Nonlinear Shallow-Water Flow on Deck

Abstract

Euler's equations have been used for nonlinear shallow-water flow on deck. The equations are simplified under the shallow-water assumption to obtain the governing equations. The Flux-Difference Splitting method is devised to solve this shallow-water flow problem. The flux-difference in the governing equations is split based on characteristic directions. The Superbee flux limiter is employed in the algorithm to make the finite-difference scheme of second order with high resolution. For two-dimensional decks, numerical results are presented to reveal the characteristics of shallowwater flow on deck. For three-dimensional decks, the Flux-Difference Splitting method together with the Fractional Step method are used, so that solutions of the shallow-water equation can be obtained by solving two sets of one-dimensional differential equations. Numerical results are presented to show the wave patterns for different modes of motion excitation. Velocity vectors in the flow field are also given to help understand the flow properties.