4,145 research outputs found
Accuracy and performance of the lattice Boltzmann method with 64-bit, 32-bit, and customized 16-bit number formats
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.Comment: 30 pages, 20 figures, 4 tables, 2 code listing
A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales
In this work it is shown how the immersed boundary method of (Peskin2002) for
modeling flexible structures immersed in a fluid can be extended to include
thermal fluctuations. A stochastic numerical method is proposed which deals
with stiffness in the system of equations by handling systematically the
statistical contributions of the fastest dynamics of the fluid and immersed
structures over long time steps. An important feature of the numerical method
is that time steps can be taken in which the degrees of freedom of the fluid
are completely underresolved, partially resolved, or fully resolved while
retaining a good level of accuracy. Error estimates in each of these regimes
are given for the method. A number of theoretical and numerical checks are
furthermore performed to assess its physical fidelity. For a conservative
force, the method is found to simulate particles with the correct Boltzmann
equilibrium statistics. It is shown in three dimensions that the diffusion of
immersed particles simulated with the method has the correct scaling in the
physical parameters. The method is also shown to reproduce a well-known
hydrodynamic effect of a Brownian particle in which the velocity
autocorrelation function exhibits an algebraic tau^(-3/2) decay for long times.
A few preliminary results are presented for more complex systems which
demonstrate some potential application areas of the method.Comment: 52 pages, 11 figures, published in journal of computational physic
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