An Immersed Boundary Method for

Modeling Bank Retreat in Delft3D

Delft Software Days 2015

5 November 2015 Aukje Spruyt1, Bert Jagers1, Alberto Canestrelli2,

Willem Ottevanger1 1 Deltares, Delft, Netherlands 2 PennState University, USA / Tidal Forecasting and

Early Warning Center (ICSPM), Venice, Italy

How to represent a meandering river?

s

n

Boundary-fitted

curvilinear co-ordinates:

Bank lines on a

rectangular grid:

How to represent migrating bank lines?

Adaptive boundary-fitted

curvilinear coordinates

bank

erosion

Disadvantages: • interpolation of all cell data to new

positions artificial smoothing

• what about hydraulic structures?

• cell deformation orthogonality

issues enhanced truncation

errors

How to represent migrating bank lines?

Immersed boundaries

(on curvilinear grids)

bank

erosion

Advantages: • no interpolation of cell data to

new positions; hydraulic

structures stay where they are

• no time-varying cell deformation

• curvilinear grid might still be

used to minimize grid size and

hence computer time and disk

space

How to represent the bank lines?

Lines (Spruyt et al, 2011): • well defined bank line

• challenges: cut-offs & parallellization

• no flow outside lines

Deep area fraction Fd(i,j): • dynamic reconstruction of bank lines

• dual bed properties if 0<Fd(i,j)<1

• average properties used during flood

How to represent migrating bank lines?

Immersed boundaries

on Cartesian mesh

Advantages: • no interpolation of cell data to

new positions; hydraulic

structures stay where they are

• no time-varying cell deformation

• easier algorithms for bank line

reconstruction and boundary

treatment at the banks

bank

erosion

Immersed Boundary Method

Numerical approach: • Cut-cell treatment for the continuity equations

• Ghost cell treatment for the momentum equations

• Simple bank-erosion model for the movement of bank lines

Immersed Boundary Method

Details:

• Canestrelli et al, 2015.

Int. J. Numer. Meth.

Fluids

DOI: 10.1002/fld.4180

Immersed Boundary Method

Results for a 2D annular test case

Also interesting

for various flow-

only applications

Round pillar

Simple meandering river

Friedkin erosion test

Q = 0.111•10-3 m3/s

i = 0.001

W = 0.05 m

Friedkin erosion test – Results

Friedkin erosion test – Results

A few more settings … time to simplify

Next steps

• Make developments available in the standard open-source

Delft3D code (by DSD 2016) & simplifying the use

• Improve flooding-and-drying algorithm

• Apply the method to a realistic river bank erosion case.

• Investigate the implementation of “bank accretion” (how to

transition a cell from low/channel to high/bank – elevation

threshold, vegetation development, …).

• Apply the method to delta simulations.

?

High

Low

Low or High?