Evolving SubGrid Turbulence for Smoke Animation

1
Evolving Sub-Grid Turbulence for Smoke Animation

• Hagit Schechter
• Robert Bridson

SCA 08
2
The Challenge
licensed under Creative Commons
3
The Goal

• Scalability
• Speed
• Realism

4
Related Work

• Kolmogorov spectrum
• Stam and Fiume 1993
• Neyret 2003
• Kim, Thürey, James, and Gross 2008
• Vorticity confinement, Vortex particles
• Fedkiw, Stam, and Jensen 2001
• Selle, Rasmussen, and Fedkiw 2005
• Park and Kim 2005

5
Contributions

• Multi-scale evolution of turbulent energy
  (K-Epsilon, Kolmogorov)
• Turbulence procedure suitable to run on a GPU
  (parallelized trivially)
• Reduced numerical dissipation of angular momentum

6
Talk Overview

• Turbulence model
• Method overview
• Large-scale simulation
• Small-scale simulation
• Results

7

• Turbulence model
• Method overview
• Large-scale simulation
• Small-scale simulation
• Results

8
Related Work (Physics)

• Kolmogorov model
• Richardson, 1922
• Kolmogorov, 1941, 1942
• K-Epsilon model
• Davidov, 1961
• Harlow and Nakayama, 1968
• Hanjalic, 1970
• Jones and Launder, 1972
• Launder and Sharma, 1974

9
Decomposition of Turbulent Flow
Large-scale flow
Sub-grid turbulence flow
10
Energy Cascade
Kolmogorov model Kinetic energy is transported
from largest scale to smaller and smaller scales
and is dissipated to heat in the smallest scales
11
The K-Epsilon Model
Viscous forces
Gained from large-scale
Dissipation at smallest scale
Our turbulence model
We use simplified viscosity term
Apply K-Epsilon to all turbulent scales
12
2D Energy Transport Model
In space
Across scales
13

• Turbulence model
• Method overview
• Large-scale simulation
• Small-scale simulation
• Results

14
Method Overview
Large-scale simulation
Small-scale simulation

• Large-scale flow
• Add forces
• Advect
• Project
• Output velocities
• Turbulence properties
• Evaluate
• Transport
• Output properties

• Small-scale flow
• Read turbulence properties
• Apply them to generate small-scale velocities
• Synthesize
• Read large-scale velocities
• Synthesize velocities
• Advance particles

15

• Turbulence model
• Method overview
• Large-scale simulation
• Small-scale simulation
• Results

16
Large-Scale Simulation

• Navier-Stokes

Buoyancy forces
temperature
gravity
FLIP MAC grid plus particles for advection
17
Turbulence Properties
For every turbulence scale
On every timestep
Evaluate, advect, and transport
turbulent energy density
18
Transport Turbulence Properties
Previous step energy
Viscous forces
Gain from larger scale
Loss to smaller scale
K-Epsilon equation
19
Preserving Angular Momentum
The problem numerical dissipation (time-split)
Advection
Projection
20
Our solution time-split predictor
Advectpredict
Projection
21

• Turbulence model
• Method overview
• Large-scale simulation
• Small-scale simulation
• Results

22
Small-Scale Simulation

• Perlin 1985, 2002

• Perlin and Neyret 2001

• Bridson et al 2007

• Our model
• Turbulence driven Curl-Noise to generate
  small-scale flow
• Synthesize with large-scale flow

23
The Procedure
Initialize Plant marker particles
On Every time-step
1. Rotate basis vectors for every turbulence scale
Time coherence turbulence driven vorticity
2. Compute small-scale velocity for every particle
Turbulence driven Curl-Noise
24
Synthesize
Update positions
!
Small-scale algorithm can be trivially
parallelized to run on a GPU
25
Results
26
To Summarize

• Capture the time evolution of turbulence
• Combine coarse grid simulation with procedural
  method that is suitable to run on a GPU
• Detail level is tunable and scalable

27
Acknowledgements

• Natural Sciences and Engineering Research
  Council of Canada, BC Innovation Council, and
  Precarn Incorporated

28
The End
Questions?