第10卷第4期 2015年8月
中国舰
船研究
Chinese Journal of Ship Research
网络出版地址:http://www.cnki.net/kcms/detail/42.1755.TJ.20150728.1725.006.html
Vol.10 No.4 Aug.2015
期刊网址：www.ship-research.com
引用格式：韩玉超，卢晓平，王中.无限区域二维势流直接边界元法精度分析[J].中国舰船研究，2015.10(4)：39-45.54.
HAN Yuchao,LU Xiaoping, W ANG Zhong. Precision analysis of the twodimensional potential flow problem in an infinite
region with the direct boundary element method[ J J. Chinese Journal of Ship Research , 2015, 10( 4 ) : 3945 ,54. 无限区域二维势流直接边界元法精度分析
韩玉超，卢晓平，王中
海军工程大学舰船工程系，湖北武汉430033
摘要：边界元法作为一种重要的数值方法已在许多领域得到广泛应用，但在船舶水动力势流理论数值计算方面，有关直接边界元法的研究并不充分，尤其是在船兴波阻力势流理论求解方面，以往的“面元法“通常是基于Hess-Smith法的间接法，这类方法在理论和数值计算上都存在着缺陷。针对船舶水动力势流理论计算，采用直接边界元法，对二维势流无界绕流算例进行系统的数值计算，并根据二维势流间题的计算结果详细探讨边界单元离散形式和单元上的数值积分方法对计算精度的影响，各项数值计算均以Matlab软件编程实现。结果表
明，采用常数单元和龙贝格积分法能够得到较准确的结果，且计算速度较快。关键调：直接边界元法；势流理论；边界离散；数值积分
中图分类号：U661.1
文献标志码：A
D0I: 10.3969/j.issn.16733185.2015.04.006
Precision analysis of thetwo-dimensional potential flowproblemin
aninfiniteregionwiththedirectboundary elementmethod
HAN Yuchao, LU Xiaoping, WANG Zhong
Department of Naval Architecture Engineering, Naval University of Engineering, Wuhan 430033, China Abstract: The Boundary Element Method (BEM) , as a key numerical method, has been widely applied in many fields. However, the research on the Direet Boundary Element Method (DBEM) for ship hydrody-namic numerical calculation problems is still insufficient, especially when it comes to the ship hydrody-namic potential flow theory. The general method - 'panel method' is based on HessSmith method, which is an Indirect Boundary Element Method (IBEM) whose major flaws exist in both theory and numeri-cal calculation. This paper, based on the ship hydrodynamic potential flow theory, adopts DBEM to calcu-late the example of twodimensional unbounded potential flow around a cylinder, and analyzes the influ-ence of the boundary element discrete forms and the numerical integral methods on the caleulation accura-cy. The results carried out by Matlab clearly indicate that using the constant element and Romberg algo-rithm method could yield high calculation speed and accuracy.
Key words: Direct Boundary Element Method (DBEM): potential flow theory ; boundary discretization; numerical integration
引言 0
根据边界积分方程中未知函数的不同，边界元法可分为直接法和间接法2种。在以往的船舶
收稿日期：20140904
基金项目：国家部委基金资助项目
兴波阻力势流理论问题求解方面，通常是采用基于Hess-Smith法的间接法")。在间接法中，边界积分方程中的未知函数并不是待定函数本身，而是作用于所考累区域边界相应线（面）上的某种虚
网络出版时间：2015-72817:25:18
作者简介：韩玉超，男.1989年生，士生。研究方向：舰铅水动力性能。E-mail：hanyuchaoa@163.com
卢晓平（通信作者）男，1957年生，博土，教授。研究方向：舰暂水动力性能。E-mail:Laixiaoping100@163.com 王中，男，1981年生，博士，讲师。研究方间：计算机辅助船舶设计制造。Email；wangxhonghj@sohu.com