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GPU Workshop: July, 2010. Scott Briggs PhD Candidate Civil/ Env . Engineering Contaminant Hydrogeology Supervisors: B. E. Sleep and B. W. Karney. Contaminant Hydrogeology. Study and management of groundwater resources. - PowerPoint PPT Presentation
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GPU Workshop: July, 2010
Scott BriggsPhD Candidate Civil/Env. Engineering
Contaminant HydrogeologySupervisors: B. E. Sleep and B. W. Karney
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)
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
Lattice Boltzmann Method: D2Q9
4
Sukop and Thorne, 2005
Parallel Plate Validation
Single Precision• 7.4 % relative error
Double Precision (below)• 0.78% relative error
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
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.
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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.
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.
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:
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
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.
Thanks