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

Yıl 2018, Cilt: 24 Sayı: 6, 952 - 959, 18.12.2018

Emin Çiftçi

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

Öz

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. 

Anahtar Kelimeler

Richards equation, Differential quadrature, Modified cubic b-spline

Kaynakça

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