مهندسی مکانیک مدرس

مهندسی مکانیک مدرس

افزایش پایداری عددی روش شبکه بولتزمن در شبیه سازی جریان های تراکم ناپذیر با اعداد رینولدز بالاتر

نوع مقاله : پژوهشی اصیل

نویسندگان
محمد رضا صارمی طهرانی 1
محسن قدیانی 1
ولی انجیل الی 2
1 دانشگاه آزاد اسلامی، واحد یادگار امام خمینی (ره)
2 دانشگاه آزاد اسلامی، واحد کرج
10.22034/MME.24.3.177
چکیده
در این مطالعه، از یک طرح جدید پادبادسو برای حل معادله پیوسته بولتزمن و توسعه کاربرد آن در حل موثر جریان­های تراکم­ناپذیر استفاده شده ‌است. مشتق زمانی در معادله بولتزمن با استفاده از طرح تفاضلات محدود پیشرو مرتبه اول و مشتق‌های مکانی آن بوسیله این طرح جدید گسسته­سازی شده­اند. علاوه بر این، اثرات ترکیبی مکانیزم تفاضل پادبادسو به همراه روش تفاضلات محدود برای بهبود پایداری روش شبکه بولتزمن استاندارد در حل مسائل با اعداد رینولدز بالا ارائه شده است. برای تایید اعتبار روش شبکه بولتزمن مبتنی بر طرح جدید پادبادسو، یک مساله ناپایا که حل تحلیلی دارد و دو مساله تراکم‎ناپذیر پایا که حل تحلیلی ندارند به صورت عددی حل شده­اند. مساله معیار اول، مساله انتقال حرارت هدایتی روی یک میله و دو مساله دیگر شامل جریان سیال روی یک صفحه تخت و جریان حفره با درپوش متحرک است. به منظور بررسی دقت و پایداری عددی روش شبکه بولتزمن مبتنی بر طرح جدید پادبادسو نتایج حاصل با روش شبکه بولتزمن استاندارد و روش شبکه بولتزمن تفاضلات محدود مقایسه شده است. روش حاضر تضمین می‌کند که بدون اعمال روش فیلترینگ، نتایج پایدارتر و دقیق‌تری نسبت­ به روش شبکه بولتزمن تفاضلات محدود به‌دست می­آید. نتایج شبیه‌سازی، کارایی روش شبکه بولتزمن مبتنی بر طرح جدید پادبادسو و تطابق مناسب آن را با حل­های تحلیلی و سایر روش­های عددی نشان­ می­دهد.
کلیدواژه‌ها
جریان تراکم ناپذیر
روش شبکه بولتزمن استاندارد
روش شبکه بولتزمن مبتنی بر تفاضلات محدود
پایداری عددی
طرح پادبادسو

موضوعات

عنوان مقاله English

Numerical Stability Enhancement of Lattice Boltzmann Method in The Simulation of Incompressible Flows with Higher Reynolds Numbers

نویسندگان English

Mohammad Reza Saremi Tehrani 1
Mohsen Ghadyani 1
Vali Enjilela 2
1 Islamic Azad University, Yadegar-e-Imam Khomeini (RAH) Shahre Rey Branch
2 Islamic Azad University, Karaj Branch
چکیده English

In this study, a new upwind scheme has been used to solve the continuous Boltzmann equation and to develop its application in the effective solution of incompressible flows. Time derivative in the Boltzmann equation has been discretized using the first-order forward finite difference scheme. The spatial derivatives in the Boltzmann equation have been discretized using this new scheme. Further, the combined effects of the upwind differential mechanism along with the finite difference method are presented to enhancement the stability of the standard lattice Boltzmann method in solving problems with high Reynolds numbers. To confirm the validation of the proposed method, one unsteady problem, this has an analytical solution, and two incompressible steady problems which have not analytical solutions, have been solved numerically. The first benchmark problem is the conductive heat transfer on a slab and two last problems are flow over a flat plate and flow in a lid-driven cavity. In order to check the numerical accuracy and stability of the proposed method, the results have been compared with the standard lattice Boltzmann method and the finite difference lattice Boltzmann method. The proposed method guarantees that without applying the filtering method, more stable and accurate results are obtained compared with the finite difference lattice Boltzmann method. The simulation results show the effectiveness of the present method and its appropriate compatibility with analytical solutions and other numerical methods.

کلیدواژه‌ها English

Incompressible Flow
Standard Lattice Boltzmann Method
Finite Difference Lattice Boltzmann Method
Numerical Stability
Upwind Scheme
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مهندسی مکانیک مدرس
دوره 24، شماره 3
اسفند 1402
صفحه 177-188