مسئله اندرکنش سیال-سازه در چهارچوب توصیف لاگرانژی-اویلری دلخواه با استفاده از رویکرد یکپارچه در حالت دوبعدی

نوع مقاله : طرح پژوهشی

نویسندگان

1 دانشجوی کارشناسی ارشد، دانشکدگان فنی، دانشکده مهندسی عمران، دانشگاه تهران، تهران، ایران

2 استاد، دانشکدگان فنی، دانشکده مهندسی عمران، دانشگاه تهران، تهران، ایران

10.22044/jsfm.2025.14062.3829

چکیده

روش تقسیم‌بندی‌شده برای حل مسائل اندرکنش سیال-سازه مستعد بروز ناپایداری‌های عددی هستند که می‌توانند منجر به عدم همگرایی در فرایند حل شوند. برای غلبه بر این چالش‌ها، استفاده از تکنیک‌های پایدارسازی و کاهش گام زمانی ضروری است. با این حال، این رویکردها به طور قابل توجهی هزینه‌های محاسباتی را افزایش می‌دهد. در این پژوهش به منظور تحلیل مسائل اندرکنش سیال-سازه فرمول‌بندی یکپارچه‌ای در چهارچوب توصیف لاگرانژی-اویلری دلخواه به‌منظور ردیابی مرزهای متحرک ارائه شده است. بدین منظور، معادلات ناویه-استوکس در حالت ناپایدار برای سیال و معادله الاستیسیته خطی برای سازه به‌صورت یکپارچه با جفت‌سازی قوی حل شده‌اند. با مقایسه عملکرد رویکرد پیشنهادی با روش تقسیم‌بندی‌شده مشخص گردید که میانگین زمان تحلیل هر گام در روش تقسیم‌بندی‌شده 51 ثانیه و در روش پیشنهادی 7 ثانیه به‌طول انجامید، که بیانگر برتری رویکرد ارائه شده در کاهش زمان محاسبات می-باشد. رویکرد ارائه شده با حذف اثرات جرم افزوده دقت حل را افزایش داده و از نوسانات ناگهانی موجود در رویکرد تقسیم‌بندی شده جلوگیری می‌نماید. همچنین با بررسی اثر وابستگی مش مشخص گردید افزایش تعداد درجات آزادی از 85452 به 1141027، باعث افزایش تنها دو درصدی فشار و جابجایی می‌شود که نشان‌دهنده وابستگی ناچیز حل مسئله به اندازه مش است.

کلیدواژه‌ها

موضوعات


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