  Fluid dynamics simulations with the lattice Boltzmann method (LBM) are very
memory-intensive. Alongside reduction in memory footprint, significant
performance benefits can be achieved by using FP32 (single) precision compared
to FP64 (double) precision, especially on GPUs. Here, we evaluate the
possibility to use even FP16 and Posit16 (half) precision for storing fluid
populations, while still carrying arithmetic operations in FP32. For this, we
first show that the commonly occurring number range in the LBM is a lot smaller
than the FP16 number range. Based on this observation, we develop novel 16-bit
formats - based on a modified IEEE-754 and on a modified Posit standard - that
are specifically tailored to the needs of the LBM. We then carry out an
in-depth characterization of LBM accuracy for six different test systems with
increasing complexity: Poiseuille flow, Taylor-Green vortices, Karman vortex
streets, lid-driven cavity, a microcapsule in shear flow (utilizing the
immersed-boundary method) and finally the impact of a raindrop (based on a
Volume-of-Fluid approach). We find that the difference in accuracy between FP64
and FP32 is negligible in almost all cases, and that for a large number of
cases even 16-bit is sufficient. Finally, we provide a detailed performance
analysis of all precision levels on a large number of hardware
microarchitectures and show that significant speedup is achieved with mixed
FP32/16-bit.
