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Fluid dynamics simulations with the lattice Boltzmann method (LBM) are verymemory-intensive. Alongside reduction in memory footprint, significantperformance benefits can be achieved by using FP32 (single) precision comparedto FP64 (double) precision, especially on GPUs. Here, we evaluate thepossibility to use even FP16 and Posit16 (half) precision for storing fluidpopulations, while still carrying arithmetic operations in FP32. For this, wefirst show that the commonly occurring number range in the LBM is a lot smallerthan the FP16 number range. Based on this observation, we develop novel 16-bitformats - based on a modified IEEE-754 and on a modified Posit standard - thatare specifically tailored to the needs of the LBM. We then carry out anin-depth characterization of LBM accuracy for six different test systems withincreasing complexity: Poiseuille flow, Taylor-Green vortices, Karman vortexstreets, lid-driven cavity, a microcapsule in shear flow (utilizing theimmersed-boundary method) and finally the impact of a raindrop (based on aVolume-of-Fluid approach). We find that the difference in accuracy between FP64and FP32 is negligible in almost all cases, and that for a large number ofcases even 16-bit is sufficient. Finally, we provide a detailed performanceanalysis of all precision levels on a large number of hardwaremicroarchitectures and show that significant speedup is achieved with mixedFP32/16-bit.

On the accuracy and performance of the lattice Boltzmann method with 64-bit, 32-bit and novel 16-bit number formats