مدل سازي سطح آب در آبخوان بين دو كانال با استفاده از روش Differential Quadrature

Modeling Water Table Rise Between Two Canal In Aquifer with Differential Quadrature Method.

تعيين موقعيت هندسي سطح آب در پروژه‌ها و زمين‌هاي كشاورزي از ديرباز مورد توجه ويژه محققين و مهندسين بوده است. اين امر معمولاً با ساده‌سازي معادلات حاكم بر جريان در محيط متخلخل و حل تحليلي آنها و يا با بكاربردن روش‌هاي عددي مانند تفاضلات محدود و حل معادله ديفرانسيل غيرخطي بوزينسك انجام شده است. در اين تحقيق از روش عددي Differential Quadrature كه در ساير زمينه‌هاي علمي مانند مكانيك جامدات توسعه يافته، جهت تعيين عمق سطح ايستابي بين دو كانال آبياري موازي در يك آبخوان با كف ناتراوا (مسطح و شيبدار) در حضور و عدم حضور تغذيه سطحي بكار رفته است. سپس نتايج حاصل از آن با نتايج حل تحليلي و حل عددي به روش تفاضالات محدود مقايسه شده كه نتايج رضايت بخشي از اين قياس بدست آمده است. از مزاياي اين روش، تعداد به‌مراتب كمتر گره‌هاي شبكه بدون از دست دادن دقت مسئله و در نتيجه كاهش زمان محاسبات و هزينه مي‌باشد.

In many of agricultural land water table is raised because of seepage from canal and surface recharge. This raised is gradually caused some problem appear in land such as waterlogging and salinity, ultimately leading to land degradation. Therefore development of agriculture and economics in that region are endangered. It is necessary before problems appear engineers and researchers consider the variation of the groundwater table.In this article that problem has selected which shows an aquifer lied on a slopping impervious barrier which is discharged by a constant discharge from the surface and two canals with (L) horizontal distance. The initial water table is located horizontally h0 above the either horizontal or slopping bottom. After recharge and canal commencement, water table starts to rise. The rate of rising depends on the rate and duration of recharge and seepage from canal.In this article, application of DQM in discretization of governing equations for chosen case study and formulation of the problem is presented. For further comparison and find more reliable answer are used three method for discretization of governing equation:1Explicit Scheme,2Implicit Scheme,3Semi Implicit Crank Nicholson Scheme.This investigation confirm that DQM has vast capability and simplicity to produce accurate results which is satisfactory compatible with Finite Difference numerical model as well as whit analytical solution while is highly efficient in time and low cost of running. The discretization scheme in this method does not establish large sets of simultaneous equation to be solved and is not sensitive to the number of grids in its mesh. There for with a very small number of grids comparing to a very large number of required grids in Finite Difference scheme produce very accurate results close to analytical solution results and create exactly the same results as Finite Difference scheme produce.