Fluid Dynamics with
Erosion
Brandon Lloyd
COMP 259
May 2003
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Overview
• Sediment transport in open channels
- Bed-load transport
- Suspensed transport
•
•
•
•
Sediment transport models
Model used for this project
Implementation issues
Future work
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Sediment Transport
• Bed-load transport: sliding,
rolling, saltating
• Suspended transport: sediment
moves through the fluid
Suspension
Sediment
Bed-load
Bed
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Bed-load transport
Once the forces acting
on particles are strong
enough to intiate motion…
Figure from Chanson, p. 200
Figure from Chanson, p. 180
… particles slide, roll,
and saltate down the
river bed at a steady
rate.
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Suspended Transport
Suspension
occurs here
• Particles entrained
at the bed-load layer
• Transported by
convection,
diffusion, and
turbulence
Figure from Chanson, p. 200
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Sediment Transport Models
• Difficult problem –
most models are
empirical.
• Usually make
simplifying
assumptions about
flow.
• Many different
formulas exist.
Table from Chanson, p. 198
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
My Model
vc,s  C1ws ,
qs  C2
v 2  vc2, s
2
s
w
hbed
 (c s  qs )( 1  P0 )
t
cs  qs  accretion
cs  qs  erosion
v : fluid velocity
vc,s : critical velocity
ws : fall velocity
Ci : constants
cs : sediment concentrat ion
P0 : porosity
• Simplified version of
model used in [Haupt
et al. 1999]
• Transport occurs above
critical velocity.
• Fluid has a transport
capacity related to
velocity.
• Concentration of
sediment relative to
capacity determines
change in terrain
h : height
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Implementation Issues
zero concentration
• Semi-Lagrangian
advection causes
mass loss in the
presence of
eddies.
• What to do at
boundaries?
backward tracing does
not see wall  mass loss.
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Implementation Issues
• Semi-Lagrangian
advection causes
mass loss in the
presence of
eddies.
• What to do at
boundaries?
Recycle concentration
(limits the time-step)
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Results
• Nice swirls of sediment with
erosion and deposition at
interactive rates (on a fast
machine .)
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Future Work
•
•
•
•
•
Add bed-load transport
Add instability based on slope
Add variable material properties
Fix spikes and improve robustness
Better handling of velocities near
heightfield.
• Experiment with and compare different
fluid/advection models
• Add a free surface
• Implement on GPU
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
References
CHANSON, H. 1999. The Hydraulics of Open Channel Flow: An
Introduction. Arnold.
HAUPT, B. J., SEIDOV, D. AND STATTEGGER, K. 1999. SEDLOB
and PATLOB: Two numerical tools for modeling climatically
forced sediment and water volume transport in large ocean
basins. In Computerized Modeling of Sedimentary Systems.
Springer-Verlag, Berlin.
WU, W., RODI, W. AND THOMAS, W. 2000. 3D numerial
modeling of flow and sediment transport in open channels.
Journal of Hydraulic Engineering, 4-15.
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL