کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
513158 866453 2009 13 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Comparison of boundary collocation methods for singular and non-singular axisymmetric heat transfer problems
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
Comparison of boundary collocation methods for singular and non-singular axisymmetric heat transfer problems
چکیده انگلیسی

This paper presents a computational study of some boundary collocation solution methods for the Laplace equation in cylindrical coordinates with axisymmetry. The methods compared are (i) the direct boundary element method (BEM), (ii) the method of fundamental solutions (MFS) with fixed sources and (iii) the Trefftz method. Relative accuracy of these methods are compared for two test problems. The first problem is a simple problem of heat transfer through a cylindrical rod which is a standard benchmark problem in this field. The second problem deals with heat transfer in silicon melt for Czochralski (CZ) process which involves a singularity in the boundary conditions at the corner of the crystal–melt interface. All the three methods indicated above are highly successful for the simple (first) problem with MFS and Trefftz being simpler to implement than the BEM. However, the Trefftz method was not effective for the second problem due to the boundary singularity and the MFS showed oscillations near the singularity point. Hence the use of higher order non-conforming elements with accurate Gauss–Kronrod integration schemes in the direct BEM method was investigated. It was found that the boundary singularity does not deteriorate the accuracy of the results if this improved numerical integration procedure is used in the direct BEM. Hence higher order elements with Gauss–Kronrod integration schemes can be used for the solution of many free interface problems encountered in crystal growth.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Engineering Analysis with Boundary Elements - Volume 33, Issue 5, May 2009, Pages 704–716
نویسندگان
, ,