# The Effect of Porous Media on Wave-Induced Sloshing in a Floating Tank
For FSI modeling, the key point is the coupling algorithm that connects the numerical methods for the fluid and rigid-body dynamics to ensure kinematic continuity (same displacement and velocity) and dynamic continuity (same pressure) on the fluid-solid interface. Many researchers considered potential-flow theory. [PERSON] [27] obtained the hydrodynamic force equilibrium of the body motion iteratively. [PERSON] [28] combined the Bernoulli equation and the motion equation of the body to derive an additional integral equation that satisfies the continuity simultaneously. His method requires little extra computational effort but avoids numerical iterations. [PERSON] [29] provided a similar formula in the implicit algorithm. [PERSON] et al. [30] studied the viscous effect around a rolling floating body through wave tank experiments. They concluded that eddy-making damping is important to calculate the roll motion. [PERSON] et al. [31] and [PERSON] et al. [32] compared several numerical schemes for the forced and free motions of a fully submerged body. Other useful methods for solving the FSI problem in potential flow can be observed in past articles [33; 34; 35]. In recent decades, more researchers study FSI problems via RANS analysis. Compared to the potential-flow model, it can describe the fluid reaction to structures more appropriately by including viscosity, the boundary layer, vortex, and breaking waves. [PERSON] et al. [36] applied the Arbitrary Lagrangian-Eulerian (ALE) framework to build a strongly coupled algorithm. [PERSON] et al. [37] used the volume-of-fluid method to capture the motion of the wave energy converter. [PERSON] [38] demonstrated the numerical results of some typical problems in ocean engineering, such as propellers, pipes, free-surface flow, and the sloshing phenomenon. [PERSON] et al. [39] compared the Lagrangian and Eulerian approaches (SPH vs. FEM) in FSI simulations. They emphasized the numerical robustness, ease of model setup, and versatility for several typical scenarios including the floating and submerged bodies and the elastic gate of a dam. More numerical approaches and their applications can be observed in textbooks [40]. This paper emphasizes the influence of porous media on the interaction between wave-induced sloshing in a tank and the dynamics of the attached floating body. The application of porous media to structural vibration control and sloshing mitigation will be addressed as well. The Eulerian-Lagrangian method was adopted for the hydrodynamic computation in both the pore-flow domain (sloshing fluid in porous media) and the pure-water domain (ambient waves). This numerical method includes the mixed-type boundary value problem (BVP) solver implemented by the boundary element method (BEM) and the free-surface particle tracker via the second-order Taylor series expansion. Similar approaches had been applied to solve wave absorption [41], shoaling [42], and the local impact of a water jet [43]. Another equivalent mechanical model was employed to calculate the sloshing responses. This mechanical model involves several sets of mass-spring-dashpot systems, hence the degree of freedom is greatly reduced and the fluid computation is replaced by a few motion equations. The nonlinear damping of the mechanical model was validated via shaking table tests [25] but the results were obtained only when the tank was subject to horizontal excitations. Therefore, the supplementary solution for the mechanical model undergoing angular excitation is provided in this paper. For the rigid-body dynamics, the Newmark time-integration method was employed to ensure numerical stability. The body dynamics can be solved as long as the hydrodynamic resultants are given. The hydrodynamic forces are not, however, known a priori; they can only be obtained by solving the BVP that involves the body dynamics as the boundary conditions. In this work, therefore, an iterative algorithm was adopted to ensure the equilibrium between the body motion and fluid reaction, i.e., [PERSON]'s second law of motion.