Implementation of the level set method for modeling the dynamics of systems with fluid interfaces

A numerical algorithm for modeling the dynamics of two immiscible fluids with deformable interfaces based on the level set method is worked out. Numerical simulations of the Rayleigh -Taylor instability development and periodical patterns that arise at the fluid interface under horizontal vibrations are carried out. Calculations are made using adaptive mesh refinement and parallel programming techniques. The results are found to be in good agreement with the numerical and experimental data known from the literature.