کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6930074 | 867658 | 2016 | 19 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Analysis and accurate numerical solutions of the integral equation derived from the linearized BGKW equation for the steady Couette flow
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Analysis and accurate numerical solutions of the integral equation derived from the linearized BGKW equation for the steady Couette flow Analysis and accurate numerical solutions of the integral equation derived from the linearized BGKW equation for the steady Couette flow](/preview/png/6930074.png)
چکیده انگلیسی
The integral equation for the flow velocity u(x;k) in the steady Couette flow derived from the linearized Bhatnagar-Gross-Krook-Welander kinetic equation is studied in detail both theoretically and numerically in a wide range of the Knudsen number k between 0.003 and 100.0. First, it is shown that the integral equation is a Fredholm equation of the second kind in which the norm of the compact integral operator is less than 1 on Lp for any 1â¤pâ¤â and thus there exists a unique solution to the integral equation via the Neumann series. Second, it is shown that the solution is logarithmically singular at the endpoints. More precisely, if x=0 is an endpoint, then the solution can be expanded as a double power series of the form ân=0ââm=0âcn,mxn(xlnâ¡x)m about x=0 on a small interval xâ(0,a) for some a>0. And third, a high-order adaptive numerical algorithm is designed to compute the solution numerically to high precision. The solutions for the flow velocity u(x;k), the stress Pxy(k), and the half-channel mass flow rate Q(k) are obtained in a wide range of the Knudsen number 0.003â¤kâ¤100.0; and these solutions are accurate for at least twelve significant digits or better, thus they can be used as benchmark solutions.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 316, 1 July 2016, Pages 416-434
Journal: Journal of Computational Physics - Volume 316, 1 July 2016, Pages 416-434
نویسندگان
Shidong Jiang, Li-Shi Luo,