn, T. and Strack, O. D. L. (1999). "Regional groundwater modeling of the Yucca Mountain site using analytic elements", Journal of Hydrology, 226 (3), pp. 167-178.
Bakker, M. and Kelson, V. A. (2009). "Writing analytic element programs in Python", Ground Water, 47 (6), pp. 828-834.
Craig, J. R. (2004). "Reactive contaminant transport modeling using analytic element flow solutions", PhD Thesis, The State University of New York, Buffalo, USA.
Craig, J. and Rabideau, A. (2006). "Finite element transport modeling using analytic element flow solutions", Water Resources Research, 42 (10), W10420.
De Lange, W. (1996). "NAGROM, a model for national groundwater management and regional and local studies", European Water Management, 6 (5), pp. 63-67.
Fitts, C. R. (2012). Groundwater Science, 2nd Ed., Academic Press, Oxford.
Kansa, E. J. (1990). "Multiquadrics—A scattered data approximation scheme with applications to computational fluid-dynamics—II solutions to parabolic, hyperbolic and elliptic partial differential equations", Computers & Mathematics with Applications, 19 (8), pp. 147-161.
Kumar, R. P. and Dodagoudar, G. (2010) "Two-dimensional meshfree modelling of contaminant transport through saturated porous media using RPIM", Environmental Earth Sciences, 61 (2), pp. 341-353.
Li, J., Chen, Y. and Pepper, D. (2003). "Radial basis function method for 1-D and 2-D groundwater contaminant transport modeling", Computational Mechanics, 32, (1-2), pp. 10-15.
Liu, G.-R. and Gu, Y. T. (2005). An introduction to meshfree methods and their programming