Extended Boussinesq equations for waves in porous media

We develop an extended Boussinesq model to predict the propagation of waves in porous media. The inertial and drag resistances are taken into account in the developed model. When these resistances are neglected, the developed equations are reduced to the extended Boussinesq equations of Madsen and Sørensen (1992) [Coastal Eng. 18, 183-204] for non-porous media The model can be applied for non-porous media as well as porous media because it does not need any matching condition at the interface between the porous and non-porous media. The developed model is verified by comparing numerical solutions to experimental data with several cases of solitary waves or sinusoidal waves interacting with a porous breakwater in one- and two-dimensional domains.