The Next Level

Getting the Same Result 12x Faster

In PreonLab 4.x, our approach to this problem was to limit the number of splitting and merging events that can occur in a simulation. This was achieved by refining not only in the region of interest, but also in a buffer zone around it. Additionally, we limited the adaptivity to only two particle levels. Unsurprisingly, feedback related to adaptive simulations usually included these two points:

• “Why am I getting fine particles outside my region of interest?”
• “I need more than two particle sizes to really speed up my application!”

In PreonLab 5.0, the splitting and the subsequent sampling correction is fast enough that it can run in every simulation step (see the article Adaptive Particle-based Aimulation in PreonLab for some details). This eliminates the need to split outside the regions of interest and reduces the overall number of particles. Merging still happens at discrete steps, but in our experience this is acceptable for most applications. We also added the option to use three instead of two particle sizes in a simulation, so that the coarsest particles have four times the diameter of the finest particles. Going from two to three particle levels does not seem like much, but it makes a big difference. If the coarsest particle has two times the diameter of the finest particle, we can reduce the number of particles by up to 8 times (in three dimensions). By adding a third particle size with four times the diameter of the finest particle, this factor increases by almost an order of magnitude to 64.

Figure 1 shows a simple setup in which a box with a hole at the bottom is filled with fluid. According to Torricelli’s law, the speed of the outflow is related to the height of the fluid above. This is a great benchmark for CFD solvers because it is possible to compute the speed of the outflow analytically. We will compare three setups: Two will use a uniform particle size with 5 mm and 1.25 mm respectively. Another setup will use three particle sizes with diameters ranging from 1.25 mm to 5 mm. To this end, a refinement domain is placed around the outflow, so that a particle size of 1.25 mm is used there. PreonLab automatically refines the particle layer between the 1.25 mm and 5 mm particles to 2.5 mm.

Figure 1 shows the high-resolution uniform simulation and the adaptive simulation side by side for a visual comparison. Figure 2 shows how the volume inside the box changes over time. The adaptive simulation produces almost the same result as the simulation with a uniform particle diameter of 1.25 mm. Both are much closer to the analytical solution than to the coarse simulation with 5 mm particle diameter.

The adaptive simulation ran more than 12 times faster than the uniform simulation with 1.25 mm particle size. This is a very promising result and shows that the adaptive solver can speed up some applications by an order of magnitude. This speed-up will vary from case to case, but we expect that all applications which simulate large fluid volumes (such as water wading) can be accelerated significantly.

Reduced computation time is the most obvious advantage of the adaptive simulation, but it is not the only one. In the Torricelli scene, the average number of particles and the disk space consumption decreases by a factor of 22. Fewer particles mean that transferring data from a cluster is much faster, viewing the results on a laptop is smoother and archiving the results requires less hard drives.