INTRODUCTION: Sediment transport in shallow water is ofconcern in many hydro-ecological problems. Erosion orsedimentation processes are not only relevant in perennialsystems as rivers, lakes, reservoirs and coastal regions, butalso in ephemeral phenomena like gullies, inundations andfloods.

Sediments are transported by water flow, and vice-versasediments have an effect on flow, due to changes of theground surface level. That two-way coupling has to be takeninto account when sediment transport is simulated incomputer models

We present a multiphysics approach of such a coupledmodel. The shallow water equations (SWE) for water heightand velocity are coupled with transport for particulatematter and a bedload equation. The non-linear system of fivedifferential equations is solved simultaneously. UsingCOMSOL Multiphysics® software a set-up is presented thatdemonstrates the feasibility of the approach.

COMPUTATIONAL METHODS: We couple the Shallow WaterEquations (SWE) (1) with equations for particular andbedload transport (2):

with total water depth H, water height above referenceheight η, velocity vector u, acceleration due to gravity g,Manning parameter n, particle concentration c, depth belowreference d=H-η, sedimentation E, re-mobilization D, andbedload porosity θ. Terms D and E are specified in terms ofsettling velocity, Shields parameter, particle diameter anddensity [1].

RESULTS: The situation sketched in Figure1 was simulated using numerical methodssolving the coupled system of eq.s (1) &(2). The Finite Element mesh was refinedat the obstacle walls, as depicted inFigure 3. See Table 1 for parameters.

CONCLUSIONS: The exampleshows that basic phenomena ofsediment transport likedeposition and depressioncreation (Figure 5) in floodingwater can be captured by a 2Dcoupled modelling approach. Theset-up could become abenchmark for coupled flow andtransport pro-cesses in rivers andchannels (1D), and duringflooding events (2D).

REFERENCES:1. Li S. and Duffy C.J., Fully coupled approach to modeling shallow water

flow, sediment transport, and bed evolution in rivers, WATER

RESOURCES RESEARCH, VOL. 47 (2011)

2. https://geographyas.info/rivers/river-landforms/

Figure 2. Depression formation behind an obstacle [2]

Figure 3. FE Mesh

Figure 4. Water table and ground surface at times t = 0.1, 0.3, 0.5 & 0.9 s

Table 1. List of parameters

Figure 5. Depression at obstacle, Wadi Abyad

Figure 1. Sketch of flood domain with a cylindrical obstacle

Multiphysics Approach to Sediment Transport in Shallow WaterE. Holzbecher, A. Hadidi

Applied Geosciences, German Univ. of Technology in Oman (Gutech), Muscat, Oman

¶h

¶t+Ñ× Hu( ) = 0

¶u

¶t+ u×Ñ( )u+ gÑH + ghn2

u

h4/3u = 0

¶c

¶t+ u×Ñ( )c-

1

HE - D( ) = 0

¶d

¶t-

1

1-qE - D( ) = 0

Results of the numerical simulation are depicted in Figure 4.

(1)

(2)

t=0.1 t=0.3

t=0.5 t=0.9

Excerpt from the Proceedings of the 2018 COMSOL Conference in Lausanne