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

2. 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

3. 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

4. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Bed-load transport Once the forces acting on particles are strong enough 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

5. 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

6. 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

7. 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

8. 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 does not see wall  mass loss.

9. 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)

10. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Results Nice swirls of sediment with erosion and deposition at interactive rates (on a fast machine.)

11. 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

12. 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.