Analysis of Motion of Sediment Evolutionary Bedforms by the Particle Finite Element Method

The numerical simulation of sediment transport coupled with evolutionary erodible bedforms is essential for the analysis of the morphodynamics of sediment structures. The erosion and evolution of a bedform is a dynamical coupled problem that must be studied with methods able to simulate the interface between the sediment flow and erodible bed.

The Particle Finite Element Method (PFEM) with movable mesh was successfully applied in the past to model free surface flows problems such as the interaction of flows with boundaries, or the strong erosion of beds subjected to high velocity flows [1].

A numerical strategy based on the new version of the Particle Finite Element Method with fixed mesh (PFEM-2) is presented for the simulation of sediment flows coupled with evolutionary erodible boundaries.

The present approach models in a Lagrangian frame with fixed mesh the evolution of a bedform using an advection–diffusion equation and is solved with the explicit time integration method PFEM-2 from [2], which permits to employ intermediate-large time steps and takes advantage of its easy computer parallelization. This approach overcomes the restrictions of previous PFEM developments applied to model the erosion, see [1], that was simulated by the conversion of soil to fluid elements leading to sudden changes in the geometry.

In this work flow and bedform are coupled in a staggered way. Flow is solved using a standard Finite Element fluid solver compatible with Arbitrary Lagrangian–Eulerian (ALE) techniques, which allows the deformation of the mesh at every time step. The evolution of bedform and flow is linked by the empirical sediment flux relation of Meyer-Peter-Müller.

The model is able to reproduce with good agreement the lab experiments of the evolution of subaqueous small dunes under different flow conditions from [3].

This research is supported by MICIIN Grant #BIA-2015-64994-P (MINECO/FEDER)

REFERENCES

[1] Oñate E, Celigueta MA, Idelsohn SR (2006) Modeling bed erosion in free surface flows by the particle finite element method. Acta Geotechnica 1(4):237–252 


[2] Bravo, R Becker P, Ortiz P (2017) Numerical simulation of evolutionary erodible bedforms using the particle finite element method. Computational Particle Mechanics 4(3):297–305.

[3] Leclair S (2002) Preservation of cross-strata due to the migration of subaqueous dunes: an experimental investigation. Sedimentology 49(6):1157–1180