Energy balance during Bragg wave resonance by submerged porous breakwaters through a mixture theory-based 6-LES-SPH model

This paper presents a numerical analysis of the time behaviors of mechanical and internal fluid energies during the Bragg wave resonance induced by two-arrayed trapezoidal submerged porous breakwaters based on a reformatted 6-LES-SPH model (Di Mascio et al., 2017). In the present work, a mixture theory is introduced into the 6-LES-SPH model by reformulating the governing equations with the incorporation of a volume fraction. In this approach, the viscous and diffusive terms are also modified by the volume fraction. The energy equation is then written for the presented model highlighting the presence of two additional components compared with the classical 6-LES-SPH formulation: one coming from the fluid compression and another one due to the dissipation both induced by the interaction of the porous structure with the fluid phase. The numerical results are validated by available experimental data for a gravity-driven mass flow passing through a porous dam case and two Bragg wave resonance by two-arrayed submerged trapezoidal porous breakwaters cases. A numerical analysis is then conducted on Bragg wave resonance by two-arrayed trapezoidal porous breakwaters, by investigating the effects of the distance between the two breakwaters and their porosity. Interesting insights about the type and magnitude of dissipation occurring during the wave-structure interaction are captured by analyzing the time evolutions of each energy component.