High order shallow water equations: application to dam break problems

Abstract

Abstract The majority of shallow flows that occur in sediment transport are turbulent, and as a result, cannot be described by shallow water equations. This paper introduces a set of shallow water equations based on the long-wave second-order approximation. The set of equations is employed in the modeling of sediment transport in coastal zones, thereby facilitating the consideration of a diverse array of civil engineering problems. The derived sediment transport model is capable of representing the coupling of sediment transport phenomena with turbulent flow in shallow regions. The proposed models utilize the concept of two-velocity vectors (comprising a mean velocity and a distortion velocity due to turbulence) in the primary flow directions. To demonstrate the efficacy of the model, a numerical scheme is employed to solve a number of dam-break problems that are well-known in the field.