Abstract




 
   

IJE TRANSACTIONS A: Basics Vol. 28, No. 4 (April 2015) 490-498   

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  SELECTION OF INTERMODAL CONDUCTIVITY AVERAGING SCHEME FOR UNSATURATED FLOW IN HOMOGENEOUS MEDIA
 
M. Sayful Islam
 
( Received: November 08, 2014 – Accepted: March 13, 2015 )
 
 

Abstract    The nonlinear solvers in numerical solution of water flow in variably saturated soils are prone to convergence difficulties. Many aspects can give rise to such difficulties, like very dry initial conditions, a steep pressure gradient and great variation of hydraulic conductivity occur across the wetting front during the infiltration of water. So, the averaging method applied to compute hydraulic conductivity between two adjacent nodes of the computational grid is one of the most important issues influencing the accuracy of the numerical solution of one-dimensional unsaturated flow equation i.e., Richards’ equation. A number of averaging schemes such as arithmetic, geometric, harmonic and arithmetic mean saturation have been proposed in the literature for homogeneous soil. The resulting numerical schemes are evaluated in terms of accuracy and computational time. It can be seen that the averaging scheme in the framework of arithmetic approach favorably to other methods for a range of test cases.

 

Keywords    Richards’ equation, Variably saturated flow, Internodal conductivity, Infiltration. Finite difference.

 

چکیده    روشهای حل غیر خطی برای حل عددی جریان آب در خاکهای اشباع شده احتمالا با مشکلات متعددی همراه است. عوامل مختلفی می توانند باعث افزایش این مشکلات شوند که از جمله آنها شرایط اولیه بسیار خشک است که موجب گرادیان فشار با شیب زیاد و تغییرات شدید هدایت هیدرولیکی در قسمت مرطوب در طی نفوذ آب می شود. بنابراین، روش متوسط گیری که برای محاسبه هدایت هیدرولیکی بین دو نقطه مجاور در آرایه محاسباتی استفاده می شود یکی از مسائل مهمی است که روی دقت حل عددی معادلات جریان غیر اشباع تک-بعدی مانند معادله ریچارد تاثیر می گذارد. الگوهای متوسط گیری مختلفی از جمله آریتمیک، ژئومتریک، هارمونیک و اشباع متوسط آریتمیک در متون برای خاکهای همگن ارائه شده است. الگوهای عددی به دست آمده از لحاظ دقت و زمان محاسبه مورد بررسی قرار می گیرند. ملاحظه می شود که الگوی متوسط گیری در چارچوب روش اریتمیک برای تعدادی از موارد بررسی شده به طور مطلوبی به روشهای دیگر نزدیک است.

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