Modeling Propagation of Long Wave Run-Up along Sloping Boundaries

Development of two-dimensional (2D) hydrodynamic model to simulate the propagation of long waves in a domain with sloping boundaries is presented in this paper. This study adopts the finite-volume method to solve hyperbolic shallow water equations and model various wave run-up problems. Godunov type HLL approximate Riemann solver is combined with divergence form of the bed slope to be able to simulate waves on irregular topography. The surface gradient method is used to have a well balanced scheme that the numerical errors can be removed. The accuracy is second order in space and time. The computational domain is constructed with unstructured triangular cells. The developed model, which is capable of simulating flow over dry and irregular domain, is run for dam break wave over a sloped bottom, tidal wave onto a sloped beach and solitary wave around a conical island. The experimental and numerical results published are used to verify the stability and accuracy of the model.