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Page 1: The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Fluid Dynamics with Erosion Brandon Lloyd COMP 259 May 2003.

The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

Fluid Dynamics with Erosion

Brandon LloydCOMP 259May 2003

Page 2: The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL 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

Page 3: The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Fluid Dynamics with Erosion Brandon Lloyd COMP 259 May 2003.

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

Page 4: The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Fluid Dynamics with Erosion Brandon Lloyd COMP 259 May 2003.

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

Page 5: The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Fluid Dynamics with Erosion Brandon Lloyd COMP 259 May 2003.

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

Page 6: The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Fluid Dynamics with Erosion Brandon Lloyd COMP 259 May 2003.

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

Page 7: The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Fluid Dynamics with Erosion Brandon Lloyd COMP 259 May 2003.

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

Page 8: The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Fluid Dynamics with Erosion Brandon Lloyd COMP 259 May 2003.

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.

Page 9: The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Fluid Dynamics with Erosion Brandon Lloyd COMP 259 May 2003.

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)

Page 10: The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Fluid Dynamics with Erosion Brandon Lloyd COMP 259 May 2003.

The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

Results

• Nice swirls of sediment with erosion and deposition at interactive rates (on a fast machine .)

Page 11: The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Fluid Dynamics with Erosion Brandon Lloyd COMP 259 May 2003.

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

Page 12: The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Fluid Dynamics with Erosion Brandon Lloyd COMP 259 May 2003.

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.


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