A naturally sharpened level-set formulation for incompressible free-surface flows

The level set method is widely employed in two-phase flow simulations due to its robustness in handling complex interface topological changes. However, it suffers from two main limitations. First, the method is not inherently mass conservative. Second, the signed-distance property of the level set field can deteriorate under strong convection, particularly in high Reynolds-number flows. Consequently, conventional level set methods often require auxiliary procedures such as sharpening (or re-distancing) and mass correction, which rely on and are sensitive to user-defined parameters and also increase implementation complexity and computational cost. Here, we present a naturally sharpened level-set formulation for incompressible air-water flows that is mass conservative and eliminates the need for these additional algorithmic steps. The resulting free-surface flow modeling and simulation framework is more efficient and robust as demonstrated through several challenging numerical test cases.