Formal derivation of a new sediment transport model using a multiscale procedure: Numerical Validation

Abstract

We study in this work structures formed under a unidirectional flow. The main problem that addresses sediment transport by aquatic flow. We present the formal derivation of a new sediment transport model by using a multiscale procedure in time and space. We consider two non-miscible layers of different materials with physical properties by including friction. Interactions at the fluid-sediment interface and those internally sediment are also taken into account. The derived model is the Saint–Venant–Exner type obtained by coupling a Saint-Venant system governing the hydrodynamic component and an Exner equation describing the morphodynamical component. The first part of this work takes into account two major contributions namely the formal derivation of new unidirectional Saint–Venant–Exner model inspired by the work in Fernández-Nieto et al. (2017) and the introduction of a new multiscale parameterization in space-time characterized by the combination of classical variability and rapid variability of solutions. However, we have limited ourselves to the case of a first order approximation which does not include viscosity terms. Further analysis of the second order approach leading to a viscous model can be deduced from the work in Fernández-Nieto et al. (2013). We also propose a numerical study of the derived model. Thus, we develop finite volume numerical schemes. The numerical approach employs a Riemann solver, and various options ranging from an exact solver to an approximate Riemann HLL-type and HLLC-type solvers. We did some numerical tests leading to consistent and effective results.

Keywords

• Formal derivation
• Navier–Stokes equations
• Saint–Venant–Exner model
• Multiscale analysis
• Finite volume schemes
• Riemann solver