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

Title data

Lehmann, Moritz ; Krause, Mathias J. ; Amati, Giorgio ; Sega, Marcello ; Harting, Jens ; Gekle, Stephan:
Accuracy and performance of the lattice Boltzmann method with 64-bit, 32-bit, and customized 16-bit number formats.
In: Physical Review E. Vol. 106 (2022) Issue 1 . - No. 015308.
ISSN 2470-0053
DOI: https://doi.org/10.1103/PhysRevE.106.015308

Project information

Project title:
Project's official titleProject's id
SFB 1357 MikroplastikSFB1357

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

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.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Biological Fluid Dynamics; Drop & Bubble Phenomena; Fluid Particle Interactions; Interaction in Fluids; Interfacial Flows; Microfluidics; Physics of Computation; Shear Flows; Vortex Flows; Classical Fluids; Complex Fluids; Lattice Models in statistical physics; numerical techniques
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics > Professor Theoretical Physics VI - Simulation and Modelling of Biofluids
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics > Professor Theoretical Physics VI - Simulation and Modelling of Biofluids > Professor Theoretical Physics VI - Simulation and Modelling of Biofluids - Univ.-Prof. Dr. Stephan Gekle
Profile Fields > Advanced Fields > Nonlinear Dynamics
Research Institutions
Research Institutions > Collaborative Research Centers, Research Unit
Research Institutions > Collaborative Research Centers, Research Unit > SFB 1357 - MIKROPLASTIK
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 500 Natural sciences
500 Science > 530 Physics
500 Science > 540 Chemistry
Date Deposited: 01 Aug 2022 07:22
Last Modified: 04 Aug 2022 09:14
URI: https://eref.uni-bayreuth.de/id/eprint/71272