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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?