Mathematical modeling of arbitrary shaped harbor with permeable and impermeable breakwaters using hybrid finite element method

Abstract

A mathematical model is developed based on the application of permeable and impermeable breakwaters utilizing the mild slope equation (MSE) to analyze the wave amplification in an arbitrary shaped harbor with variable bathymetry. Finite element method (FEM) coupled with analytical approximation is described as Hybrid FEM, which is used to solve the MSE and Helmholtz equation in bounded and unbounded domains (open Sea region), respectively. The validation of the present numerical scheme is conducted by comparing the simulation results with the existing studies and the convergence analysis is also conducted to verify the accuracy of the numerical scheme. The effects of energy dissipation, bottom friction, and variable wave transmission through impermeable and permeable breakwaters are investigated to understand the resonance phenomenon in rectangular port. In addition, the current numerical scheme is implemented on a real Paradip port, Odisha, India at six different key locations, and for the first time the effect of breakwaters placed at the entrance and in the bounded region, along with bottom friction, and partially reflecting port boundary are investigated. The breakwaters with small permeability/transmission coefficient have high efficiency to reduce the wave resonance inside the port.