مدل‌سازی و تحلیل عددی جریان تحت شرایط آبیاری جویچه‌ای

نوع مقاله: مقاله پژوهشی

نویسندگان

1 دانش‌آموخته کارشناسی ارشد آبیاری و زهکشی، دانشگاه علوم کشاورزی و منابع طبیعی، ساری، ایران

2 استادیار گروه مهندسی آب دانشگاه علوم کشاورزی و منابع طبیعی، ساری، ایران

3 استاد گروه مهندسی آب دانشگاه علوم کشاورزی و منابع طبیعی، ساری، ایران

4 مدرس گروه ریاضی دانشگاه پیام نور مازندران، ایران

چکیده

به منظور شبیه­سازی توام جریانات کم عمق روی سطح خاک و نفوذ به درون آن، معادلات سنت- ونانت بسط داده شد. با توجه به عدم وجود راه حل تحلیلی جهت حل این نوع معادلات، از این رو محققین جهت حل این مسائل روش­های عددی را پیشنهاد می­کنند. در تحقیق حاضر از بین مدل­های هیدرولیکی آبیاری سطحی مدل هیدرودینامیک کامل به دلیل شبیه­سازی دقیق جریان و از بین روش­های عددی دو الگوی عددی شامل خطوط مشخصه (HD-CH) و صریح لکس انتشاری (HD-LAX) برای گسسته­سازی معادلات حاکم بر آبیاری سطحی استفاده و در ادامه برنامه­ای کامپیوتری به کمک زبان برنامه­نویسی متلب تهیه شد. جهت ارزیابی روش­های عددی از چهار سری داده­های جویچه­ای استفاده شد، که این داده­ها از طریق آزمایش در مزرعه مورد اندازه­گیری قرار گرفت. هم­چنین روش پیشنهادی در شرایط یکسان با مدل هیدرودینامیک نرم­افزارهای SIRMOD و SRFR مورد مقایسه و اعتبار­سنجی قرار گرفت. یافته­ها نشان داد که هر دو الگوی عددی در شرایط جویچه­ای با دقت مناسبی فرآیندهای مختلف جریان را شبیه­سازی می­کنند. با این حال نتایج شاخص­های ارزیابی نشان می­دهد مدل  HD-LAXبه واسطه روش حل دارای دقت مرتبه دوم است، و با متوسط ضریب تبیین، آماره­ی خطا و کارایی مدل (834/0، 36/1، 91/0و 815/0، 43/1، 88/0) به­ترتیب برای مرحله پیشروی و پسروی و خطای نسبی (44/7- و 8/19) درصد در برآورد حجم آب نفوذ یافته و رواناب، هم­چنین زمان محاسباتی کم­تر جهت شبیه­سازی فرآیندهای مختلف جریان جویچه­ای از دقت بالاتری نسبت به روش HD-CH برخوردار است. نتایج بررسی محاسباتی توسط روش پیشنهادی HD-LAX در مقایسه با روش­های HD-SIRMOD و HD-SRFR نشان داد که در مرحله پیشروی روش پیشنهادی و مدل HD-SIRMOD اختلاف معنی­داری ندارند در حالی که مدل HD-SRFR در سطح یک درصد با مقادیر مشاهده­ای دارای اختلاف می­باشد.

کلیدواژه‌ها


عنوان مقاله [English]

Modelling and Numerical Analysis of Flow under Furrow Irrigation

نویسندگان [English]

  • Ali Koulaian 1
  • Mohammad Ali Gholami Sefidkouhi 2
  • Mirkhalegh Ziatabar Ahmadi 3
  • Hossein Dadashzadeh 4
1 M.S. Graduated of Irrigation and Drainage, University of Sari Agricultural Sciences and Natural Resources., Sari., Iran
2 Assistant Professor, Water Engineering Department, University of Sari Agricultural Sciences and Natural Resources., Sari., Iran
3 Professor, Water Engineering Department, University of Sari Agricultural Sciences and Natural Resources., Sari., Iran
4 Department of Mathematics, Payame Noor University of Mazandran., Iran
چکیده [English]

In order to simulate shallow flowson the soil surface and penetration into the depth, the Saint-Venant equations were developed. Due to the lack of analytical solutionfor solving these types of equations, researchers generally suggest numerical methods as a solution.In the present study, from the hydraulic models of surface irrigation, the full hydrodynamic model due to its accurate simulation of the flow, and from the numerical methods, two numerical models, includingthe characteristic line method (HD-CH) and the explicit diffusiveLAXmethod (HD-LAX), were used to discretize the governing equations of surface irrigation. Afterwards, a computer program was developed using MATLAB programming language.In order to evaluate the numerical methods, four furrow data series were used, which were measured through testing in the farm. In addition, under the same conditions, the proposed method was compared with the hydrodynamic model of SIRMOD and SRFR softwares and was consequently validated. The perceived results revealedthat both numerical models simulate various flow processes under furrow conditionsatan acceptable accuracy.However, the results of the evaluation indicators demonstrated that the HD-LAX model, due to the solution method of the second degree of accuracy, withthe average coefficient of determination, error statistics, and model efficiency of (0.834, 1.36, 0.91) and (0.815 , 1.43, 0.88), respectively forthe forward and backward stages, and with the relative errors of 7.44 % and 19.8 %, has a higher accuracy than the HD-CH model,in estimating the volume of water infiltration and runoff, and it also needsless computational time for simulating different furrow flow processes.The results of calculations, through comparing the proposed HD-LAX method with the HD-SIRMOD and HD-SRFR methods, showed thatin the forward stage, the proposed method and the HD-SIRMOD model do not have any significant difference,while the HD-SRFR model, at the confidence level of 1%,has some differences with the observed values.

کلیدواژه‌ها [English]

  • Furrow irrigation
  • Full Hydrodynamics
  • LAX
  • Method of Characteristics
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