An explicit one-dimensional model based on the extended Boussinesq equations was established to calculate solitary wave propagation in vegetated and non-vegetated waters. This model adopts a hybrid solution combining the finite difference (FD) and the finite-volume (FV) methods. This hybrid model can also simulate wave propagation as the FV solution of a non-linear shallow water equations (NSWE) model by removing the higher order Boussinesq terms. The resistance force caused by vegetation is added into a source term in the momentum equation. The interface fluxes are evaluated using the Harten-Lax-van Leer (HLL) approximate Riemann solver with reconstruction technique, providing a robust method to track the moving shoreline. This model is used to simulate solitary wave run-up on a sloping bed with vegetation and to evaluate wave attenuation through a vegetation zone. It is found that the model reasonably predicts wave height attenuation in cases where there is combined vegetation in a flat bed, implying that vegetation may cause energy loss in solitary wave propagation. The larger wave height and the larger vegetation density cause the larger wave attenuation for solitary waves through vegetation water. A positive correlation is found between wave attenuation and wave height. Modeling vegetation through the use of a source term in momentum equations is proved to provide a reasonable estimation for the amount of wave height attenuation that may occur through wetland marshes.

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