The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Fluid Dynamics with Erosion
Brandon LloydCOMP 259May 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
Sediment
Suspension
Bed-load
Bed
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Bed-load transport
Once the forces actingon particles are strongenough to intiate motion…
… particles slide, roll, and saltate down the river bed at a steady rate.
Figure from Chanson, p. 180
Figure from Chanson, p. 200
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
• 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
height :
porosity :
ionconcentratsediment :
constants:
velocityfall:
velocitycritical :
velocityfluid :
erosion
accretion
1
,
0
0
2
2,
2
21
h
P
c
C
w
v
v
qc
qc
)P)(q(c t
h
w
vvCqwCv
s
i
s
c,s
ss
ss
ssbed
s
scssc,s
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?
zero concentration
backward tracing doesnot 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.
