Shallow Water Moment Models for Bedload Transport Problems

Abstract

In this work a simple but accurate shallow model for bedload sediment transport is proposed. The model is based on applying the moment approach to the Shallow Water Exner model, making it possible to recover the vertical structure of the flow. This approach allows us to obtain a better approximation of the fluid velocity close to the bottom, which is the relevant velocity for the sediment transport. A general Shallow Water Exner moment model allowing for polynomial velocity profiles of arbitrary order is obtained. A regularization ensures hyperbolicity and easy computation of the eigenvalues. The system is solved by means of an adapted IFCP scheme proposed here. The improvement of this IFCP type scheme is based on the approximation of the eigenvalue associated to the sediment transport. Numerical tests are presented which deal with large and short time scales. The proposed model allows to obtain the vertical structure of the fluid, which results in a better description on the bedload transport of the sediment layer.

Macro-micro decomposition for consistent and conservative model order reduction of hyperbolic shallow water moment equations: A study using POD-Galerkin and dynamical low rank approximation

“…It was shown that the HSWME yield accurate results while preserving hyperbolicity of the model equations [29]. Recently, the model has been applied to sediment transport [17] and analysis of steady states and equilibrium stability has been performed [21,28].…”

“…The model is based on a hyperbolic regularization of [32] using techniques from kinetic theory [15,30]. The increased accuracy of the model was shown in numerical simulations, including sediment transport [17]. However, the HSWME also lead to a higher computational cost and memory footprint due to additional nonlinear equations for the expansion coefficients of the polynomial velocity profile.…”