Wavelet Turbulence for Fluid Simulation
Appearing in ACM SIGGRAPH 2008
New!  2012 Technical Academy Award and related press

Four frames of smoke around a sphere. Left halves show the underlying simulation, right halves apply our algorithm.

Theodore Kim
Cornell University
Nils Thürey
ETH Zurich
Doug James
Cornell University
Markus Gross
ETH Zurich

We present a novel wavelet method for the simulation of fluids at high spatial resolution. The algorithm enables large- and small-scale detail to be edited separately, allowing high-resolution detail to be added as a post-processing step. Instead of solving the Navier-Stokes equations over a highly refined mesh, we use the wavelet decomposition of a low-resolution simulation to determine the location and energy characteristics of missing high-frequency components. We then synthesize these missing components using a novel incompressible turbulence function, and provide a method to maintain the temporal coherence of the resulting structures. There is no linear system to solve, so the method parallelizes trivially and requires only a few auxiliary arrays. The method guarantees that the new frequencies will not interfere with existing frequencies, allowing animators to set up a low resolution simulation quickly and later add details without changing the overall fluid motion.

Paper download [PDF, 9.9 MB]
Video download [MOV, 70 MB]
Source code
Presentation Slides [PDF, 32.7 MB]


A large smoke plume synthesized from a simulation that was 7 times smaller.

Video download [MOV, 12 MB]

Flow around a spherical obstacle. We synthesized a 400 x 400 x 400 grid from a 50 x 50 x 50 grid. Each frame took an of average 30 seconds on a four core workstation.

Video download [MOV, 7.5 MB]

Flow around a complex obstacle. We synthesized a 720 × 576 × 576 grid from a 80 × 64 × 64 grid. Each frame took less than two minutes on an eight core workstation.

Video download [MOV, 6 MB]

A comparison between a low resolution simulation, a linearly upsampled simulation, and our algorithm.

Video download [MOV, 6 MB]

Comparision of a 12800 × 25600 × 12800 simulation to a 50 x 100 x 50 simulation using particle-based densities. The frames averaged 170s a frame on an eight core machine and used 180 MB of extra memory.

Video download [MOV, 10 MB]

Same simulation as the previous video with an obstacle added.

Video download [MOV, 16 MB]