Math and computer simulation wizzes at the University of North Carolina at Chapel Hill have just taken a nice step forward in granular simulation by approaching the problem with math heretofore not applied to dynamic granular modeling. It's really quite impressive.
"Free-flowing Granular Materials with Two-way Solid Coupling"
Here are some rendered examples of their methodology at work:
The math and modeling of granular impacts and scattering have previously been handled with formulas based on fluid dynamics. Due to a granular system's potential lack of cohesion and possible compressibility, it's inaccurate to deduce the movement of particles using earlier methods.
Using the particle-in-cell method:
Their new approach uses multiple iterations of a Lagrangian number crunch to give a visual output of change in position per frame. A scalar field allows averages to be assigned to particles. More precise crunching is occurring at the center of multiple spread out bubble-like areas on the field. Instead of computing the values for every single tiny particle, "macroscopic" clumps of a wider area have centers that are valued, then graphed outwards to other particles in terms of averages.
In this new system, the essential values needed to be assigned to matter are:
- Frictional Stress
Fluid dynamics is just not enough:
A granular system's properties allow for stability in a pile according to its friction coefficient.
Spheres placed in sand, even when denser than the sand, can be supported due to internal friction.
Here we can see the inaccuracies of previous methods:
[Above] "A column of granular material is simulated using Zhu and Bridson’s method  (top) and our method (bottom)."
Narain and Gola's work may be favorable over previous methods both due to its 1) accuracy, as well as 2) the ability to trade off quality-over-precision / precision-over-quality as an easily implemented option. Whenever computation is involved, that flexibility is very valuable.
In their words:
"We achieved this through a novel mathematical treatment of granular flow that robustly handles the complex interplay of internal stresses in the granular material. In addition, we developed a generalization of the particle-in-cell method that maintains a good distribution of particles in general compressible flows."
To delve deeper into the math and details:
Visit their site HERE or go straight to the pdf HERE.
Narain, R., Golas, A., & Lin, M. (2010). Free-flowing granular materials with two-way solid coupling ACM Transactions on Graphics, 29 (6) DOI: 10.1145/1882261.1866195
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