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حل تحلیلی معادله انتقال آلاینده در انواع شبکه رودخانه با لحاظ عبارت منبع گسترده | ||
تحقیقات آب و خاک ایران | ||
دوره 53، شماره 5، مرداد 1401، صفحه 1057-1077 اصل مقاله (2 M) | ||
نوع مقاله: مقاله پژوهشی | ||
شناسه دیجیتال (DOI): 10.22059/ijswr.2022.341884.669250 | ||
نویسندگان | ||
محمدجواد فردادی شیلسر؛ مهدی مظاهری* ؛ جمال محمدولی سامانی | ||
گروه مهندسی و مدیریت آب، دانشکده کشاورزی، دانشگاه تربیت مدرس، تهران، ایران | ||
چکیده | ||
در پژوهش حاضر، حل تحلیلی معادله انتقال آلودگی با لحاظ عبارت منبع گسترده و شرط اولیه، برای یک شبکه رودخانه عام در یک دامنه محدود با ضرایب ثابت بهازاء شرایط مرزی بالادست و پاییندست از نوع دیریکله با روش تبدیل لاپلاس انجام گرفت. وجود عبارت منبع و شرط اولیه، پیچیدگی محاسبات را بهلحاظ یافتن جواب خصوصی معادله دیفرانسیل معمولی دوچندان میکند. بهمنظور ارزیابی حل تحلیلی موجود، دو مثال فرضی ارائه گردید، که در هر کدام، مدلسازی بر روی دو نوع شبکه شاخهای و حلقهای با درنظر گرفتن یک منبع آلودگی گسترده انجام گرفت. دادههای ورودی برای مدلسازی هر یک از شبکههای رودخانه دلخواه شامل، مقادیر سرعت، ضریب پراکندگی، طول شاخهها، سطح مقطع جریان و غلظتهای ورودی از مرزها و منبع گسترده میباشد. با محاسبه ماتریسهای انتشار و بیلان جرم لاپلاسگرفته شده (با تاثیر منبع گسترده در آن) در شبکه رودخانه براساس ماتریس نحوه اتصال و ماتریس دادهها، یک دستگاه معادلات غیرخطیای برحسب متغیر s لاپلاس ایجاد میشود، که با حل آن، ماتریس غلظت آلودگی و بهتبع آن غلظت آلودگی در هر گره با الگوریتم لاپلاسگیری وارون عددی محاسبه میشود. بهمنظور اعتبارسنجی حل تحلیلی پیشنهادی از حل عددی استفاده شد. نتایج نشان داد که شاخصهای آماری R2، جذر میانگین مربع خطاها و میانگین خطای مطلق در بهترین حالت بهترتیب 86/99%، 0099/0 و 0067/0 کیلوگرم برمترمکعب برای مسیر 1456 و در بدترین حالت بهترتیب 20/95%، 0309/0 و 0194/0 کیلوگرم برمترمکعب برای مسیر 23456 شبکه حلقهای بوده و دو حل مذکور انطباق خوبی با یکدیگر داشته و نشاندهنده عملکرد مطلوب حل تحلیلی موجود و جایگزینی آن بهجای حل عددی بهدلیل دقت بالاتر در شبکه رودخانه میباشد. | ||
کلیدواژهها | ||
تابع توزیع غلظت؛ روش تبدیل لاپلاس؛ ضرایب ثابت؛ مدلسازی ریاضی؛ معادله جابهجایی-پراکندگی-واکنش-منبع | ||
مراجع | ||
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