Numerical simulation of free-surface flow using the level-set method with global mass correction

A new numerical method that couples the incompressible Navier-Stokes equations with the global mass correction level-set method for simulating fluid problems with free surfaces and interfaces is presented in this paper. The finite volume method is used to discretize Navier-Stokes equations with the two-step projection method on a staggered Cartesian grid. The free-surface flow problem is solved on a fixed grid in which the free surface is captured by the zero level set. Mass conservation is improved significantly by applying a global mass correction scheme, in a novel combination with third-order essentially non- oscillatory schemes and a five stage Runge-Kutta method, to accomplish advection and re-distancing of the level-set function. The coupled solver is applied to simulate interface change and flow field in four benchmark test cases: (1) shear flow; (2) dam break; (3) travelling and reflection of solitary wave and (4) solitary wave over a submerged object. The computational results are in excellent agreement with theoretical predictions, experimental data and previous numerical simulations using a RANS-VOF method. The simulations reveal some interesting free-surface phenomena such as the free-surface vortices, air entrapment and wave deformation over a submerged object.