Making lighter work of calculating fluid and heat flow

Tokyo, Japan – Scientists from Tokyo Metropolitan University have re-engineered the popular Lattice-Boltzmann Method (LBM) for simulating the flow of fluids and heat, making it lighter and more stable than the state-of-the-art. By formulating the algorithm with a few extra inputs, they successfully got around the need to store certain data, some of which span the millions of points over which a simulation is run. Their findings might overcome a key bottleneck in LBM: memory usage.

From rocket fuel and drainpipes to the inner workings of organisms, simulations of fluids and heat play a crucial role at the cutting edge of science and engineering; not only can they help engineers predict the outcome of new designs, they can draw back the curtain for scientists on fluid behavior in places where measurements might be impossible. However, while the prospects are limitless, the simulations themselves are limited by finite computing resources and power. Despite tremendous leaps in computing, scientists are always looking for more efficient simulations which can help them tackle bigger, more complex problems.

The Lattice-Boltzmann Method (LBM) is a widely used algorithm for simulating the flow of fluids and heat. By connecting the flow of fluids to the movement of parcels of fluid on a grid, the LBM is popular in part due to how easy it is to parallelize calculations, making it fast on light hardware, and even faster on supercomputers. Yet, it faces a major drawback in the amount of information it needs to store during the calculation. Like with all lattice-based methods, LBM simulations need to store information associated with every grid point over which a simulation is run. With every extra piece of information, the amount of memory jumps by a multiple of the number of points. These can restrict the number of points that can be placed in a certain amount of space, introducing errors and limiting the length and time scales over which simulations can be run.

In a leap forward for the LBM, Associate Professor Toshio Tagawa and doctoral student Yoshitaka Mochizuki from Tokyo Metropolitan University have introduced modifications to the LBM, namely an extra input which automatically fixes gradient information, how certain values change from one point to another. Specifically, these inputs are encoded into a “non-equilibrium” formulation of the equations governing fluid/heat flow, where inputs or “optional moments” efficiently account for gradients. The key to this method is that these moments make it possible to efficiently recover information which might otherwise need to be explicitly stored in “equilibrium” formulations. This leads to significant reduction in memory usage. They applied their method to a range of benchmarks, including both heat and fluid flow in a range of systems, finding excellent accuracy and good stability.

In some cases, the team found that the memory usage was slashed by around a half. This could easily be the difference between a large simulation fitting and not fitting in the memory of a computing system. Given the broad range of applications of LBM, their innovation promises big savings on time and resources for both science and industry.

This work was supported by Tokyo Metropolitan University.