In the Lattice Boltzmann method particles are allowed to move and collide on a lattice. The rules governing the collisions are designed such that the time-average motion of the particles is consistent with the Navier-Stokes equations.

The visualizations were created using a variety of standard scientific visualization techniques and software. The two-dimensional images were created by taking a cross-section of of the three-dimensional model and mapping fluid density to color and intensity.

In the three-dimensional images, fluids are depicted with isosurfaces and volume visualization techniques using color, intensity, and transparency to indicate fluid density. Fluid movement is expressed by assembling visualizations at a series of time steps into animations. The three-dimensional images also use isosurfaces to delineate the structure of the medium such as the sandstone, or the surface of the tube structure within which the fluid flow is being modeled.

Visualization helps develop a conceptual framework for understanding complex physical processes. In particular with fluid flow, visual comparisons with experiment are important to validate models.

The Lattice Boltzman method has multiple advantages including

	Time and space efficient computations that are straightforward to parallelize
	Handles complex boundaries without difficulty
	Direct link between microscopic and macroscopic phenomena

	Parallelization of lattice Boltzman Method.
	Nicos S. Martys, Jack F. Douglas. Critical Properties and Phase Separation in Lattice Boltzmann Fluid Mixture, Physical Review E, Volume 63, 031205, February 27, 2001.
	Nicos S. Martys, John Hagedorn, Delphine Goujon, Judith E. Devaney, Large Scale Simulations of Single and Multi-Component Flow in Porous Media, presented at The International Symposium on Optical Science, Engineering, and Instrumentation, SPIE July 18-23, 1999, Denver, Colorado, published in Proceedings of SPIE, Volume 3772.

	Collaborating Scientist: Nick Martys
	Parallel computing: John G. Hagedorn
	Visualization: John G. Hagedorn
	Group Leader: Judith E. Terrill

The Lattice Boltzmann method is useful for computing fluid flow in complex geometries like random porous media. The images shown are two 64x64x64 portions of Fontainebleau sandstone acquired via X-ray microtomography. See Martys, Hagedorn, Goujon and Devaney for details.

7.5% porosity

22% porosity

Two dimensional cross section of two component fluid flow through porous media.

	QuickTime (51 MB)
	AVI (51 MB)

Measured and modeled permeabilities of Fontainebleau sandstone medium.

Two animations of the Taylor-Tomitaka instability. These two animations depict the same data from different vantage points .

Oblique view

Side view

Lattice Boltzmann simulation of phase separation of a 15% - 85% relative composition fluid mixture (an off-critical mixture) under steady shear. The quench depth parameter is 0.287 and the reduced shear rate is 0.56.

	Low resolution animation (11 MB)
	High resolution animation (28 MB)