Numerical simulation of saturated-unsaturated 2D- unsteady flow toward drain using finite volume method

آب و خاک

Article 6, Volume 28, Issue 3, July 2014, Pages 546-555   

Document Type: Research Article

DOI: 10.22067/jsw.v0i0.30623

Author

rasool ghobadian^*

Razi University, Kermanshah

Abstract

To drainage design and management it is necessary water flow toward drain, water table variation between drains and drainage discharge have been simulated. With recent development in numerical method, it is possible the none-linear differential equation governing saturated-unsaturated flow in soil is numerically solved. In this study a computer model has been developed in which two dimensional equation of saturated-unsaturated flow in soil is solved using finite volume method and Crank-Nicolson scheme. The soil hydrodynamic properties function and soil moisture characteristic curve proposed by Van Genuchten were employed. After model calibration and evaluation, water table variation between two drains with 20 m distance and installation depth of 1.2 m was simulated. The result showed during discharge phase water table falls very fast at the first and then falling speed reduces until reach a constant value. During recharge phase water table raises very low at the first and then rising speed increase. Drainage discharge has similar behavior same as water table. Drainage discharge has a lag time related to time that recharge begins. In this study the lag time was 3.125 day.

Keywords

Richards' equation; Numerical simulation; drainage discharge; Finite Volume Method

References

1- بهبهانی س.م.ر.، و رحیمی خوب ع. 1381. شبیه سازی جریان ناپایدار دو بعدی آب بطرف زهکش ها. مجله علوم کشاورزی و منابع طبیعی، سال نهم، شماره اول. صفحات 162 تا 167.

2- شایان نژاد م. 1387. اصول طراحی سیستم‌های زهکشی. انتشارات دانشگاه شهر کرد،256 صفحه.

3- جعفری ج.، ناظمی ا.ح.، صدرالدینی س.ع. و افروزی ع. 1392. اندازه گیری و برآورد تراز سطح ایستابی و میزان تخلیه زهکشی در جریان غیرماندگار. فصلنامه علمی پژوهشی مهندسی آبیاری و آب، سال 3، شماره 11، صفحات 115 تا125.

4- فرهادی ل.، و آشتیانی ب. 1384. تحلیل عددی معادله جریان آب در ناحیه غیراشباع. مجله تحقیقات منابع آب ایران. جلد 1 شماره 1، صفحات 29تا 39.

5- عزیزی پور م.، و محمودیان شوشتری م. 1391. حل عددی معادله ریچاردز در جریان غیراشباع با استفاده از روش حجم محدود. مجله علوم و مهندسی آبیاری، جلد 35 شماره 2، تابستان 91، صفحه 65 تا 72.

6- نوری ح.، لیاقت ع.، پارسی نژاد م.، و وظیفه دوست م. 1389 . ارزیابی مدل آگروهیدرولوژیکی SWAP در برآورد نوسانات سطح ایستابی و شدت جریان زهکشی زیرزمینی. مجله دانش آب و خاک، سال بیستم، شماره 2، صفحات 157 تا 172.

7- Brooks R.H. and Corey A.T. 1964. Hydraulic properties of porous media.Hydrol. Pap. 3, Colo. State Univ., Fort Collins.

8- Clement T.P., William R.W. and Fred J.M. 1994. A physically based, two-dimensional, finite-difference algorithm for modeling variably saturated flow, Journal of Hydrology, 161: 71-90

9- Leij F.J., Russel W.B. and Lesch S.M. 1997. Closedform expressions for water retention and conductivity data. Ground water, 35:848-858‏.

10- Menziani M., Pugnaghi S. and Vincenzi S. 2007. Analytical solutions of the linearized Richards’ equation for discrete arbitrary initial and boundary conditions‏. Journal of Hydrology, 332:214-225.

11- Mualem Y. 1976. A catalogue of the hydraulic properties of unsaturated soils. Research Project Report , No. 442, Technion, Israel Institute of Technology, Haifa.

12- Samani J.M.V., and Fathi P. 2009. Estimation of unsaturated soil hydrodynamic parameters using inverse problem technique, J. Agric. Sci. Technol, 11: 199-210

13- Simpson M.J. and Clement T.P. 2003.Comparison of finite difference and finite element solutions to the variably-saturated flow equation, Journal of Hydrology, 270: 49-64

14- Van Genuchten M.T. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil Sci. Soc. Am. J. 44(5):892-898

15- Versteeg H.K., Malalasekera W. 1995. An introduction to computational fluid dynamics - The finite volume method. Longman Group Ltd. P, 255.