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

Öz

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.

Anahtar Kelimeler

• Richards denklemi,Diferansiyel kuadratur,Modifiye kübik b-spline

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

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 4^th 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. 

Keywords

• Richards equation,Differential quadrature,Modified cubic b-spline

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