Explicit numerical algorithm for non-hydrostatic fluid dynamics equations based on the CABARET scheme

The article presents a non-hydrostatic model of the dynamics of a stratified slightly compressible fluid with a free-surface. An explicit scheme CABARET-NH (CABARET Non-Hydrostatic) for the numerical solution of the constructed system of differential equations in mixed Eulerian-Lagrangian coordinates based on the balance-characteristic scheme of the CABARET class is described. The well-balanced property of the numerical scheme is proved. The results of calculations of the free-surface oscillation problem are presented.