On the damping coefficients of sponge layer in Boussinesq equations

The damping coefficients of the sponge layer in Boussinesq equations are derived theoretically. The damping coefficients are expressed by explicit functions that are in terms of the relative water depth and a distance measured from a starting coordinate of the sponge layer. Numerical experiments show that the proposed damping coefficients work efficiently on reducing the energy of reflected waves from the sponge layer. The present result differs from former researches in which the free parameters in the damping coefficients are suggested by numerical tests to control the effect of the sponge layer. It is found that the values of damping coefficients increase with the increase of the relative water depth. The numerical tests were performed to verify the applicability and validity of the present approach by using second-order fully Boussinesq equations. The numerical example for waves propagating over a submerged bar bathymetry is fairly compared with experimental data.