| A front tracking method is developed for the two and three dimensional free surface problems. In two dimensions, cubic splines are used to fit the interface and compute the geometric parameters related to the free surface (e.g. volume fraction of fluid, normal direction and curvature of the interface). The normal stress boundary conditions are added on the exact location of the interface. The tangential stress boundary conditions are enhanced with the least squares technique when the velocity boundary conditions are extrapolated. Cartesian grid method (or cut-cell method) is used to discretize the governing equations and treat the interface as a sharp discontinuity. In three dimensions, the two dimensional front tracking method is extended. The triangulated surface meshes are used to represent the free surface and compute the geometric parameters. The volume fraction of fluid and the surface area cut by the interface in a Cartesian control volume are computed in terms of Boolean operations. This method is applied to implement LES of free surface flows in an open channel with small amplitude waves. The numerical results are satisfactory when compared to experimental and DNS data. |
