  This paper presents a specific way to develop High-Order Absorbing Boundary
Conditions (HABC) of the Pad{\'e} family on a Coupled Hydrodynamic Wave Model
(CHWM) especially with surface tension effect (small scales in space). Inspired
by the Neumann-Kelvin model, the CHWM is composed by a fluid - basin model to
allow to use multiple objects below the surface coupled to a free surface model
with a small added mass surface term. With the surface tension effect, we
introduce new coefficients (similar as 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. So, we propose a useful specific
compatibility condition, and a strong reduction of the Pad{\'e} approximation
in particular in the water case.
