A hybrid FV/FD scheme for a novel conservative form of extended Boussinesq equations for waves in porous media

International audienceThis paper introduces a conservative form of the extended Boussinesq equations for waves in porous media. This model can be used in both porous and non-porous media since it does not requires any boundary condition at the interface between the porous and non-porous media. A hybrid Finite Volume/Finite Difference (FV/FD) scheme technique is used to solve the conservative form of the extended Boussinesq equations for waves in porous media. For the hyperbolic part of the governing equations, the FV formulation is applied with a Riemann solver of Roe approximation. Whereas, the dispersive and porosity terms are discretized by using FD. The model is validated with experimental data for solitary waves interacting with porous structures and a porous dam break of a one-dimensional flow