Modeling Viscous Fluid Flow with a Billion Particle Simulation

The research paper is “A Fast Unsmoothed Aggregation Algebraic Multigrid Framework for the Large-Scale Simulation of Incompressible Flow”, presented at the ACM SIGGRAPH 2022 conference. Full text is available at the link. Here is the abstract.

Multigrid methods are quite efficient for solving the pressure Poisson equation in simulations of incompressible flow. However, for viscous liquids, geometric multigrid turned out to be less efficient for solving the variational viscosity equation. In this contribution, we present an Unsmoothed Aggregation Algebraic MultiGrid (UAAMG) method with a multi-color Gauss-Seidel smoother, which consistently solves the variational viscosity equation in a few iterations for various material parameters. Moreover, we augment the OpenVDB data structure with Intel SIMD intrinsic functions to perform sparse matrix-vector multiplications efficiently on all multigrid levels. Our framework is 2.0 to 14.6 times faster compared to the state-of-the-art adaptive octree solver in commercial software for the large-scale simulation of both non-viscous and viscous flow.


Another amazing technology! Does this forebode the next revolution in materials science/engineering? Or merely incremental advances?


The focus here is mostly on computer graphics rendering of physical materials that have, so far, either defied realistic simulation or required intractable amounts of computation. But the general mathematical techniques and programming methods to implement them may be applicable in areas such as computational fluid dynamics to simulate wind tunnel testing and mixing of fluids and combustion instability in rocket engines.