Nonhydrostatic model for free surface flow interaction with structures

Abstract

AbstractSimulating fluid–structure interactions is important in many engineering applications. Navier–Stokes based models can accurately simulate free surface flows and efficiency is improved by transforming the equations into the sigma‐coordinate system in which the grid follows the free surface and bottom. This approach lacks the ability to simulate wave overturning and splashing, but it has been demonstrated to accurately simulate breaking waves. Incorporating structures in a free surface flow model is challenging. Many existing techniques require complex grids and cumbersome interpolation. The immersed boundary method avoids complicated grids by overlaying the object on the grid. Interpolation is still required at the object boundary, which may not conserve mass. It is also difficult to compute the force acting on the body. Conservation may be reclaimed by embedding the object into the mesh. However, this may result in small (cut) cells and numerical instability unless they are merged with neighboring cells. In this article, a new model is proposed and constructed using a modified sigma coordinate transformation. This limits the model to simulating objects that can be represented by upper and lower surfaces that are functions of x and y, but still allows for many simulations of engineering interest. In exchange for this compromise, several advantages are gained including: efficiency, mass conservation, and easy estimation of force. Model accuracy is demonstrated by comparing numerical predictions with analytical solutions and laboratory measurements for free surface flows interacting with a horizontal cylinder and NACA 0012 foil.