We are looking at viscous flow, but faster

By redesigning how fluids are simulated, KAUST researchers have demonstrated speed improvements of more than 10x over previous state-of-the-art for slow-flowing viscous liquids.

Modeling the behavior of liquids is important for a wide range of applications, from industrial processes and medical devices to computer graphics and visual simulations.

But despite years of development and more than 100 years of known physics, the ability to accurately simulate liquid flow remains the most computationally challenging aspect of creating a digital replica of the real world. is one of

This is because the flow and behavior of a liquid is determined by both the pressure distribution through the liquid and, for viscous liquids, the pressure-dependent internal resistance to its flow. Accurately computing these complex and time-varying distributions is very computationally intensive, so many optimization schemes have been developed to speed up this computational process at the expense of accuracy.

Han Shao, Libo Huang, and Dominik Michels have now made a major breakthrough in the computational speed of viscous liquids by combining efficient mathematics with the low-level parallel computing capabilities of modern computer processors.

“Fluid dynamics simulation has long been an evergreen topic in computer graphics research, and existing methods still have a lot of potential for performance improvements,” says Shao. “In this work, we propose the Unsmoothed Aggregation Algebraic Multigrid method as an elegant multigrid framework that fully utilizes modern CPU capabilities and introduces new numerical methods.”

The research team started with the idea that more efficient mathematical methods could be used for the basic matrix-vector calculations needed to compute the pressure distribution through a liquid. It can also simplify computation of trivial values ​​at fluid boundaries.

Essentially, researchers can show that when many values ​​in the matrix are the same, as is the case with most viscous liquids, one calculation can be used over many elements, skipping many calculations. I made it.

The team then took advantage of the synergies of combining efficient matrix-vector math code with the single-instruction, multiple-data (SIMD) capabilities of modern CPUs. This allows the same operation to be applied to many data inputs at the same time. This allowed us to build a modeling approach that could simulate viscous fluids up to 15x faster than the current state of the art (Houdini physics engine).

“Our framework is ready for industrial users to speed up their simulations, with the code available on the project website,” says Shao.