On Derivation and Physical Interpretation of Level Set Method-Based Equations for Two-Phase Flow Simulations

The level set (LS) method is one of the most popular and recent methods for two-phase flow simulation. However, its origin and governing equations rely heavily on mathematical sources. The present work attempts mass and volume conservation law-based derivation of the LS advection equation and the continuity equation, respectively, for two-phase flow with phase change. Physical interpretation of the Heaviside function and the Dirac delta function, used in the LS method, is done here in a novel way and the resulting expressions are used in the derivations. The diffused interface, used in the LS method, is shown to introduce negligible error on a sufficiently fine grid.