ye zhao, zhi yuan and fan chen kent state university, ohio, usa
TRANSCRIPT
Enhancing Fluid Animation with Adaptive, Controllable and Intermittent Turbulence
Ye Zhao, Zhi Yuan and Fan ChenKent State University, Ohio, USA
Turbulent Fluid “Turbulence is an irregular motion
which in general makes its appearance in fluids, gaseous or liquid”▪ Taylor and von Kármán 1937
Turbulent World
Turbulent Fluid “Turbulence is an irregular motion
which in general makes its appearance in fluids, gaseous or liquid”▪ Taylor and von Kármán 1937
Model them ?
Model them !
However Turbulent fluids are “very hard to
predict”▪ Taylor and von Kármán 1937
Very large degree of freedom Reynolds number (Re)▪ Kitchen faucet: Re = 10000
Intrinsic fluctuation Stochastic Intermittent
Modeling Turbulence Pure direct numerical simulation
Not practical for high Re number Limited computational resources Wind tunnel used in real experiments
Simulation + Synthetic noise U + u’
Previous work: synthetic noise Frequency domain (Fourier)
Stam and Fiume 93, Rasmussen et al. 03
Curl operation on Perlin noise▪ Narain et al. 08, Schechter et al. 08
Wavelet noise▪ Kim et al. 08
Particles in artificial boundary layer Pfaff et al. 09
Previous work: energy transport Define energy transport between octaves
of noise fields following Kolmogorov 1941 theory (K41): energy cascade Linear model ▪ Schechter et al. 08
Advection-reaction-diffusion PDE▪ Narain et al. 08
Locally assembled wavelets▪ Kim et al. 08
Decay of particles▪ Pfaff et al. 09
Previous work: noise integration Relation between u′ and U following
K41 Advect gas by u′and U together▪ Stam and Fiume 93, Rasmussen et al. 03
Artificial seeding▪ Schechter et al. 08
Local kinetic energy▪ Kim et al. 08
Viscous hypothesis▪ Narain et al. 08, Pfaff et al. 09
Previous work: noise integration Consistent temporal evolution of u′
with respect to U Distortion detection▪ Kim et al. 08
Empirical rotation scalar field▪ Schechter et al. 08
Special noise particles▪ Narain et al. 08
Vortex particles▪ Pfaff et al. 09
Our solution Noise synthesis
Direct Fourier domain generation Following prescribed energy spectrum
Noise fields as random forces inside a turbulence integration module
Adding forces for animation control
Solenoidal noise field Divergence free in Fourier domain
Spectrum control Energy spectrum defines parameter Gaussian control of spectrum
Large variation
Spectrum control (cont.) Multiple scale field
KolmogorovStyle
An arbitraryChoice
Use the fields as random forces Noise fields as forces so that they
are A small group of force fields is enough Pre-computed Randomly selected Reusable
Introduced turbulence Continuous energy injection Model unresolved small-scale effects Compensate loss in numerical
computing
Turbulence integration module
Existing Simulation
IntegrationSolver
Noise Forces
U
f
u
u
qU + (1-q)u
Feedback
Enabling a feedback control in the integration Natural coupling Control flexibility
Large q: turbulent results close to U Small q: significant turbulence from U
Animation
Adaptive and conditional control Force integration makes it easy
What: different scales and spectra
How: conditions from physical/artificial rules
Where: local, critical, interested regions
When: intermittency
Force coupling Determine force magnitude Velocity condition
Strain rate
Distance to obstacles
Vorticity
Scalar density
Intermittency Alternations in time between nearly
non-turbulent and chaotic behavior
Extremely hard by direct simulation
We use temporal control in forcing integration With randomly varied time intervals
Animation
Animation: SPH
Conclusion Pros
Turbulence to coarse, existing, ongoing simulation
Natural integration with random forcing No extra boundary handling Adaptive, conditional turbulence Use precomputed, reusable synthetic
noise Generally independent of solvers Handful control for animators
Conclusion (cont.) Cons.
Not physically exact in spectrum control▪ Local force integration▪ Gaussian function in noise scales
Forced integration ▪ Extra computing load▪ Artificially provided parameters may not
always appropriate
Future work More integration conditions
More noise synthesis schemes
Local random force generation
Acknowledgment U.S. National Science Foundation
Grant IIS-0916131 Anonymous reviewers Theodore Kim and Nils Thuerey Rama Hoetzlein Nvidia Paul Farrel
Thanks!
Enhancing Fluid Animation with Adaptive, Controllable and Intermittent Turbulence