حل معکوس (در زمان) معادله انتقال آلودگی در رودخانه با استفاده از طرح حافظ گروه

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه مهندسی و مدیریت آب، دانشکده کشاورزی، دانشگاه تربیت مدرس، تهران، ایران

2 گروه مهندسی و مدیریت آب، دانشکده کشاورزی، دانشگاه تربیت مدرس، تهران، ایران.

چکیده

  امروزه بسیاری از منابع آب­های سطحی و زیرزمینی در اثر ورود پساب­های ناشی از مواد مختلف در معرض آلودگی قرار می­گیرند. با توجه به اینکه اکثر روش­ها جهت بازیابی تابع شدت آلودگی برای آب­های زیرزمینی انجام ‌گرفته است، ارائه روشی جهت بازیابی تابع شدت آلاینده در رودخانه­ها با شرایط جریان پیچیده­تر می­تواند مورد توجه قرار گیرد. در این پژوهش هدف محاسبه تابع شدت منبع آلاینده بوده که بر اساس تحقیقات صورت گرفته تاکنون این مسئله با استفاده از راه‌حل عددی طرح حافظ گروه مورد مطالعه قرار نگرفته است. طرح حافظ گروه روشی دقیق برای حل مسائل بدخیم است که در این نوشتار با استفاده از این روش، معادله یک‌بعدی جابه­جایی-پراکندگی با ضرایب متغیر حل‌ شده است. اساس روش حل معکوس ارائه ‌شده به این صورت است که با حل سیستم­های دینامیکی در گام‌های زمان­های منفی، یک معادله کلی حاصل می­شود که قادر به حل معادلات دیفرانسیل معمولی خواهد بود. پاسخ­های برگشتی این معادله را به همگرایی لازم می­رساند و از واگرا شدن داده­ها جلوگیری می­نماید. در این پژوهش سه مثال جهت نشان دادن دقت طرح مستقیم و معکوس حافظ گروه ارائه‌ شده است. ابتدا با استفاده از حل مستقیم مقدار غلظت آلاینده در رودخانه با ضرایب متغیر محاسبه ‌شده است و به‌منظور صحت­سنجی حل مستقیم از حل عددی تمام ضمنی تفاضل محدود استفاده‌ شده است. مقایسه نتایج این دو روش با شاخص­های آماری، انطباق این دو مدل در روش مستقیم را نشان می­دهد. در گام بعد با دو مثال مختلف با استفاده از حل طرح معکوس حافظ گروه به شبیه‌سازی تابع شدت آلاینده در بالادست رودخانه پرداخته می­شود و پس از شبیه­سازی و صحت­سنجی مدل معکوس با حل مستقیم، ارزیابی این روش با استفاده از شاخص­های آماری انجام می­شود که نتایج دقت خوب این روش را نشان می­دهد.
 

کلیدواژه‌ها


عنوان مقاله [English]

Backward Solution (in-time) of the Pollution Transport Equation in River Using Group Preserving Scheme

نویسندگان [English]

  • Amir mohammad Saadat 1
  • Mehdi Mazaheri 2
  • Jamal MV Samani 1
1 Department of Water Engineering and Management, Faculty of Agriculture, Tarbiat Modares University, Tehran, Iran
2 Department of Water Engineering and Management, Faculty of Agriculture, Tarbiat Modares University, Tehran, Iran.
چکیده [English]

Today, most of the surface water and groundwater resources are exposed to contamination by different materials sewage. because most of the methods have been used to restore the pollution intensity function for groundwater, representing a method to restore pollution intensity function in rivers with more complex flow conditions is considerable. this research aim is to calculate the intensity function of the contamination source, by the numerical solution of group preserving scheme, which has not been observed in other researches done so far. Group preserving scheme is an accurate method to solve ill-posed problems. By implementing this method the one-dimensional advection-dispersion equation with variable coefficients has been solved. The principle of the introduced backward solution method is that by solving the dynamic systems in negative time steps, a general equation will be obtained, which can solve ordinary differential equations. The responses of this equation will lead to convergence of the equation and prevent the divergence of the data. three examples have been presented to show the accuracy of the forward and backward group preserving scheme, Firstly, using direct solutions of the river, the intensity of pollution concentration in the river is calculated, and the implicit finite difference method is applied to verify the accuracy of the direct solutions. In the direct method, the results of the two models were compared with statistical indexes in order to demonstrate the conformity of the two models. In the next step, by solving the backward group preserving scheme in two different examples, the concentration of pollutants upstream is simulated. Following the simulation and verification of the inverse model by direct solution, statistical indexes are used to evaluate the effectiveness of this method.

کلیدواژه‌ها [English]

  • Numerical Solution
  • Reverse Method
  • Backward Group Preserving Scheme
  • Advection-dispersion Equation
  • Numerical Method of Lines
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