A homotopy boundary element method model based on modified potential flow with nonlinear dissipative conditions

This study develops a general three-dimensional homotopy boundary element method (HBEM) model for analyzing wave-induced hydrodynamic problems of marine structures. Artificial dissipative surfaces are introduced into fluid domains where wave energy dissipation is non-negligible. The mass flux across these surfaces remains continuous, while local head loss is assumed to occur on both sides of these surfaces. Quadratic (nonlinear) pressure loss conditions are imposed on these dissipative surfaces to equivalently represent the viscous dissipation effect. In solving the boundary value problem, the conventional boundary integral equation derived from the second Green's theorem is applied to the structure surfaces, whereas a hypersingular boundary integral equation is deduced for the dissipative surfaces. After discretizing all boundaries into a series of constant panels, an algebraic system is obtained from the two types of boundary integral equations. The application of quadratic pressure loss conditions renders this system nonlinear, which is solved using the homotopy analysis method. The proposed HBEM model is validated by considering the problems of fluid resonance in narrow gaps and wave resonance in moonpools. The calculated results are in excellent agreement with both analytical results in the literature and numerical results based on a direct iteration method. Moreover, with an appropriately calibrated dissipation coefficient, the calculated results of the free surface amplitude inside narrow gaps and moonpools agree well with published experimental measurements. The present HBEM model can offer a reliable and efficient computational tool for the hydrodynamic analysis of wave–structure interaction.