A coupled level-set and volume-of-fluid method for simulating axi-symmetric incompressible two-phase flows

A coupled level-set and volume-of-fluid (CLSVOF) method, combining the advantages of LS method and VOF method, is presented for simulating axi-symmetric incompressible liquid–gas flow problems. In this method, the interface is implicitly captured by the LS function, and the VOF function is used as a complement to remedy the mass conservation problem aroused in the advection and re-initialization of LS function. We propose a novel explicit algebraic relation between the LS function and VOF function to achieve the coupling of the two methods. Four typical axi-symmetric liquid–gas flow problems, including an equilibrium spherical liquid drop suspending in a quiescent gas environment, a liquid drop falling under the action of gravitational force, a single spherical gas bubble rising in a container filled with quiescent liquid, and the Rayleigh–Taylor instability aroused in a cylindrical container are simulated to validate the CLSVOF method. It is shown that the calculation results obtained by the CLSVOF method agree well with the theoretical solutions and experimental results.