کاربرد مدل ریاضی در پدافند غیرعامل زیستی: شبیه‌سازی جریان آلاینده در آب‌های زیرزمینی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشیار گروه مهندسی عمران، دانشکده فنی و مهندسی، دانشگاه محقق اردبیلی، اردبیل، ایران

2 دکتری تخصصی ریاضیات کاربردی، دانشکده علوم ریاضی، گروه ریاضیات و کاربردها، دانشگاه محقق اردبیلی، اردبیل، ایران

چکیده

آلودگی منابع آبی یکی از چالش‌های مهم و اساسی زندگی انسان و رفاه همه موجودات زنده است. وجود شکاف‌های مدیریتی در این منطقه حیاتی، آسیب‌پذیری‌هایی را برای حملات بالقوه بیوتروریستی و آلودگی منابع آب ایجاد می‌کند. یک رویکرد ضروری و عملی برای مدیریت منابع آب زیرزمینی، به ویژه در شناسایی زمان و مکان انتشار آلاینده‌ها در آب، شامل استفاده از مدل‌های ریاضی حاکم بر جریان آلاینده است. در مقایسه با سایر روش های عملی، مدل‌سازی ریاضی راه حل قابل اعتماد و مقرون به صرفه‌ای را ارائه می‌دهد که از نظر محاسباتی امکان پذیر است. هدف اصلی این تحقیق شبیه‌سازی تابع شدت آلاینده اولیه (در t=0) از طریق یک مسئله معکوس ریاضی در زمان معکوس است. این موضوع به عنوان یکی از مهمترین چالش‌ها در مدیریت و مهندسی منابع آب می‌باشد که توجه محققین را به خود جلب کرده است. در این تحقیق، ابتدا یک مدل ریاضی از جریان آلاینده در آب‌های زیرزمینی ارائه می‌شود، که در آن تابع شدت آلاینده اولیه مجهول است. سپس، یک روش عددی جدید بر اساس روش شبه جواب (pseodu-solution method)، تقریبی برای این تابع با استفاده از ترکیب خطی چند جمله‌ای‌های برنشتاین محاسبه می‌شود. مدل‌ ریاضی با یک مثال بصورت عددی تحلیل و بررسی می‌شود. نتایج عددی بدست آمده نشان می‌دهد که با استفاده تابع شدت آلاینده در هرلحظه t>0، می‌توان تابع شدت آلاینده اولیه را با دقت بالا شبیه‌سازی کرد. برای سطح خطای δ=0.01 در داده‌های ورودی، جواب تقریبی به دست آمده از طریق روش عددی معرفی شده، حداکثر خطای 4 درصد را نشان می‌دهد.

کلیدواژه‌ها


عنوان مقاله [English]

Application of Mathematical Model in Biological Passive Defense: Simulation of Pollution Flow in Groundwater

نویسندگان [English]

  • Houshyar Eimani kalehsar 1
  • Younes Talaei 2
1 Civil Engineering Department, Engineering Faculty, University of Mohaghegh Ardabili, Ardabil, Iran
2 Department of Mathematics and Applications, University of Mohaghegh Ardabili, Ardabil, Iran
چکیده [English]

Pollution of water resources poses a significant and fundamental challenge to human life and the well-being of all living organisms. The presence of management gaps in this critical area creates vulnerabilities for potential bioterrorist attacks and contamination of water sources. An essential and practical approach to managing groundwater resources, particularly in identifying the time and location of pollutant releases into water, involves the utilization of mathematical models    governing pollutant flow. Compared to other practical methods, mathematical modeling offers a reliable and cost-effective solution that is computationally feasible. The primary objective of this research is to simulate the initial pollutant intensity function (at t=0) through a mathematical backward in time inverse problem. This issue stands as one of the foremost challenges in water resources management and engineering, garnering significant attention from researchers. In this study, initially, a mathematical model of pollutant flow in groundwater is presented, where the  initial pollutant intensity function is unknown. Then, a new numerical method based on the      pseudo-solution method is employed to calculate an approximation for this function using a linear combination of Bernstein polynomials. The mathematical model is numerically analyzed and   scrutinized through a specific example. The numerical results indicate that the initial pollutant intensity function can be precisely simulated by utilizing the pollutant intensity function at any time t>0. For an error level of δ=0.01 in the input data, the approximate solution obtained through the introduced numerical method exhibits a maximum error of 4%.
 

کلیدواژه‌ها [English]

  • Groundwater Pollution
  • Simulation of Intensity Pollution Function
  • Inverse Problem
  • Passive Defense

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