Padé-type high-order absorbing boundary condition for a coupled hydrodynamic wave model with surface tension effect

This paper addresses the design and validation of High-Order Absorbing Boundary Conditions (HABC) of the Padé family on a Coupled Hydrodynamic Wave Model (CHWM) especially with surface tension effect (with small spatial scales). Inspired by the Neumann–Kelvin model, the CHWM comprises a fluid model enabling the consideration of multiple objects located immediately beneath the surface, coupled with a free surface model that incorporates a small added mass surface term. With the surface tension effect, we introduce new coefficients (similar to Higdon coefficients) on each HABC (for the surface model and the basin model) to ensure the continuity of the two HABC at the interface between the coupled models. Consequently, we propose a useful specific compatibility condition, and a significant reduction of the Padé approximation particularly in the water case.