1D–2D Numerical Model for Wave Attenuation by Mangroves as a Porous Structure

Abstract

In this paper, we investigate wave attenuation caused by mangroves as a porous media. A 1-D mathematical model is derived by modifying the shallow water equations (SWEs). Two approaches are used to involve the existing of mangrove: friction term and diffusion term. The model will be solved analytically using the separation of variables method and numerically using a staggered finite volume method. From both methods, wave transmission coefficient will be obtained and used to observe the damping effect induced by the porous media. Several comparisons are shown to examine the accuracy and robustness of the derived numerical scheme. The results show that the friction coefficient, diffusion coefficient and vegetation’s length have a significant effect on the transmission coefficient. Moreover, numerical observation is extended to a 2-D SWEs, where we conduct a numerical simulation over a real bathymetry profile. The results from the 2-D numerical scheme will be validated using the data obtained from the field measurement which took place in Demak, Central Java, Indonesia. The results from this research will be beneficial to determine the characteristics of porous structures used for coastal protection.