Simulating the dynamics of a fluid with a free surface in a gravitational field by a CABARET method

An explicit conservative-characteristic CABARET method is proposed for calculating the dynamics of a fluid with a free surface in a gravitational eld in a weakly compressible approximation. The developed method has the second order of approximation in time and space, minimum computational template of one space-time cell and minimum numerical viscosity. A difference scheme is tested on problems with various values of the surface tension coefficient and gravitational acceleration with various signs,including the problem of the development of the Rayleigh-Taylor instability. Taking into account the forces of surface tension makes it possible to get rid of high-frequency oscillations on the free surface when calculating unstable problems and regularizes the solution.