Implementation of ADER scheme for a bore on an unsaturated permeable slope

The paper details the implementation of the Godunov-type finite volume Arbitrary high order schemes using Derivatives (ADER) scheme for the case of a large source term in the continuity equation of the nonlinear shallow water equations. The particular application is the movement of a bore on a highly permeable slope. The large source term is caused by the infiltration into the initially unsaturated slope material. Infiltration is modelled as vertical downwards piston-like flow with Forchheimer quadratic parameterisation of the resistance law. The corresponding ODE is solved using the fourth-order Runge-Kutta method. The surface and subsurface flow models have been tested by comparison with analytical solutions. Example predictions of surface bore propagation and wetting front propagation are presented for a range of slope permeabilities. The effects of permeability on bore run-up, water depths and velocities are illustrated. The ADER scheme is capable of handling the source term, including the extreme case when this term dominates the volume balance.