A Coupled Hydro-Morphodynamic Model for Sediment Transport using the Moment Approach

Sediment transport is crucial in the hydro-morphodynamic evolution of free surface flows in shallow water environments, which is typically modeled under the shallow water assumption. In classical shallow water modeling for sediment transport, the vertical structure of the flow is collapsed into a depth-averaged and near-bed velocity, usually reconstructed empirically, e.g., using a parameterized logarithmic profile. In practice, large variations from such empirical profiles can occur. It is therefore essential to resolve the vertical structure of the velocity profile within the shallow water framework to better approximate near-bed velocity. This study introduces a model and simulations that incorporate vertical velocity variations and bottom erosion-deposition effects in sediment transport, providing a computationally efficient framework for predicting sediment dynamics in shallow water environments. We employ the so-called moment model approach for the velocity variation, which considers a polynomial expansion of the horizontal velocity in the scaled vertical direction. This allows the use of a complex velocity profile with an extended set of variables determined by the polynomial basis coefficients, resolving the vertical structure as part of the solution. The extended model comprises four components: (1) the standard shallow water equations; (2) moment equations governing evolution of the basis coefficients; (3) an evolution equation for sediment concentration; and (4) a transport equation for the bed. This enables a coupled model for bedload and suspended load transport. We use a hyperbolic regularization technique to ensure model stability and realistic eigenvalues. Several numerical tests, including dam-break cases with and without wet/dry fronts, validate our results against laboratory data.