Interface-Capturing Method for Free-Surface Plunging and Breaking Waves

This paper presents an interface-capturing method for two-phase flows with large-amplitude free-surface motion. The method is developed by embedding the level-set equation in the momentum balance equations via dependency of the material properties on the signed distance field. Subsequent derivation of the fine-scale variational equation that is facilitated by the Variational Multiscale (VMS) framework leads to interfacial terms that stabilize the moving interface. These interfacial terms are operational across the zero contour of the signed distance field that implicitly represents the air-water interface. For plunging free-surface motions, the method is augmented with a reinitialization process that is based on a stabilized form of the Eikonal equation and reconstructs the signed distance field. Conservation of mass in extreme free-surface motions is maintained via a mass-conservation term that is based on the notion of minimizing the error in the computed signed distance field. Benchmark test cases of two-dimensional (2D) and three-dimensional (3D) dam-break problems are presented to validate the method and show its range of applicability.