Solitary wave run up and overtopping by a semi-implicit finite-volume shallow-water Boussinesq model

A semi-implicit finite-volume method is described for solving the nonlinear shallow-water equations with the incorporation of Boussinesq terms in a novel manner, allowing runup, rundown and. overtopping on impermeable surfaces of variable slope. The model assumes continuous flow, as it is in reality, in contrast to the Riemann-solver approach for capturing discontinuities. Zero pressure gradient is specified at the wet/dry interface. The theory with Boussinesq terms is valid for small wave heights and mild slopes and reduces to the nonlinear shallow-waler equations in initially dry areas. The scheme is tested for solitary waves on a horizontal, frictionless bed and applied to runup on various slopes. Comparisons with experiment without breaking are in close agreement. With breaking a numerical filter enables good prediction of maximum runup, although not of profiles during breaking.