Boundary element method with parameterized elements for problems of potential flow velocity field

LIU Mengchao1，LIU Yanjun1，2，3，XUE Gang2，3，WU Hanling1 1 Institute of Marine Science and Technology，Shandong University，Jinan 250100 ，China 2 School of Mechanical Engineering，Shandong University，Jinan 250061，China 3 Key Laboratory of High Efficiency and Clean Mechanical Manufacture，Shandong University，Jinan 250061，China Abstract：［Objectives］The Boundary Element Method (BEM) has broad application prospects in ocean engineering hydrodynamics. In order to promote the application of BEM in ocean engineering hydrodynamics，［Methods］ the integral equation is established according to boundary integral method and a parameterized element BEM is adopted. This meta-method solves the potential flow problem and obtains the velocity potential of the flow field. The numerical calculations are performed on the basis of classic examples，the mathematical solutions are compared and error analysis is performed. Under the two-dimensional problem，the discontinuous parameterization element BEM and parameterized element BEM are used to solve the potential flow velocity field. Under the three-dimensional problem，a parameterized element BEM is used to solve the potential flow velocity field problem. ［Results］ The results show that under the two-dimensional problem，the discontinuous parameterized element BEM is used to solve the potential flow problem with high precision and efficiency，and the ideal numerical solution can be obtained with fewer elements. The parameterized element BEM under the three-dimensional problem is faster in calculation and can obtain better average relative accuracy，but some points have large margins of error and require the improvement of the algorithm or the introduction of another element to be solved.［Conclusions］ When the parameterized element BEM is used to solve the potential problem in ocean engineering， the numerical calculation implementation process is more concise and can be developed into a general method for solving the hydrodynamic problems of ships，such as ship motion. Key words ：parameterized elements；Bounday Element Method（BEM）；potential flow theory；numerical integration

收稿日期：2018 - 01 - 07 网络出版时间：2018-8-31 16:37基金项目：国家重点研发计划—战略性国际科技创新合作重点专项（2016YFE0205700）；国家自然科学基金委员会山东省人民政府联合基金重点支持项目（U1706230）；山东大学基本科研业务经费资助项目（2016JC035）作者简介：刘梦超，男，1991年生，硕士生。研究方向：海洋工程水动力学。E-mail：liumengchaosdu@163.com刘延俊（通信作者），男，1965年生，博士，教授。研究方向：流体动力控制，机械系统智能控制与动态检测，海洋可再生能源与深海探测技术及装备开发。E-mail：lyj111ky@163.com