Abstract. This paper considers two-dimensional numerical simulation of the run-up of nonlinear surface gravity waves on the basis of Navier-Stokes equations. The statement of the problem is formulated and its boundary and initial conditions are described. A discrete model is constructed using the method of splitting with respect to physical processes. A discrete finite-element model of this problem is developed taking into account the cell fill factor. The conservativeness of the discrete model was investigated and the approximation error of the finite-difference scheme is found. The results of a two-dimensional numerical simulation of the run-up of nonlinear surface gravity waves on coastal structures of shallow-water offshore areas are presented.

Received: October 16, 2012

AMS Subject Classification: 76D33

Key Words and Phrases: Navier-Stokes equations, numerical simulation, splitting method, run-up of nonlinear surface gravity waves

Download paper from here.