Numerical modeling of solitary and cnoidal waves propagating over a submerged bridge deck

An initial component in the study of tsunami and storm surge wave forces on a submerged bridge deck is the development of a two-dimensional numerical model of solitary and cnoidal waves propagating over a submerged plate based on the Navier-Stokes (N-S) equations. Results are compared with numerical models based on a non-linear dispersive shallow water wave theory known as the Green-Naghdi (G-N) theory of water waves. Solitary and cnoidal waves are modeled using the open source computational fluid dynamics library OpenFOAM which solves the N-S equations by use of the finite volume method. Solitary waves are initiated by implementing a user defined velocity boundary condition based on the G-N theory and cnoidal waves are initiated using Waves2Foam, a wave generation toolbox developed for OpenFOAM. Results for the surface elevation on and around the bridge deck obtained by solving the N-S equations are compared with the numerical results obtained through the G-N theory. Even though these are two different solvers, solving two different sets of equations, preliminary analysis shows generally good agreement between the N-S and G-N solvers, with the propagation speed, wave amplitude and soliton fission being nearly identical. By solving these problems by two different methods, we are able to increase our confidence in the accuracy of our predictions of wave loads on coastal bridges.