Numerical modelling of three-dimensional variable-density flows by the multilayer hydrostatic model based on the CABARET scheme

The article is devoted to the extension of the multilayer hydrostatic model CABARETMFSH to the case of three spatial variables. The model describes the dynamics of a fluid with a variable density and a free surface. The hyperbolic decomposition algorithm gives a representation of the matrix of the system as a product of 4$\times$4 matrices, the eigenvalues of each of which are always real. An explicit CABARET scheme is used to solve the system of hyperbolic equations in each layer. To validate the model, the problem of a threedimensional fluid flow with a variable density is used. The numerical calculations are in satisfactory agreement with experimental data.