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This paper presents a non-hydrostatic two-dimensional vertical (2DV) numerical model for the simulation of wave-porous structure problems. The flow in both porous and pure fluid regions is described by the extended Navier-Stokes equations, in which the resistance to flow through a porous medium is considered by including the additional terms of drag and inertia forces. The finite volume method (FVM) in an arbitrary Lagrangian-Eulerian (ALE) description is employed to discretize the flow and transport equations. A two-step fractional method has been deployed to solve the governing equations. In the first step, the momentum equations in the absence of pressure field were solved to compute an intermediate velocity. The second fractional step consisted of bringing the pressure terms back into the equations, and calculating the pressure field by solving the extended continuity equation and the momentum equations excluding advective and diffusive terms and drag force components. By substitution of the approximations of the pressure derivatives into momentum equations, and subject to the continuity constraint, the pressure Poisson equation was obtained. The solution of the pressure Poisson equation led to a linear system of equations in the form of a block tri-diagonal matrix with the pressures as unknowns. The second step was completed by computing the updated velocity values. In the present numerical model, two types of boundary conditions, namely Dirichlet and Neumann boundary conditions were adapted to solve the governing equations. The Dirichlet boundary condition was set to zero for normal velocities at impermeable bottom and the Neumann boundary condition was considered to be equal to zero for normal gradient of the tangential velocities at impermeable bed and also the left side of the computational domain. At open boundaries, where required, by setting the dynamic pressure equal to zero at the end of the numerical domain, a free exit for water was considered. The newly developed model in the absence of porous medium was verified by comparing the numerical simulations with the analytical solutions of a solitary wave propagation in a constant water depth. The newly developed model was then employed to simulate the solitary wave interaction with a permeable submerged breakwater. Based on the numerical results, when the solitary wave front reaches the offshore side of the submerged breakwater, due to the hydraulic jump formation, the flow is separated from the top of the obstacle and small clockwise vortices are generated at the leading edge of the breakwater. As the wave passes over the breakwater, the primary vortex grows in size and penetrates into the deeper layers of water. It was also seen that, due to the drag and inertia resistance forces of the porous medium, the velocity inside the permeable breakwater was noticeably smaller than that on the top of the breakwater. The comparisons between the numerical results and experimental measurements for time histories of water displacements, spatial distributions of free surface elevation, velocity fields and velocity profiles in both horizontal and vertical components, showed the capability of the newly developed model in predicting wave interaction with permeable submerged breakwater.

Keywords: Wave-porous structure interaction, Submerged breakwater, Extended Navier-Stokes equations, Finite volume method (FVM), Arbitrary Lagrangian-Eulerian (ALE)

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