# شبیه‌سازی عددی شکست سد با روش اجزاء محدود و المان‌های غیرخطی یک‌بعدی، بررسی موردی سد ارداک

نویسندگان

چکیده

در این پژوهش ابتدا معادله‌های آب‌های کم‌عمق تشریح شده و برای کاربرد مدل عددی اجزاء محدود،‏ معادله‌های حاکم به روش ریلی‌ریتز گسسته‌سازی و ماتریس سختی جزء و کل محاسبه شده است. با حل دستگاه معادله‌های حاکم به روش‌ غیر‌صریح،‏ عمق و سرعت جریان در طول کانال و در زمان‌های مختلف به‌ دست آمده است. مدل عددی با المان‌های سه،‏ پنج و هفت گرهی با نتایج عددی سایر پژوهش‌گران صحت‌سنجی و هماهنگی مناسبی مشاهده شد. از نتایج این پژوهش آن است که به‌دلیل استفاده از المان‌های غیر‌خطی،‏ اغتشاش‌های حاصل از حل غیر‌صریح به طور مؤثری نسبت به مدل‌های خطی کاهش یافته است. بعد از اطمینان از عملکرد صحیح مدل اجزاء محدود،‏ شکست سد ارداک مشهد به‌عنوان بررسی موردی آورده شده است. در این بررسی از سه زبری معادل (لوتر،‏ پاولوفسکی و هورتون) برای مدل‌سازی عددی پدیده شکست سد و محاسبه عمق و سرعت آب در زمان و مکان‌های مختلف در طول رودخانه،‏ استفاده شد. در طول مسیر پایین‌دست حداکثر عمق متوسط در پایین‌دست 78‎/24 متر با زبری معادل پاولوفسکی بوده و حداکثر سرعت نیز 05‎/15 متر بر ثانیه با زبری معادل لوتر در زمان 100 ثانیه است.

کلیدواژه‌ها

عنوان مقاله [English]

### Numerical Simulation of Dam Break Using Finite Element Method and 1D Non-linear Elements (Case Study: Ardak Dam)

نویسندگان [English]

• reza karimi
• Ali akhtari
چکیده [English]

In this research, the shallow-water equations are described and the governing equations are discretized using Rayleigh–Ritz method in order to assemble the required local and global stiffness matrices. The depths and the velocities of fluid flow throughout the channel and at different times are acquired by solving the governing equations using non-explicit methods. The obtained results from the numerical model with three, five and seven node elements were compared to the pre-existing results of other researchers, and it was observed that they are in a reasonably good agreement. It was concluded that employing the non-linear elements, oscillations induced by using linear models can be efficiently reduced. Subsequently, the model was utilized to investigate Ardak dam-break as a case study. In this study, three equivalent-roughnesses (Horton, Lotter and Paw?owski) were used for the numerical simulation of the flow induced by dam-break and to calculate water depths and velocities at different times and places through the river. The maximum average-depth throughout the river was 24.78m with using Paw?owski roughness, and the maximum average-velocity was calculated 15.05m/s by using Lotter roughness at t=100s.In this research, the shallow-water equations are described and the governing equations are discretized using Rayleigh–Ritz method in order to assemble the required local and global stiffness matrices. The depths and the velocities of fluid flow throughout the channel and at different times are acquired by solving the governing equations using non-explicit methods. The obtained results from the numerical model with three, five and seven node elements were compared to the pre-existing results of other researchers, and it was observed that they are in a reasonably good agreement. It was concluded that employing the non-linear elements, oscillations induced by using linear models can be efficiently reduced. Subsequently, the model was utilized to investigate Ardak dam-break as a case study. In this study, three equivalent-roughnesses (Horton, Lotter and Paw?owski) were used for the numerical simulation of the flow induced by dam-break and to calculate water depths and velocities at different times and places through the river. The maximum average-depth throughout the river was 24.78m with using Paw?owski roughness, and the maximum average-velocity was calculated 15.05m/s by using Lotter roughness at t=100s.In this research, the shallow-water equations are described and the governing equations are discretized using Rayleigh–Ritz method in order to assemble the required local and global stiffness matrices. The depths and the velocities of fluid flow throughout the channel and at different times are acquired by solving the governing equations using non-explicit methods. The obtained results from the numerical model with three, five and seven node elements were compared to the pre-existing results of other researchers, and it was observed that they are in a reasonably good agreement. It was concluded that employing the non-linear elements, oscillations induced by using linear models can be efficiently reduced. Subsequently, the model was utilized to investigate Ardak dam-break as a case study. In this study, three equivalent-roughnesses (Horton, Lotter and Paw?owski) were used for the numerical simulation of the flow induced by dam-break and to calculate water depths and velocities at different times and places through the river. The maximum average-depth throughout the river was 24.78m with using Paw?owski roughness, and the maximum average-velocity was calculated 15.05m/s by using Lotter roughness at t=100s.In this research, the shallow-water equations are described and the governing equations are discretized using Rayleigh–Ritz method in order to assemble the required local and global stiffness matrices. The depths and the velocities of fluid flow throughout the channel and at different times are acquired by solving the governing equations using non-explicit methods. The obtained results from the numerical model with three, five and seven node elements were compared to the pre-existing results of other researchers, and it was observed that they are in a reasonably good agreement. It was concluded that employing the non-linear elements, oscillations induced by using linear models can be efficiently reduced. Subsequently, the model was utilized to investigate Ardak dam-break as a case study. In this study, three equivalent-roughnesses (Horton, Lotter and Paw?owski) were used for the numerical simulation of the flow induced by dam-break and to calculate water depths and velocities at different times and places through the river. The maximum average-depth throughout the river was 24.78m with using Paw?owski roughness, and the maximum average-velocity was calculated 15.05m/s by using Lotter roughness at t=100s.

کلیدواژه‌ها [English]

• Ardak dam.-Finite Element-nonlinear element-Dam break-Numerical model-