Water Wave Diffraction by a Vertical Circular Cylinder Using Scaled Boundary Finite Element Method

The Scaled Boundary Finite Element Method (SBFEM) is a rather new semi-analytical method that combines the merits of finite element and boundary element methods. The SBFEM method uses weighted residual technique and finite elements to weaken and discretize the governing differential equation only on the boundary of the problem and then solves the resulted system of weakened ordinary differential equations in the radial direction, analytically. In this article, the boundary-value problem of water wave diffraction by a vertical circular cylinder has been solved by SBFEM method. Only the circular boundary is discretized with one-dimensional finite-elements. The governing partial differential equation is transformed to a system of ordinary differential equations, whose numerical solution on the nodes of circular boundary is obtained with the aid of analytical solutions that satisfy the far field boundary condition. The comparison of hydrodynamic parameters such as total velocity potential, wave elevation and horizontal component of wave excitation force with those obtained from analytical and other numerical methods shows high accuracy and efficiency of the present SBFEM method.