The shallow water equations are widely applied for the simulation of flow routing in rivers and floodplains, as well as for flood inundation mapping. From a mathematical point of view, they are a hyperbolic system of nonlinear partial differential equations, whose numerical integration is sometimes computationally burdensome. For this reason, the interest of many researchers has been focused on the study of simplified forms of the original set of equations, which requires less computational effort. One of the most commonly applied simplifications consists in neglecting the inertial terms, which changes the hyperbolic model to a parabolic one. The effects of such a choice on the outputs of the simulations of flooding events are controversial and an important topic of debate. In the present paper, two numerical models, recently proposed for the solution of the complete and zero-inertia forms of the shallow waters equations, are applied to several unsteady flow routing scenarios. We simulate synthetic and laboratory studies, starting from very simple geometries and moving towards complex topographies. Analyzing the role of the terms in the momentum equations, we try to understand the effect, on the computed results, of neglecting the inertial terms in the zero-inertia formulation. We analyze the computational costs.
Comparative Analyses between The Zero-Inertia and Fully Dynamic Models of the Shallow Waters Equations for Unsteady Overland Flow Propagation
