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