Modeling of the climbing of nonlinear surface gravity waves on the basis of Navier-Stokes equations

The paper deals with the problem of numerical modeling of the climbing of nonlinear surface gravity waves on the basis of Navier-Stokes equations. The two-dimensional formulation of the problem is considered, and the boundary and initial conditions are defined. The decomposition method for physical processes is used to construct a discrete model capable of accounting for the factor of filled cells. The results of two-dimensional numerical modeling of the process of climbing of nonlinear surface gravity waves on shallow water areas are presented.