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Journals / Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi / 2018 / Cilt: 24 - Sayı: 6

Modelling soil water movement under unsaturated conditions with the Modified Cubic B-Spline Differential Quadrature method

Doymamış koşullarda toprak suyu hareketinin Modifiye Kübik B-Spline Diferansiyel Kuadratur yöntemi ile modellenmesi

Emin ÇİFTÇİ
Pages
952–959
Publication Date
2018-12-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

On account of its simplicity, efficiency and high accuracy, this method can be an appropriate option for the numerical solution of this type of problems.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This study focuses on modelling moisture movement in the unsaturated soil zone with the use of the Modified Cubic B-Spline Differential Quadrature method.
📊
Key Findings & Data:The differential quadrature method was employed to evaluate the spatial derivatives of the equation variables, and the 4th order Runge-Kutta Method was used to march the solution in time.
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Conclusion & Impact:On account of its simplicity, efficiency and high accuracy, this method can be an appropriate option for the numerical solution of this type of problems.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Richards denklemi · Diferansiyel kuadratur · Modifiye kübik b-spline

Abstract

This study focuses on modelling moisture movement in the unsaturated soil zone with the use of the Modified Cubic B-Spline Differential Quadrature method. The numerical solution of the Richards Equation, which is commonly used in the field of hydrogeology for describing soil moisture movement, was investigated. The differential quadrature method was employed to evaluate the spatial derivatives of the equation variables, and the 4th order Runge-Kutta Method was used to march the solution in time. To verify the accuracy of the developed model, three test cases having different boundary conditions were taken into consideration. The retrieved results are seen to be in good agreement with the values provided by the analytical and other available numerical techniques. On account of its simplicity, efficiency and high accuracy, this method can be an appropriate option for the numerical solution of this type of problems.

Özet

Bu çalışma, toprak suyunun doymamış bölgedeki hareketinin Modifiye Kübik B-Spline Diferansiyel Kuadratur yöntemi ile modellenmesi üzerine kurulmuştur. Toprak nemi hareketini tanımlamak için hidrojeoloji alanında sıklıkla kullanılan Richards denkleminin sayısal çözümü irdelenmiştir. Bu denklemde yer alan parametrelerin konum türevlerini hesaplayabilmek için diferansiyel kuadratur yöntemi, problemi zamanda ilerletebilmek için 4. mertebeden Runge-Kutta yöntemi kullanılmıştır. Geliştirilen modelin verdiği sonuçların doğruluğunun ölçülebilmesi için farklı sınır koşullarına sahip üç örnek uygulama ele alınmıştır. Elde edilen sonuçlar mevcut analitik ve diğer sayısal yöntemlerin verdiği sonuçlarla büyük tutarlılık göstermektedir. Etkili, basit, verimli, kolay uygulanabilir ve yüksek doğrulukta sonuç veriyor oluşu, ele alınan yöntemin bu tip problemlerin sayısal çözümü için uygun bir tercih olabileceğine işaret etmektedir.

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Cite This Article

ÇİFTÇİ, E. (2018). Modelling soil water movement under unsaturated conditions with the Modified Cubic B-Spline Differential Quadrature method. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, Cilt: 24 - Sayı: 6, 952–959. https://ajindex.com/articles/42268

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References (15)

  1. Buckingham E. “Studies on the Movement of Soil Moisture”. USDA Bureau of Soils, Bulletin 38, Washington, DC, 1907.
  2. Richards LA. “Capillary conduction of liquids through porous mediums”. Physics, 1(5), 318-333, 1931.
  3. Philip JR. “General method of exact solution of the concentraton-dependent diffusion equation”. Australian Journal of Physics, 13(1), 1-12, 1960.
  4. Sander GC, Parlange JY, Kuhnel V, Hogarth WL, Lockington D, O’Kane JPJ. “Exact nonlinear solution for constant flux infiltration”. Journal of Hydrology, 97(3-4), 341-346, 1988.
  5. Warrick AW, Lomen DO, Islas A. “An analytical solution to Richards' equation for a draining soil profile”. Water Resources Research, 26(2), 253-258, 1990.
  6. Parlange JY, Hogarth WL, Barry DA, Parlange MB, Haverkamp R, Ross PJ, Steenhuis TS, DiCarlo DA, Katul G. “Analytical approximation to the solutions of Richards' equation with applications to infiltration, ponding, and time compression approximation”. Advances in Water Resources, 23(2), 189-194, 1999.
  7. Chen, JM, Tan, YC, Chen, CH. “Analytical solutions of one-dimensional infiltration before and after ponding. Hydrological Processes”. 17(4), 815-822, 2003.
  8. Celia MA, Bouloutas ET, Zarba RL. “A General mass-conservative numerical solution for the unsaturated flow equation”. Water Resources Research, 26(7), 1483-1496, 1990.
  9. Clement TP, William RW, Molz FJ. “A physically based two-dimensional, finite-difference algorithm for modeling variably saturated flow”. Journal of Hydrology, 161(1-4), 71-90, 1994.
  10. Miller, CT, Williams, GA, Kelley, CT, Tocci, MD. “Robust solution of Richards' equation for non uniform porous media”. Water Resources Research, 34(10), 2599-2610, 1998.
  11. Kumar CP. “A numerical simulation model for one-dimensional ınfiltration”. Journal of Hydraulic Engineering, 4(1), 5-15, 1998.
  12. Shahraiyni HT, Ashtiani BA, “Comparison of finite difference schemes for water flow in unsaturated soils”. International Scholarly and Scientific Research & Innovation. 2(4), 226-230, 2008.
  13. Forsyth PA, Wu YS, Pruess K. “Robust numerical methods for saturated-unsaturated flow with dry initial conditions in heterogeneous media”. Advances in Water Resources, 18(1), 25-38, 1995.
  14. Bergamaschi L, Putti M. “Mixed finite element and Newton-type linearizations for the solution of Richards’ equation”. International Journal for Numerical Methods in Engineering, 45(8), 1025-1046, 1999.
  15. He X, Ren L. “An adaptive multiscale finite element method for unsaturated flow problems in heterogeneous porous Media”.