## 1 Introduction  
Wave tanks are essential facilities for conducting fluid dynamics experiments that explore the interaction between water waves and structures. One side of the tank is usually fitted with a wave generator to create waves defined by the user. However, if the wave absorber on the opposite side of the tank is inadequately designed, it may cause undesirable reflections that deteriorate the reliability of the experiments, and cause delays in the experiment owing to the waiting time needed for disappearing residual waves in a tank after the wave generator is stopped. Depending on the size of the wave tank, wave absorbers of different shapes and materials are utilized. Porous plates, known for their effectiveness in dissipating wave energy and minimizing wave reflections, are commonly employed as passive wave absorbers. The authors in [1] reviewed and investigated existing wave absorbersin 48 wave basins around the world. According to the report, wave absorbers utilizing porous plates are predominantly categorized into vertical, horizontal, and inclined types. Vertical wave absorbers necessitate several porous plates with gradually reducing porosity to attain the desirable wave absorption efficiency. Therefore, this configuration requires substantial installation space and frequently results in resonance between the plates. Horizontal porous plates have demonstrated exceptional effectiveness in dissipating wave energy, making them useful for coastal protection and improving harbor calmness. Studies referenced in [2; 3] explored the performance of horizontal porous plates through the boundary element method (BEM) and the matched eigenfunction expansion method (MEEM), respectively. The energy dissipation capacity of horizontal porous plates largely depends on their porosity. This energy dissipation is considered by the porous boundary condition, particularly [PERSON]'s model [3; 4; 5; 6; 7], which outlines the linear correlation between velocity and pressure drop. In ref. [5], the authors developed an analytical model for wave-absorbing systems based on [PERSON]'s model. Their analytical solution using a MEEM, and their numerical solution using a multi-domain BEM, were validated through a series of experiments. These research findings indicate that the optimal values for wave absorption efficiency are a slope angle of 10\({}^{\circ}\) and a plate porosity of 0.1. Additionally, the local shape of the porous plate (e.g., slits, circular holes, rectangular holes, etc.) was found to have no significant impact on energy dissipation [5; 8; 9]. As an alternative energy dissipation model, several authors have considered the quadratic relationship between pressure drop and velocity. The authors in [10] were the first to derive an expression for long-wave head loss in porous walls. Several authors in articles [11; 12] extended the work of those in ref. [10] to investigate wave interactions with porous plates. The authors of [13; 14] examined energy dissipation through porous plates by employing an equivalent quadratic velocity model that incorporates both inertial and drag effects. Subsequently, another article [15] examined wave energy dissipation caused by a horizontal slotted plate using a quadratic velocity model with a CFD-determined drag coefficient. They validated their findings by comparing them with CFD-based numerical simulations and experimental results. The boundary element method (BEM) has been effectively utilized in wave problems due to its distinct advantages over other domain-based methods such as the Finite Difference Method (FDM) and Finite Element Method (FEM). The BEM reduces the problem's dimensionality by one order, simplifying calculations and enhancing accuracy through its integral formulation. Numerous researchers have extended the application of the BEM to study wave interaction with porous structures [5; 16; 17; 18; 19].