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1 MULTIPHYSICS SIMULATION USING GPU Arman Pazouki Simulation-Based Engineering Laboratory Department of Mechanical Engineering University of Wisconsin - Madison

2 Acknowledgements Prof. Dan Negrut Dr. Radu Serban Hammad Mazhar Andrew Seidl Colleagues from Simulation Based Engineering Laboratory, University of Wisconsin- Madison National Science Foundation NVIDIA 2

3 Motivation and Background 3

4 Motivation 4

5 Fluid Flexible Bodies Rigid Bodies 6/30/2014 5

6 Fluid Simulation: SPH Continuity: Momentum (Navier-Stokes): Lagrangian Kinematics: Weakly Compressible model XSPH W b r ab a h Shepard Filtering S J. Monaghan, Smoothed particle hydrodynamics, Reports on Progress in Physics 68 (1) (2005) M. Liu, G. Liu, Smoothed particle hydrodynamics (SPH): An overview and recent developments, Archives of Computational Methods in Engineering 17 (1) (2010)

7 Neighbor Search and GPU programming Case Study: How GPU can affect an algorithmic design VS 7

8 Algorithm 1 Core property: saving contacts list Parallel threads: Bins Successful for rigid body dynamics: O(1e7) Advantages Failed for SPH: O(1e6) One calculation per intersection Possibility of re-using contacts list Arbitrary shapes 8

9 Algorithm 2 Core property: find intersection whenever needed Advantage. More process, less memory Fixed size spheres Parallel threads: Particles Reduces memory access Improves cache hits. Screen shot from particles demo, NVIDIA CUDA (CUDA Samples) 9

10 Rigid and Flexible Bodies Dynamics 3D rigid body dynamics Dynamics dvi Fi dt M i dω J T J ω dt Kinematics dx dt i i i i i i V dqi 1 T Gi i, dt 2 q T q i i 1 0 i i 0 z y z 0 x y x 0 q y q q q G q z qw q x q y qw qz q y q x x w z E. Haug, Computer aided kinematics and dynamics of mechanical systems, Allyn and Bacon Boston, A. Shabana, Dynamics of Multibody Systems, Cambridge University Press, Gradient-deficient ANCF beam element Dynamics Me + Q Q Q e Q = T T 11 EA11 dx + EI dx g T Q = AS g dx a Q = S 312 T e g a s ( x ) F a Kinematics e e L r L rx e = ; r( x, e) = S( x) e ; v( x, e) = S( x) e R r R r x S shape function matrix 10

11 Fluid-Solid Interaction Boundary Condition Enforcing (BCE) markers for no-slip condition Rigidly attached to the solid body (hence their velocities are those of the corresponding material points on the solid) Hydrodynamic properties from the fluid Rigid bodies/walls Flexible beams 11

12 Parallelization thrust::reduce_by_key to reduce surface reaction forces and torques on to nodal values Custom kernels to update solid objects Fine grain parallelization Position Rotation Velocity Angular velocity 12

13 Example Simulations 13

14 Flow in porous media Example applications Oil Recovery Biology Diffusion of macromolecules within tissues Blood flow through muscles 14

15 Simulation of dense suspensions Dense suspension Finite size particles (rigid bodies) interaction Drafting, Kissing, and Tumbling (DKT) Short range interactions Lubrication and collision Flow characteristics Particle Reynolds number 1.0 Channel Reynolds number: 66 Channel Dimension: (1.1, 1.0, 1.0) m Volumetric concentration: 40% Computational aspects 23,000 rigid ellipsoids: (1.5, 1.5, 2.0) cm 2,000,000 SPH markers. Simulation performed on a single GPU, NVIDIA GTX seconds of dynamics 72 hrs to complete. Animation shows the channel mid-section 15

16 Interacting rigid and flexible objects in channel flow 16

17 Performance 17

18 Scaling analysis on NVIDIA GeForce GTX 680 Rigid body dynamics Flexible body dynamics Fluid flow 18

19 Scaling analysis (all together, table) 19

20 Validation 20

21 Particle migration in 2D and 3D Poiseuille flow Transient Poiseuille flow Cylinder in channel flow Sphere in pipe flow, Effect of rigid body rotation T. Inamuro, K. Maeba, F. Ogino, IJMF 26 (12) (2000) J. Morris, P. Fox, Y. Zhu, JCP 136 (1) (1997) J. Schonberg, E. Hinch, JFM 203 (1) (1989) 517. D. Oliver, Nature (194) (1962) B. H. Yang, J. Wang, D. D. Joseph, H. H. Hu, T.-W. Pan, and R. Glowinski, JFM 540 (2005) 109. A Lagrangian-Lagrangian Approach APS- Pittsburgh For the Simulation of FSI Problems 21

22 Radial distribution of particles in suspension [1/2] 192, 10 hour long simulation 14 seconds real time Bootstrapping method,95% confidence interval ar0.07 a av l L ( )( )( ) [0,0.69] R R Re 60, 0.027% Increasing distance from inlet G. Segre, A. Silberberg, Nature (189) (1961) 2. 22

23 Applications 23

24 Hanging flexible beam in viscose fluid Flexible cantilever in contained fluid Track position of beam tip 24

25 Flow cytometry using microfluidic techniques Fluorescence and laser-beam cell sorting Limited particle size, a 50 m Unknown effect of external field on cell viability Purification of 3D micro-tissues and cell aggregates Finite size particles, a m 25

26 Work in progress 26

27 Thank You! Chrono::FSI (Project Chrono: Simulation Based Engineering Lab (SBEL) University of Wisconsin-Madison 27

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