Shallow Water Moment Models for Bedload Transport Problems (Communications in Computational Physics, 2021)
In this work a simple but accurate shallow model for bedload sedimenttransport is proposed. The model is based on applying the moment approach to theShallow Water Exner model, making it possible to recover the vertical structure of theflow. This approach allows us to obtain a better approximation of the fluid velocityclose to the bottom, which is the relevant velocity for the sediment transport. A general Shallow Water Exner moment model allowing for polynomial velocity profiles ofarbitrary order is obtained. A regularization ensures hyperbolicity and easy computation of the eigenvalues. The system is solved by means of an adapted IFCP schemeproposed here. The improvement of this IFCP type scheme is based on the approximation of the eigenvalue associated to the sediment transport. Numerical tests arepresented which deal with large and short time scales. The proposed model allows toobtain the vertical structure of the fluid, which results in a better description on thebedload transport of the sediment layer.