A hybrid finite-volume/finite-difference-based one-dimensional Boussinesq model for waves attenuated by vegetation

Abstract

A hybrid finite-volume/finite-difference scheme is proposed to solve the one-dimensional Boussinesq equations for wave attenuation by vegetation. The effect of vegetation is included as a source term in a form of drag force. The convective part of the equations is discretized by the finite-volume method, while the finite-difference method is used to discretize the remaining terms. The variable values for the local Riemann problem at each cell face are calculated by a fourth-order MUSCL reconstruction method. The source terms and the dispersion terms are discretized using the centered finite-difference schemes up to fourth-order accuracy. The unsteady terms are discretized by the second-order MUSCL-Hancock scheme. The discretized continuity equation is solved explicitly, while the discretized momentum equation is solved using the Thomas algorithm. The developed Boussinesq model is tested with analytical solutions and reported experimental data. To further validate the model, the computed results are compared with the experimental data observed in two vegetated wave flumes. It is demonstrated that the developed model is suitable for predicting wave propagation in vegetated water bodies.