The Harmonic Polynomial Cell (HPC) method is a recently proposed efficient and accurate method for solving the Laplace equation, which represents the velocity potential by a linear superposition of a set of complete harmonic polynomials within each cell to solve the potential flow problem. The procedure has approximately 4th-order accuracy, while its resulting matrix is sparse similarly as the other field solvers. In this paper, the hydrodynamic performance of three 2D sections, rectangular, semicircular and Wigley III, is calculated based on the HPC method. To deal with the problem of sharp angle singularities of the object surface as well as mixed boundary conditions for the corners in the computational domain, a single-node hybridize condition is given in this study. By comparing the simulation results of added mass and damping with the experimental data, it shows that the HPC method can give slightly better simulation results compared with the Boundary Element Method (BEM). This study indicates that the proposed hybridization condition has a bit of improvement in the hydrodynamic performance prediction of the HPC method. In addition, a range of selections of calculation domain transverse and longitudinal size and grid scale is suggested in the framework of the HPC method. The present study makes several contributions to the efficient and stable calculation of subsequent complex sections.
In marine hydrodynamics, numerous numerical methods for calculating the hydrodynamic response of ships have been proposed and developed for application. With the development of computers and the emergence of more and more ship motion problems that cannot be solved by slicing theory, the three-dimensional potential flow theory has attracted the interest of more scholars. The Boundary Element Method (BEM) is the most commonly used method for solving 3D potential flow problems. According to the Green's function employed in the boundary integral equation, the panel methods can usually be divided into two categories: Rankine source method and free surface Green's function method. Since Hess and Smith (1964) first used the BEM to solve a 3D object flow around problem without free surface, the Rankine source approach has been widely used in the ship wave problems (Dawson, 1977; Peng et al., 2014) and seakeeping problems (Bertram and Thiart, 1998; Zhang et al., 2010). The other method, the free-surface Green's function, can automatically satisfy the free surface and radiation conditions in the boundary integral equation, so the singularities are only needed to be distributed on the wetted body surface. Because the coefficient matrix for the unknowns is full, the computational time and memory required by the BEM increase strongly as the number of unknowns increases. However, regardless of the two approaches, the computation time and memory required for the BEM increase dramatically with the number of unknowns because the coefficient matrix for the unknowns is full.
