A coupled non–saturated model for cohesionless sediment transport

Abstract

A continuous formulation and a suitable finite element numerical method are intro- duced for simulating interactions between fluid flow and evolving bedforms. Sed- iment transport is modeled by solving the non–equilibrium saltation dynamics of non-cohesive grains. The approach integrates the Navier–Stokes equations for in- compressible fluid flow, a conservation equation to track evolution of the fluid–solid interface, and mass and momentum equations governing sediment dynamics. The latter conservation laws are depth–integrated over the saltation layer, resulting in a reduced–dimensional framework that improves computational efficiency. A built–in explicit procedure enables a straightforward two–way coupling between sediment and fluid dynamics. To stabilize flow computations and ensure the positivity of key variables, such as saltation layer density and sediment thickness, the numerical algorithm is a non–oscillatory finite element method (NFEM); its positive definite characteristic is essential for flows in combined erodible/non–erodible scenarios. Numerical experiments assess the model response for transient conditions, includ- ing wind tunnel environments and sand dune–atmospheric boundary layer interac- tions. Among other features, test’s setups are designed to explore advantages of the proposed model under severe transient conditions in comparison with results of standard saturated flow based models.