CABARET scheme is an explicit conservative-characteristic second order finite volume scheme for hyperbolic PDEs. It has a computational template of minimal size and it is time-reversible (non-dissipative) if monotonization procedures are not used. In this work, we present several key modifications to the algorithm, which allowed us to use CABARET in different problems in oceanology, fluid-structure interaction, transonic flows and thermoacoustic instability. These modifications include: approximation of moving boundaries and free surfaces, time-reversible sonic point processing algorithm, approximations on a sphere, modeling problems with a time delay, hydrostatic and non-hydrostatic oceanological models. Some verification results are provided.

This is a joint work with V. Goloviznin, A. Solovjev, Pavel A. Mayorov, and Petr A. Mayorov