A coupled mathematical model is developed based on the non-linear Boussinesq equation (BE) for shallow water waves to investigate the influence of the periodic non – linear long waves inside the irregular domain. A coupled numerical model based on the solution of the BE in a bounded region with the incorporation of the effects of viscous dissipation, dispersion, convective non-linearities, and variable bathymetry is obtained by using Galerkin Finite Element Method (GFEM), and an analytical approach based on Fourier-Bessel series solution for the scattered waves in unbounded region. The current coupled numerical model is validated by comparing the simulation results with existing studies. Moreover, the accuracy of the current scheme is also examined using convergence analysis for the rectangular domain. The present numerical model is applied on T and TT–shaped harbors to investigate the role of geometry to induce the amplification. In addition, the current approach implemented on the realistic Paradip port, Odisha, India, and Pohang New Harbor (PNH), South Korea at six record stations for practical implication. Therefore, the present numerical model can be utilized to construct/redesign an artificial port in the coastal region including variable bathymetry considering the effect of partial reflection, dissipation, and convective non – linearities