Non-Hydrostatic Model for Solitary Waves Passing Through a Porous Structure

The non-hydrostatic depth-integrated model we developed to study solitary waves passing undisturbed in shape through a porous structure, involves hydrodynamic pressure. The equations are nonlinear, diffusive, and weakly dispersive wave equation for describing solitary wave propagation in a porous medium. We solve the equation numerically using a staggered finite volume with a predictor-corrector method. To demonstrate our non-hydrostatic scheme's performance, we implement our scheme for simulating solitary waves over a flat bottom in a free region to examine the balance between dispersion and nonlinearity. Our computed waves travel undisturbed in shape as expected. Furthermore, the numerical scheme is used to simulate the solitary waves pass through a porous structure. Results agree well with results of a central finite difference method in space and a fourth-order Runge-Kutta integration technique in time for the Boussinesq model. When we quantitatively compare the wave amplitude reduction from our numerical results to experimental data, we find satisfactory agreement for the wave transmission coefficient.