Evolving Sub-Grid Turbulence for Smoke Animation

Hagit Schechter

Robert Bridson

SCA 08

The Challenge

licensed under Creative Commons

The Goal

Scalability Speed Realism

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

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

Talk Overview

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

Turbulence model

Method overview

Large-scale simulation

Small-scale simulation

Results

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

Decomposition of Turbulent Flow

sl UUU

Large-scale flow Sub-grid turbulence flow

forces viscous

forces inertial

/Re

LV

L

V ss

1l 3l2l

Kolmogorov model:

Kinetic energy is transported from largest scale to smaller and smaller scales and is dissipated to heat in the smallest scales

Energy Cascade

k

tD

kD

k

T

The K-Epsilon Model

Viscous

forces

Gained from

large-scale

Dissipation at

smallest scale

We use simplified viscosity term kApply K-Epsilon to all turbulent scales

Our turbulence model:

)()()( bbP

b kkk

In space

Across scales

2D Energy Transport Model

Turbulence model

Method overview

Large-scale simulation

Small-scale simulation

Results

Method Overview

Large-scale flow Add forces Advect Project Output velocities

Turbulence properties Evaluate Transport Output properties

Large-scale simulation Small-scale simulation

Small-scale flow Read turbulence

properties Apply them to generate

small-scale velocities

Synthesize Read large-scale

velocities Synthesize velocities Advance particles

Turbulence model

Method overview

Large-scale simulation

Small-scale simulation

Results

Navier-Stokes

0

11)(

u

fPuut

u

Dt

uD

Buoyancy forces

gsCTTCb sambT

Large-Scale Simulation

temperature gravity

FLIP: MAC grid plus particles for advection

Turbulence Properties

)(bijkE

Evaluate, advect, and transport

For every turbulence scale

On every timestep

turbulent energy density

)()1(

)(

)(1,,

)(1,,

)(,1,

)(,1,

)(,,1

)(,,1

)()(

6bijk

bijk

bijk

bkji

bkji

bkji

bkji

bkji

bkji

bijk

bijk

EtEt

Et

EEEEEEt

EE

Previous step

energy

Viscous forces

Gain from

larger scale

Loss to

smaller scale

Transport Turbulence Properties

k

tD

kD

k

TK-Epsilon

equation

Preserving Angular Momentum

Advection Projection

The problem: numerical dissipation (time-split)

13

1~ nnnpredicted vvvv

Our solution: time-split predictor

Advect+predict Projection

Turbulence model

Method overview

Large-scale simulation

Small-scale simulation

Results

Small-Scale Simulation

Perlin 1985, 2002

321 ,,,

3,2,1,,

txv

itxNtx ii Bridson et al 2007

Perlin and Neyret 2001

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

2. Compute small-scale velocity for every particle

Initialize: Plant marker particles

On Every time-step:

The Procedure

1. Rotate basis vectors for every turbulence scale

Time coherence: turbulence driven vorticity

Turbulence driven Curl-Noise

)(bijkE

Synthesize

),(),(),( txutxutxu sl

Small-scale algorithm can be trivially parallelized to run on a GPU !

Update positions

Results

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

Acknowledgements

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

The End

Questions?