Accuracy and performance of the lattice Boltzmann method with 64-bit, 32-bit, and customized 16-bit number formats

Abstract

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 customized 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.

Modeling of vertical microplastic transport by rising bubbles

“…In this work we use the Volume-of-Fluid (VoF) lattice Boltzmann method (LBM) implementation FluidX3D [34,[42][43][44][45][46][47] that has been extended to simulate rising bubbles with Hoshen-Kopelman [48] volume tracking and the ideal gas law…”

“…The method is thoroughly validated in [34,[44][45][46][47]49]. VoF provides three classes of Cartesian grid pointsfluid, interface and gas.…”

Vertical transport of microplastics by rising bubbles

“…In this work we use the Volume-of-Fluid (VoF) lattice Boltzmann method (LBM) implementation FluidX3D [31,[39][40][41][42][43][44] that has been extended to simulate rising bubbles with Hoshen-Kopelman [45] volume tracking and the ideal gas law…”

“…The method is thoroughly validated in [31,[41][42][43][44]46]. VoF provides three classes of Cartesian grid points -fluid, interface and gas.…”

A graphic processing unit implementation for the moment representation of the lattice Boltzmann method

“…On the other hand, the streaming population arrays can only have one type of coalesced access, either read or write, since they move toward different grid lattices. Lehmann et al 36 pointed out that having a coalesced write and misaligned read is preferable, which is what we adopt. Therefore, the post‐collision populations for the neighboring lattices are stored together instead of grouped by the streaming target.…”