Augmented HLL Riemann solver including slope source term for 1D mixed pipe flows

In this paper, the augmented version of finite volume Harten–Lax–van Leer (HLL) solver, including source terms, is extended to free-surface and pressurized mixed pipe flows over complex and frictional topography. This augmented HLL Riemann solver is employed for the flux approximation at the cell interface, where source terms are split into two parts based on the wave propagation speed. The friction term is treated using a splitting implicit method to maintain stability over dry beds. The Preissmann slot method is adopted to reproduce pressurized flow in the conduit. The performances of the numerical model are investigated by several numerical tests and compared with existing methods showing clear improvements.