New physically based approach of mass conservation correction in level set formulation for incompressible two-phase flows

A novel physically based mass conservation model is developed in the framework of a level set method, as an alternative to the Heaviside function based formulation classically employed in the literature. In the proposed volume fraction based level set approach, expressions for volume fraction function for each interfacial computational cell are developed, and are subsequently correlated with the corresponding level set functions. The volume fraction function, derived from a physical basis, is found to be mathematically analogous to the Heaviside function, except for a one-dimensional case. The results obtained are compared with the benchmark experimental and numerical results reported in the literature. Finally, transient evolution of a circular bubble in a developing shear flow and rising bubbles in a static fluid, are critically examined. The Cox angle and the deformation parameter characterizing the bubble evolution are critically examined. An excellent satisfaction of the mass conservation requirements is observed in all case studies undertaken.