1. Profiling fluid flow past an
immersed object with CUDA
An Independent Study By
Aritra Kumar Nath

2. Lattice Boltzmann Method
• For simulating fluid flow
• Based on the microscopic kinetic equation for the particle distribution
function.
• Fictive particles propagating and colliding over lattice mesh
• Per node Density & Velocity used to determine macroscopic properties of
fluid (pressure, fluid velocity, viscosity)
• Linear so less computation intensive
• Straightforward parallel implementation

3. Lattice Boltzmann Method
• Simulation domain divided into 2D lattice (D2Q9)
• Each node with packet distribution
• Packet distributions have associated velocity vectors

4. Packet Distribution
0 v 0 -v 0 v -v -v v
0 0 v 0 -v v v -v -v
{ vqi , i = 0 . . . 8} =

5. Lattice Boltzmann Method
• Finite differencing used to compute new packet distributions
• Values computed iteratively
• Packet distributions based updated based on values in the previous
time step
• The Lattice Boltzmann equation:

6. Simulation Driver Rules
• Collision
• Propagation
ρ= ∑pqi u= 1/ρ ∑pqi vqi

7. Boundary Conditions
• Full-Bounce Back
• Half-Bounce Back

8. Implementation on GPU
• Symmetric velocity vector orientation in every node
• Scope for Parallelism inherent
• All velocity vectors with same direction grouped together for
computation
• Three primary kernels used are for:
– Collision
– Propagation
– Calculating boundary conditions
• NVIDIA GEForce 310M used

9. Velocity Vectors Resolved
Division of the D2Q9 model, according to its velocity directions. (Image
courtesy: GPU-Based Flow Simulation with Complex Boundaries)

10. Flow Chart - LBM Computation
(Image Courtesy: GPU-Based Flow Simulation with Complex
Boundaries)

11. LBM Fluid Simulation - Graphic
Visualization

12. Studying Flow Profiles of Fluids
• The following simulation parameters are variable:
– Lattice dimensions
– Fluid Viscosity
– Maximum Velocity
• The following values for the microscopic fictive particles are computed:
– Nodal velocity (microscopic fictive particles)
– Density (rho)
• The values obtained will further influence macroscopic fluid properties

13. Studies Results & Observation
• Study 1:
Compare different iteration sequences same simulation parameter values:
Parameter Value Set:
– Simulation Parameter:
– Fluid Viscosity: 0.05
– Maximum Fluid Velocity: 0.01
• Study 2:
Compare the same iteration sequence with different simulation parameter values
without causing turbulence:
Parameter Value Set 1:
-- Fluid Viscosity: 0.8
-- Maximum Fluid Velocity: 0.1
Parameter Value Set 2:
-- Fluid Viscosity: 0.01
-- Maximum Fluid Velocity: 0.1

14. Studies Results & Observation
• Study 3:
Compare the same iteration sequence with different simulation parameter
values random turbulence:
Parameter Value Set:
– Simulation Parameter:
– Fluid Viscosity: 0.05
– Maximum Fluid Velocity: 0.01