Evaluation of the modified 3D free-surface Green's function for potential flow in a numerical towing tank

Abstract

What is derived in this paper is the potential flow around the marine structures in the numerical towing tank. The Green's formula and image method is employed to solve the boundary value problem. The Green's function satisfies the Laplace equation and the boundary conditions on the bottom, walls and free surface. The Green's function consists of three parts. The first part is correlated with spatial spacing between the source and a field point. The second part consists of the free surface disturbance. The radiation condition is dealt with in the third part to ensure that the waves vanish upstream of the source. An infinite series is obtained for each part of the Green's function using the image method. Effects of the numerical towing tank's width and depth on the solution are investigated, and the flow patterns due to the presence of a singularity with constant strength in the uniform flow are computed. Uniform motion of a submerged sphere and ellipsoid are simulated and compared with the analytical solutions and other numerical results. Wave profiles are computed for a sphere and an ellipsoid to show the effect of the tank width on the solution.