شبیه سازی مسئله شکستن سد بر روی بستر فرسایش پذیر با استفاده از روش بدون شبکه حداقل مربعات گسسته شده با نقاط همگام
محورهای موضوعی : مقالات برگرفته از پایان نامه
بابک فضلی مالیدره
1
(دانشکده فنی و مهندسی، گروه مهندسی آب، دانشگاه آزاد اسلامی واحد علوم و تحقیقات تهران، ایران)
سید عباس حسینی
2
(دانشکده فنی و مهندسی، گروه مهندسی آب، دانشگاه آزاد اسلامی واحد علوم و تحقیقات تهران، ایران)
کلید واژه: رسوب, روش بدون شبکه, شکست سد, حداقل مربعات, بسترمتحرک,
چکیده مقاله :
روشهای بدون شبکه طی دهه های اخیر به مجموعه روشهای عددی اضافه شده، و بستر مناسب و وسیعی را در زمینه های علمی، تحقیقاتی و مهندسی فراهم آورده‌اند. استفاده از روشهای بدون شبکه هنوز به گستردگی روشهای اجزاء محدود در مسائل مهندسی نمی‌باشد ولی چه بسا فعلاً این روشها شرایطی را مشابه با زمانی که روش اجزاء محدود شروع به گسترش نمود سپری می نمایند. در این تحقیق، روش بدون شبکه حداقل مربعات گسسته شده با نقاط همگام که اصطلاحاً (CDLSM) نام گرفته است، پیشنهاد گردیده و مفاهیم، روابط ریاضی و تنظیم مربوط به این روش به طور کامل ارائه گردیده اند. در این شبیه سازی نقاط همگام جهت کارائی بیشتر و زمان محاسبات پائین‌تر با استفاده از روش حداقل مربعات، و نیز استفاده از گروه به جای انتگرال (حالت گسسته) به کار برده شده است. بر اساس روش مذکور پدیده شکست آنی سد در حالات مختلف حل و جهت صحت سنجی آن نیز با مقایسه حل حاصل با حل تحلیلی مسائل آزمایشی معیار، و نیز داده‌های آزمایشگاهی موجود استفاده گردیده است. مقایسه بین نتایج عددی با داده های تحلیلی و آزمایشگاهی موجود، نشان می دهد که روش مزبور علاوه بر کارائی بالا، مباحث مربوط به تکانه یا ناپیوستگی را به‌خوبی شبیه سازی می نماید.
Meshless methods have been added to numerical methods in recent decades, and have provided a wide range of scientific, research and engineering fields. The use of Meshless methods is still not extent to the finite element methods in engineering issues, but these methods may now be similar to those of the time when the finite element method begins to expand. In this research, a discrete least square meshless method with collocation points CDLSM is proposed. The concepts, mathematical relations, and formulation of this method are fully presented. In this simulation, collocation points are used for more efficiency and lower computing time by using least squares method, as well as using the series instead of integrals (discrete mode). Based on this method, the dam failure phenomenon has been solved in different cases and its verification has been used by comparison with analytical solution with experimental data whenever it is available. Comparison of numerical results with existing analytical and experimental data shows that the method has high efficiency and simulates the shock or discontinuity.
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