ABSTRACT
This paper presents a novel high-order approximate Riemann solver capable of treating porous and bottom discontinuities, in the framework of the 1D Shallow Water Equations with porosity. To this purpose, a new set of well-balanced governing equations, based on the isotropic porosity parameter, is derived, and the novel augmented non-conservative Riemann problem is solved adopting the path-conservative DOT scheme, which is robust, general and entropy satisfying. The implementation in the ADER framework, together with a Total Variation Diminishing reconstruction, allows achieving a non-oscillatory second order accurate scheme in both space and time. The proposed numerical solver preserves the quiescent flow condition, which is a crucial task of the SWEs modeling, over a non-flat bottom and with a non-uniform porous field. Finally, the numerical model is validated against a selection of Riemann problems, which develop across porosity discontinuities and bed steps including shocks and transonic rarefactions.
