Modeling of non-breaking and breaking solitary wave run-up using FORCE-MUSCL scheme

A numerical model based on the non-linear shallow water equations is developed to investigate the propagation and run-up of both non-breaking and breaking solitary waves. The present model utilizes an explicit centered scheme in conjugation with monotonic upstream scheme of conservation laws to estimate interface fluxes along with the surface gradient method for source term treatment. An optimal third-order total variation diminishing Runge-Kutta explicit scheme is used for time integration of the semi-discretized equations. The proposed scheme is second order accurate in space and time and capable of efficiently capturing the breaking induced discontinuities in flow depth. The model accurately represents a breaking wave as a moving bore or a hydraulic jump and shows a remarkable property of mass conservation during the entire run-up and run-down motions. The numerical results satisfactorily agree with available analytical solutions, experimental data as well as with three existing run-up laws.