Pad{\'e}-type High-Order Absorbing Boundary Condition for a Coupled Hydrodynamic Wave Model with Surface Tension Effect

TL;DR

This paper develops a high-order Padé-type absorbing boundary condition for a coupled hydrodynamic wave model that includes surface tension effects, ensuring accurate wave absorption at model boundaries.

Contribution

It introduces a novel Padé-type high-order absorbing boundary condition tailored for coupled hydrodynamic models with surface tension, including compatibility conditions and coefficient modifications.

Findings

Effective boundary condition reduces wave reflection.

Ensures continuity at model interfaces.

Improves accuracy for small-scale surface tension effects.

Abstract

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.