Investigation of Bragg resonant reflection of linear and nonlinear water waves by multiple fixed floating structures based on viscous meshfree method

Abstract

The Bragg resonant reflection of linear and nonlinear water waves over a classical Bragg structures is numerically studied. The Smoothed Particle Hydrodynamics (SPH) method is a Lagrangian meshfree method, and SPH is adopted based on the code DualSPHysics, which takes the effect of viscosity into consideration. The sensitivity of particle spacing and a benchmark test to the transmission coefficient is analyzed. In the propagation of both linear and nonlinear water waves over Bragg floating structures, the Bragg resonant reflection occurs when the wavelength (λ) is about double of the spacing (L). The phase upshift can be observed in the cases of linear and nonlinear water waves, which means the minimum transmission coefficient appears when 2L/λ>1.0, and the phase upshift occurs with the increase of the width of floating in the nonlinear water waves. Besides, in the resonant case with three or more floating structures, the transmitted wave height is reduced by more than 70.9% and 73.5% relative to the incident wave height under linear and nonlinear water waves, respectively. The results give a reference for the design of wave attenuation in floating periodic structures in both linear and nonlinear water waves based on the Bragg rules.