Abstract. The paper considers two-dimensional numerical simulation of nonlinear gravity wave run-up to a steep coastal slope. The problem is formulated, boundary and initial conditions are described, the numerical model is based on Navier-Stokes equations. The 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. Two-dimensional run-up model of a surface wave to a steep coastal slope, generation of reflected run back and their superposition are presented.

Received: February 13, 2013

AMS Subject Classification: 76D33

Key Words and Phrases: numerical simulation, Navier-Stokes equations, splitting method, run-up of surface gravity waves, reflection at steep coastal slope, superposition of run-up and run back waves

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