CFD simulation of two- and three-dimensional free-surface flow

The paper describes the implementation of moving-mesh and free-surface capabilities within a 3-d finite-volume Reynolds-averaged-Navier–Stokes solver, using surface-conforming multi-block structured meshes. The free-surface kinematic condition can be applied in two ways: enforcing zero net mass flux or solving the kinematic equation by a finite-difference method. The free surface is best defined by intermediate control points rather than the mesh vertices. Application of the dynamic boundary condition to the piezometric pressure at these points provides a hydrostatic restoring force which helps to eliminate any unnatural free-surface undulations. The implementation of time-marching methods on moving grids are described in some detail and it is shown that a second-order scheme must be applied in both scalar-transport and free-surface equations if flows driven by free-surface height variations are to be computed without significant wave attenuation using a modest number of time steps. Computations of five flows of theoretical and practical interest—forced motion in a pump, linear waves in a tank, quasi-1d flow over a ramp, solitary wave interaction with a submerged obstacle and 3-d flow about a surface-penetrating cylinder—are described to illustrate the capabilities of our code and methods. Copyright © 2003 John Wiley & Sons, Ltd.