Conservative Eulerian method for numerical investigation of the hydrodynamics of liquids with a free surface

An effective numerical method is suggested for investigation of the hydrodynamics of liquids with a free surface. The method is a conservative Eulerian method that is useful for investigation of processes with turbulent behavior of the surface of the liquid that are accompanied by generation of waves, splash, spatter, etc. In the present method, apart from hydrodynamic equations, a transfer equation is used to describe transfer of the liquid phase. A method of numerical solution free from grid diffusion is suggested for this equation. It is proved that the conservative Eulerian method is adequate quantitatively for modeling the motions of a liquid with a slight deformation on its surface and adequate qualitatively for complicated motions.