A Hyperbolic Moment Based Shallow Water Model for Coupled Bedload Suspended Load Morphodynamics with Variable Density

Abstract

In this paper, we develop the Hyperbolic Shallow Water Exner Moment model with Erosion and Deposition (HSWEMED), extending the shallow water moment framework to capture coupled morphodynamics with erosion and deposition. HSWEMED introduces a suspended-sediment concentration equation, couples concentration-dependent mixture density with the momentum and higher-order moment equations, and includes source terms due to erosion and deposition. Starting from the incompressible Navier-Stokes equations for a water-sediment mixture, we derive a coupled system consisting of the shallow water equations, moment equations for polynomial velocity coefficients, a depth-averaged suspended-sediment equation, and an Exner equation for bedload transport with erosion-deposition coupling. Although the transported scalar is depth-averaged, we reconstruct a low-order vertical concentration profile consistent with the moment representation of velocity, providing the near-bed concentration needed in the closure. We prove hyperbolicity through hyperbolic regularization and derive dissipative energy balance relations for lower-order models. Numerical results are obtained with a path-conservative finite-volume scheme based on a Lax-Friedrichs-type flux. Several dam-break tests, including wet/dry front cases, are validated against laboratory experiments, showing improved accuracy over existing shallow water moment models. The proposed HSWEMED provides a mathematically well-posed and computationally efficient framework for morphodynamic simulations.