A Simplified Numerical Method for Simulating the Generation of Linear Waves by a Moving Bottom

Abstract

In this study, simplified linear numerical method that can simulate wave generation and transformation by a moving bottom is introduced. Numerical analysis is conducted in wave number domain after continuity equation, linear dynamic and kinematic free surface boundary conditions and linear kinematic bottom boundary condition are Fourier transformed, and the results are expressed in space domain by an inverse Fourier transform. In the wavenumber domain, the dynamic free water surface boundary condition and the kinematic free water surface boundary condition are numerically calculated, and the velocity potential in the mean water level (<i>z</i> = 0) satisfies the continuity equation and the kinematic bottom boundary condition. Wave generation and transformation are investigated when the triangular and rectangular shape of bottoms move periodically. The results of the simplified numerical method are compared with the results of previous analytical solutions and agree well with them. Stability of numerical results according to the calculation time interval (△<i>t</i>) and the calculation wave number interval (△<i>k</i>) was also investigated. It was found that the numerical results were appropriate when △<i>t</i>≤<i>T</i>(period)/1000 and △<i>k</i>≤π/100.