مقایسه عملکرد ماتریس‌های پیش‌شرطی در گستره‌ی وسیعی از جریان‌های داخلی و خارجی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشکده مهندسی دانشگاه فردوسی مشهد / مشهد / ایران

2 دانشگاه فردوسی مشهد/ مشهد/ ایران

3 دانشگاه فردوسی مشهد/مشهد/ایران

چکیده

در این پژوهش ابتدا با توجه به ماتریس ژاکوبین پیش‌شرطی برحسب متغیرهای بقایی، بردارهای ویژه، مقادیر ویژه و مقادیر مشخصه به‌صورت یکپارچه برای سه روش ترکل، چوی-مرکل و اریکسون استخراج می‌گردد. بدین‌منظور این روش‌‌های پیش‌شرطی در یک الگوریتم چگالی‌مبنا دو بعدی با روش بالادستی "رو" و یک شبکه بی‌سازمان برای معادلات اولر توسعه داده می‌شود. دقت و نرخ همگرایی این روش‌های پیش‌شرطی برای جریان‌های خارجی حول ایرفویل NACA0012 ، ایرفویل سه المانه 30P-30N و جریان داخل کانال با برامدگی در شرایط مختلف جریان مورد بررسی قرار می‌گیرد. این پژوهش نشان می‌دهد که استفاده از روش‌های پیش‌شرطی نه‌تنها نرخ همگرایی را برای جریان قابل و غیر قابل تراکم افزایش میدهند; بلکه دقت حل را برای جریان تراکم‌ناپذیر را نیز نسبت به روش کلاسیک به‌طور چشمگیر بهبود می‌دهد. همچنین مقایسه روش‌های پیش‌شرطی نشان می‌دهد که هر سه روش از نظر دقت، جواب‌های تقریبا یکسانی را ارائه می‌دهند. اما از نظر نرخ همگرایی، روش پیش‌شرطی ترکل نرخ همگرایی بهتری را ارایه می‌دهد.

کلیدواژه‌ها


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