Meatballs - Smoothed Particle Hydrodynamic Overview Simulator and - - PowerPoint PPT Presentation
Meatballs Jennine Nash and Thomas Klein Meatballs - Smoothed Particle Hydrodynamic Overview Simulator and Renderer Goals SPH Solver Equations Why CUDA? Jennine Nash and Thomas Klein Results References Carnegie Mellon University
Meatballs Jennine Nash and Thomas Klein Overview Goals SPH Solver Equations Why CUDA? Results References
Jennine Nash and Thomas Klein
Carnegie Mellon University jmnash@andrew.cmu.edu, twklein@andrew.cmu.edu
May 9, 2014
Meatballs Jennine Nash and Thomas Klein Overview Goals SPH Solver Equations Why CUDA? Results References
1 Overview 2 Goals 3 SPH Solver Equations 4 Why CUDA? 5 Results 6 References
Meatballs Jennine Nash and Thomas Klein Overview Goals SPH Solver Equations Why CUDA? Results References
SPH is used to model liquid flows Too computationally intensive to simulate billions of particles or a truly continuous flow SPH creates discrete particles which function as moving bodies of fluid Kernel function updates a particles’ properties based on the values of other nearby particles
Meatballs Jennine Nash and Thomas Klein Overview Goals SPH Solver Equations Why CUDA? Results References
Realistic-looking liquid particle simulator using a smooth-particle hydrodynamics solver Implemented on both the CPU and GPU (with CUDA) Compare implementation runtimes to each other to determine the benefit of using CUDA
Meatballs Jennine Nash and Thomas Klein Overview Goals SPH Solver Equations Why CUDA? Results References
Position rj Velocity vj Pressure Pj Density ρj Mass mj Each property (with the exception of mass) is updated according to the values of the properties of the other particles
Meatballs Jennine Nash and Thomas Klein Overview Goals SPH Solver Equations Why CUDA? Results References
For two particles i and j, x = |ri − rj| h is a smoothing constant adjusted to determine the distance over which particles have effects Let x = r
h
W (r, h) =
1 πh3
1 − 3
2x2 + 3 4x3
0 ≤ x ≤ 1
1 4(2 − x)3
1 ≤ x ≤ 2 x ≥ 2 [Cossins, 2010]
Meatballs Jennine Nash and Thomas Klein Overview Goals SPH Solver Equations Why CUDA? Results References
∇W (r, h) = ∂
∂r W (r, h)
=
1 πh4
9 4x2 − 3x
0 ≤ x ≤ 1 −3
4(2 − x)2
1 ≤ x ≤ 2 x ≥ 2 [Cossins, 2010] ∇jWij =
∂ ∂rj W (|ri − rj|, h) = ∇W (r, h)∂|ri−rj| ∂rj
= ∇W (r, h)1
r (ri − rj)
∇iWij = −∇jWij ∇jWji = −∇jWij
Meatballs Jennine Nash and Thomas Klein Overview Goals SPH Solver Equations Why CUDA? Results References
We defined a small global time step ∆t All values on the right-hand sides of the equations were calculated during the previous time step Position: rj := rj + ∆tvj Velocity: vj := vj − ∆t
mi
ρ2
j + Pi
ρ2
i
Density: ρj :=
i
miWji (density effectively changes due to particles being close together) [Schechter, 2012] Pressure: Pj := 2000 ρj
ρ0
7 − 1
based on the mass and volume [Schechter, 2012]
Meatballs Jennine Nash and Thomas Klein Overview Goals SPH Solver Equations Why CUDA? Results References
Works well with CUDA warps because unlikely to diverge Each particle calls same functions, and kernel likely to be skipped over in all 32 threads in the warp Every particle is independent because computations only depend on the time step before
Meatballs Jennine Nash and Thomas Klein Overview Goals SPH Solver Equations Why CUDA? Results References
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Meatballs Jennine Nash and Thomas Klein Overview Goals SPH Solver Equations Why CUDA? Results References
Meatballs Jennine Nash and Thomas Klein Overview Goals SPH Solver Equations Why CUDA? Results References
Meatballs Jennine Nash and Thomas Klein Overview Goals SPH Solver Equations Why CUDA? Results References
Peter J. Cossins (2010) Smoothed Particle Hydrodynamics http://arxiv.org/abs/1007.1245v2 Hagit Schechter and Robert Bridson (2012) Ghost SPH for Animating Water ACM Transactions on Graphics 31(4), article 61 http://dl.acm.org/citation.cfm?doid=2185520.2185557
Meatballs Jennine Nash and Thomas Klein Overview Goals SPH Solver Equations Why CUDA? Results References