A sigma coordinate 3D k-ε model for turbulent free surface flow over a submerged structure

A fully three-dimensional unsteady flow model is developed to simulate free surface flow over a submerged structure. A new sigma coordinate is used to map the physical domain containing the wavy free surface and uneven bottom to a rectangular prism, and to keep the size of the submerged block unchanged in the sigma coordinate system. The numerical difficulty encountered in the conventional sigma coordinate system in which the block changes dynamically due to the time varying free surface is thus eliminated. A split operator scheme is used in the numerical solution so that different numerical schemes can be purposely chosen to deal with the distinctive mathematical and physical characteristics of the phenomena at different steps. k-ε model is used in the parameterization of turbulence due to its efficiency and reasonable performance. The model is applied to simulate the propagation of a solitary wave with good results. It is subsequently used to simulate a free surface flow against a submerged cube with one face perpendicular (or 45° inclined) to the flow. The numerical results compare favorably with the experimental measurements. In particular, no excessive turbulent kinetic energy is accumulated at the impingement regions.