Playing Poseidon

1. Playing Poseidon A Lattice Boltzmann Approach to Simulating Generalised Newtonian Fluids Nitish Tripathi, P. J. NarayananCenter for Visual Information and Technology International Institute of Information Technology, Hyderabad

2. Goal • Interactive simulation and visualisation of Generalised Newtonian Fluids (GNF). • Simulate Newtonian and non-Newtonian fluids using a common framework in realtime for reasonable domain sizes. • Demonstrate the potential to scale to larger domain sizes using MultiGPU implementation.

3. Generalised Newtonian Fluids • Newtonian Fluids - Viscosity independent of shear rate • Non-Newtonian Fluids – • Shear thinning or pseudoplastic - Viscosity decreases with increasing shear rate • Shear thickening or dilatant - Viscosity increases with increasing shear rate Shear Stress Shear Rate

4. Generalised Newtonian Fluids • Newtonian Fluids - Viscosity independent of shear rate • Non-Newtonian Fluids – • Shear thinning or pseudoplastic - Viscosity decreases with increasing shear rate • Shear thickening or dilatant - Viscosity increases with increasing shear rate Shear Stress Shear Rate

5. Generalised Newtonian Fluids • Newtonian Fluids - Viscosity independent of shear rate • Non-Newtonian Fluids – • Shear thinning or pseudoplastic - Viscosity decreases with increasing shear rate • Shear thickening or dilatant - Viscosity increases with increasing shear rate Shear Stress Shear Rate

6. Generalised Newtonian Fluids • Newtonian Fluids - Viscosity independent of shear rate • Non-Newtonian Fluids – • Shear thinning or pseudoplastic - Viscosity decreases with increasing shear rate • Shear thickening or dilatant - Viscosity increases with increasing shear rate Shear Stress Shear Rate

7. Our Approach • Lattice Boltzmann Method (LBM) for simulation • A mesoscopic approach - particles (logical in nature) collide at grid centers and progress to neighbours in fixed directions. Particle in a LBM grid • Truncated Power Law to calculate the localised viscosity for non-Newtonian fluids • Marching Cubes for visualisation of the fluid • Exploit the inherent parallelism of LBM coupled with an efficient memory access pattern to create a fast GPU implementation

8. What is a power law fluid

9. Lattice Boltzmann Method Velocity vectors for D3Q19

10. Particle Distribution Functions

11. Basic LBM • Streaming step - Read neighbours’ distribution function for corresponding directions and update Streaming DFs • Collision step - Calculate density and velocity for each cell, collide them and update the distribution functions using the following functions.

12. Basic LBM • Streaming step - Read neighbours’ distribution function for corresponding directions and update Streaming DFs • Collision step - Calculate density and velocity for each cell, collide them and update the distribution functions using the following functions.

13. Free Surface LBM • Cells are differentiated on the basis of whether they contain fluid, gas or form the interface between them • Interface cells are partially filled with liquid • As the liquid progresses, the cells get relabelled according to the amount of fluid they hold • The interface cells define the boundary of the fluid Liquid surface and lattice cells

14. Overview of the algorithm • We build upon the algorithm given by “Free Surface Lattice-Boltzmann fluid simulations with and without level sets” by Thuerey et al. Overview of Free Surface LBM

15. Overview of the algorithm • We build upon the algorithm given by “Free Surface Lattice-Boltzmann fluid simulations with and without level sets” by Thuerey et al. Overview of Free Surface LBM

16. Overview of the algorithm • We build upon the algorithm given by “Free Surface Lattice-Boltzmann fluid simulations with and without level sets” by Thuerey et al. Overview of Free Surface LBM

17. Overview of the algorithm • We build upon the algorithm given by “Free Surface Lattice-Boltzmann fluid simulations with and without level sets” by Thuerey et al. Overview of Free Surface LBM

18. Overview of the algorithm • We build upon the algorithm given by “Free Surface Lattice-Boltzmann fluid simulations with and without level sets” by Thuerey et al. Overview of Free Surface LBM

19. Overview of the algorithm • We build upon the algorithm given by “Free Surface Lattice-Boltzmann fluid simulations with and without level sets” by Thuerey et al. Overview of Free Surface LBM

20. Overview of the algorithm • We build upon the algorithm given by “Free Surface Lattice-Boltzmann fluid simulations with and without level sets” by Thuerey et al. Overview of Free Surface LBM

21. Parallel Implementation using CUDA • Data stored in global memory • Double buffering for storing DFs • Assigned one thread per cell • Each warp works on cells lying in the same row, leading to optimised access Data requirement for each cell Thread Mapping with Grid Elements

22. Multiple GPUs • Use two GPUs on the same system to further scale the problem • Data divided into 2 parts by slicing the grid along the z-axis • For data on the boundary, neighbours reside on the other GPU, so boundary slice is transferred • Data transfer overlapped with the computation. Overlap of data transfers with computation

23. Results Performance of the Dam Break Experiment on various GPUs Performance of the Dam Break Experiment on single and multi-GPUs Performance measured in Million Lattice Updates per Second (MLUPS)

24. Visualisation Intermediate frames for Dam Break Experiment for a Newtonian Fluid on a 1283 grid, running at an average of 5 fps with 50 LBM iterations per frame Intermediate frames for interactive simulation of a Newtonian fluid on a 1283 grid, running at an average of 6.6 fps with 50 LBM iterations per frame. The user can add fluid drops while simulation is running

25. Videos Interactive Newtonian fluid simulation Dam Break

26. Non-Newtonian Characteristics Shear ThinningDisplays more fluidity (decrease in viscosity) upon impact with the ground Shear ThickeningDisplays folding on itself, signifying resistance (increase in viscosity) upon impact NewtonianNo change in viscosity upon impact with the ground

27. Flow through a tube Shear thinning fluid through a tube of varying cross section. The dye particles change colour according to the change in viscosity.

28. Flow between parallel plates • A motion parallel to two parallel is simulated. The fluid lamina in contact with the two plates will not move on account of its viscosity • Newtonian fluid curve follows a parabolic path • Non-Newtonian fluid curve flattens on approaching the center of the channel Normalised velocity profiles for Newtonian and shear thinning fluids

29. Conclusions & Future Work • We presented a system to simulate and visualise both Newtonian and non-Newtonian fluids accurately using a single algorithm. • We have dealt with laminar flows in this work. A study on turbulent fluids using LBM is an interesting area for future work. • Visual quality of the simulations can be enhanced using ray-tracing. • Building upon our work to simulate out of core grids (5123 and above) is another interesting area for future work.

30. Our Publications • Tripathi, N. and Narayanan, P.J. Generalized newtonian fluid simulations. 2013 Fourth National Conference on Computer Vision, Pattern Recognition, Image Processing and Graphics (NCVPRIPG-2013). Jodhpur, India. • Jain, Somay and Tripathi, Nitish and Narayanan, P. J. Interactive Simulation of Generalised Newtonian Fluids Using GPUs. Proceedings of the 2014 Indian Conference on Computer Vision Graphics and Image Processing (ICVGIP-2014). Bangalore, India.

31. Related Work • Particle Level Sets - Enright et al “A hybrid particle level set method for improved interface capturing” • Smoothed Particle Hydrodynamics - Desbrun et al“A new paradigm for animating highly deformable bodies” • Lattice Boltzmann Method (LBM) - Thuerey et al “Free Surface Lattice-Boltzmann fluid simulations with and without level sets” • Parallel implementation of bulk LBM - • 2D implementation - Tolke et al “Implementation of a lattice boltzmann kernel using the compute unified device architecture developed by nvidia” • 3D implementation - Bailey et al “Accelerating lattice boltzmann fluid flow simulations using graphics processors” • MultiGPU LBM implementations - Januszewski et al “Sailfish: A flexible multi-GPU implementation of the lattice Boltzmann method”

32. Action taken on reviews • The benefits of combination of Non-Newtonian Fluids and LBM are wide. The combinations however haven’t been practically put to use in a commercial way. Reasons? • The Navier Stokes’ equations have been explained in the thesis for a reader with basic understanding of calculus and Newton’s laws of motion. However, we will simplify it further and explain it easily. • If required we can also look at adding simulations from different Eulerian and Lagrangian approaches, to make the thesis more interesting. Although it may divert attention from the central theme. Suggestions on the same are welcome.

33. Thank You!