A semi-Lagrangian splitting method for the numerical simulation of sediment transport with free surface flows

Sébastien Boyaval (1, 2) , Alexandre Caboussat (3) , Arwa Mrad (4) , Marco Picasso (4) , Gilles Steiner (5, 6)

1 Saint-Venant - Laboratoire d'Hydraulique Saint-Venant / Saint-Venant laboratory for Hydraulics
2 MATHERIALS - MATHematics for MatERIALS
3 Geneva School of Business Administration
4 MATHICSE - Mathematics Institute of Computational Science and Engineering [Lausanne]
5 EPFL - Ecole Polytechnique Fédérale de Lausanne
6 Ycoor Systems SA

We present a numerical model for the simulation of 3D poly-dispersed sediment transport in a Newtonian flow with free surfaces. The physical model is based on a mixture model for multiphase flows. The Navier–Stokes equations are coupled with the transport and deposition of the particle concentrations, and a volume-of-fluid approach to track the free surface between water and air. The numerical algorithm relies on operator-splitting to decouple advection and diffusion phenomena. Two grids are used, based on unstructured finite elements for diffusion and an appropriate combination of the characteristics method with Godunov’s method for advection on a structured grid. The numerical model is validated through numerical experiments. Simulation results are compared with experimental results in various situations for mono-disperse and bi-disperse sediments, and the calibration of the model is performed using, in particular, erosion experiments.

Mots clés: Particle flow; Sediment transport; Mixture model; Free surface flow; Operator splitting

Domaines: Mathématiques [math]; Analyse numérique [math.NA]; Physique [physics]; Mécanique [physics]; Mécanique des fluides [physics.class-ph]

Sébastien Boyaval, Alexandre Caboussat, Arwa Mrad, Marco Picasso, Gilles Steiner. A semi-Lagrangian splitting method for the numerical simulation of sediment transport with free surface flows. Computers and Fluids, 2018, 172, pp.384-396. ⟨10.1016/j.compfluid.2018.04.002⟩. ⟨hal-01940147⟩