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

Chinese Journal of Ship Research - - CONTENTS -

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