Cartesian spatial derivatives of boundary element solutions on the exact free surface of fully nonlinear numerical wave tanks

Abstract

The convergence and stability of the fully nonlinear simulation in a three-dimensional potential numerical wave tank is vulnerable along the time marching algorithm of the free surface, as integrating the boundary element's solution into the high-order time integration of the free surface can trigger the numerical instability in the material node approach. Although this matter was identified in some of the prior studies on three-dimensional wave tanks, the approximation of the velocity components plays a crucial role in the sustainability of a simulation. Therefore, a methodology for deriving the Cartesian components of the fluid particles’ velocity over the exact free surface is proposed in this paper. Various circumstances come across while determining the velocity components of fluid particles, which are the function of the location of the free surface nodal points. Since plenty of prior techniques have been based on the tangential derivatives of the free surface boundary value from the previous iteration, the disruption in the convergence of the model occurs most often. Hence, achieving a generic algorithm that merely depends on the boundary element solutions, is a highly important achievement for retaining the stability and simultaneously the convergence of the solution.