Novel variable reconstruction and friction term discretisation schemes for hydrodynamic modelling of overland flow and surface water flooding

Due to the recent advances in computing and data acquisition technologies, numerical models solving 2D shallow water equations (SWEs) are now widely used predicting overland flow surface flooding process natural catchments. In catchment-scale flood modelling, addition calculation of convective terms that usually achieved through local Riemann problems capture transient dynamics, correct discretisation source is also essential handle complex domain topography ensure accurate stable solutions. The external forces induced by gravity bed friction create key drive change momentum SWEs affect stability accuracy adopted scheme, especially for applications involving very depth (e.g. wet dry fronts, flows). Herein, new schemes introduced reconstruct face values variables a fully implicit algorithm improved discretise stiff terms, context developing Godunov-type finite volume hydrodynamic model simulation depth. Five analytical test cases considered validate resulting results compared with those produed two alternative schemes. performance further demonstrated reproducing event 2500 km2 Eden Catchment, UK.