Study on the Improved Radiation Boundary Conditions Based on the Quadratic B-spline Rankine Panel Method

This study presents a higher-order Rankine source method that is based on a biquadratic B-spline scheme with an improved radiation boundary condition. This method solves flow problems under all t conditions, where t ¼ Uu including the undercritical condition (t < 0.25); this condition is present when a ship undergoes slow translational _g , motion. The proposed method is thus more flexible than the many Rankine-source models in the literature that are applicable only to the overcritical condition (t > 0.25). Specifically, the improved radiation boundary condition is derived from upstream Seto radiation boundary conditions and by incorporating the Rayleigh damping distribution over a free surface; the improved condition is explicit and efficient for solving flow problems. In evaluations, the proposed method yields accurate solutions for unsteady flows, which are produced by an oscillating, translationally moving submerged singularity. The method is also compared against asymptotic solutions and against analytic solutions obtained using a three-dimensional translating-pulsating-source Green function.