VOF Method in Two-Stage Fourth Order Time-Stepping Framework

The fraction volume of fluid (VOF) method is a successful approach to track the dynamics of free boundaries thanks to its flexibility, efficiency and simplicity. And various efficient numerical methods have been developed to solve the associated VOF equation. This paper applies the two-stage fourth order accurate time discretization in [21, SIAM J. Sci. Comput., 38 (2016), pp. 3045-3069] for the evolution of the VOF equation, aiming to provide a compact diffuse-interface algorithm simple for implementation, in order to incorporate with CFD shock-capturing schemes for the simulation of multi-material/phase problems with sharp interfaces. As such, the algorithm is decoupled from those for fluid flows as long as the velocity of the interface is given. Numerical results demonstrate the high resolution and high-fidelity for the interface capturing.