1. GPU Workshop: July, 2010 Scott Briggs PhD Candidate Civil/Env. Engineering Contaminant Hydrogeology Supervisors: B. E. Sleep and B. W. Karney

2. Contaminant Hydrogeology Study and management of groundwater resources. We use computer models to determine the best approach and expected results of a given system. Research specialization in zones of fractured rock using bioremediation. Bioremediation: the degradation of contaminants to natural or safe levels. (ex. Hydrocarbons, chlorinated solvents)

3. Lattice Boltzmann Methods for Modeling Rock Fractures Fluid flow emerges from the simulation of the intrinsic particle streaming and collision processes. Can incorporate micro-scale interactions: – Changing and complex boundaries. – No-slip condition. – ‘External’ forces – such as gravity and/or biofilm-fluid interactions. Parallelization of LBM algorithms: – Minimal overhead due to discretized domain and locality requirements of LBM. 3

4. Lattice Boltzmann Method: D2Q9 4 Sukop and Thorne, 2005

5. Parallel Plate Validation Single Precision 7.4 % relative error Double Precision (below) 0.78% relative error

6. Backward facing step Validation Qualitative results equal to those of Armaly et al. (1983) Re = 100: Reattachment at 3 Step heights Re = 150: Reattachment at 4 Step heights Re = 200: Reattachment at 5 Step heights

7. Cubic Law in Rock Fracture Flow The cubic law is an approximation of the N-S equations for laminar flow through parallel plates Traditionally the cubic law has been used in rock fracture hydrogeology. However there was a need to account for: – Surface roughness at varying scales – Inertial effects due to tortuosity of fracture – Contact area in 3D Method of comparison: Take cubic law: Compare flow rates between model and cubic law.

8. Rock Fracture Sample #1 Flow Comparison to Cubic Law Flow rate: 8.1% deviation for Re of 0.06,.6 and 6. – Re = 60 deviation of 10% – Re = 600, deviation of 20% (τ approaching 0.5) – Brush and Thompson (2003) found 10% deviation from cubic law using Stokes (low Re) simulations.

9. Rock Fracture Sample #2 Flow Comparison to Cubic Law Flow rate: 50-55% deviation for Re = 0.0006, through Re = 60. – Brown (1987) found the Cubic law to hold within 50% – Tsang (1984) suggested a order of magnitude or more variation could occur due to tortuosity.

10. Rock Fracture Flow Insights Clearly the literature is divided about the cubic law, as are our results. Exactly why we chose LBM and the use of the GPU made is possible. LBM method allows for much more insight into the flow dynamics within the fracture, something not allowed by cubic law approximation. Bioremediation:

11. Performance Results Metric: Million Lattice Updates Per Second (MLUPS) Typical CPU today: 6.2 MLUPS Typical Single precision CUDA: 400 MLUPS (Tolke, 2008). – Single precision – Geforce 8800 Ultra Our code for a similar grid size: 46.2 MLUPS – Double precision – Geforce 260 Core 216 Remember double precision = 1/8 single precision

12. Future Work Bioremediation: Implementation of bacterial populations dynamics on GPU. Implementation of random number generator needed for above. Optimization on Fermi. Generally reduce resource requirements and ‘branchyness’ of code.

13. Thanks