Esoteric Twist: An Efficient in-Place Streaming Algorithmus for the Lattice Boltzmann Method on Massively Parallel Hardware

Geier, Martin; Schönherr, Martin

doi:10.3390/computation5020019

Cited by 49 publications

(22 citation statements)

References 28 publications

(36 reference statements)

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“…There are different possibilities to compute these derivatives. Here we choose to introduce an additional distribution function g i jk with six discrete velocities from which the following derivatives are computed: The distributions g i jk undergo the same streaming algorithm as the distributions f i jk which means that no non-local operations are introduced into the lattice Boltzmann algorithm other than the usual streaming step and the EsoTwist algorithm for streaming can be applied [112]. However, a different way of computing finite differences might also be used.…”

Section: Appendix A4: Collisionmentioning

confidence: 99%

Under-resolved and large eddy simulations of a decaying Taylor–Green vortex with the cumulant lattice Boltzmann method

Geier

Lenz

Schönherr

et al. 2020

Theor. Comput. Fluid Dyn.

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We present a comprehensive analysis of the cumulant lattice Boltzmann model with the three-dimensional Taylor–Green vortex benchmark at Reynolds number 1600. The cumulant model is investigated in several different variants, using regularization, fourth-order convergent diffusion and fourth-order convergent advection with and without limiters. In addition, a cumulant model combined with a WALE sub-grid scale model is being evaluated. The turbulence model is found to filter out the high wave number contributions from the energy spectrum and the enstrophy, while the non-filtered cumulant methods show good correspondence to spectral simulations even for the high wave numbers. The application of the WALE turbulence model appears to be counter productive for the Taylor–Green vortex at a Reynolds number of 1600. At much higher Reynolds numbers ($${\hbox {Re}}=160{,}000$$ Re = 160 , 000 ) a deviation from the ideal Kolmogorov theory can be observed in the absence of an explicit turbulence model. Cumulant models with fourth-order convergent diffusion show much better results than single relaxation time methods.

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Section: Appendix A4: Collisionmentioning

confidence: 99%

Under-resolved and large eddy simulations of a decaying Taylor–Green vortex with the cumulant lattice Boltzmann method

Geier

Lenz

Schönherr

et al. 2020

Theor. Comput. Fluid Dyn.

Self Cite

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“…Due to this explicit nature and the beneficial communication pattern, it suites today's distributed memory high-performance computer architectures extremely well. In addition, its stream-collide structure also maps well on GPUs (see Geier and Schönherr [10]). Still, the LBM should not only be seen as a means for simulating flows governed by the Navier-Stokes equations but also allows the solution of different systems of partial differential equations (see for example Kataoka and Tsutahara [14] and Chai et al [5]).…”

Section: Introductionmentioning

confidence: 91%

A structured approach to the construction of stable linear Lattice Boltzmann collision operator

Otte

Frank

2020

Computers & Mathematics with Applications

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We introduce a structured approach to the construction of linear BGK-type collision operators ensuring that the resulting Lattice-Boltzmann methods are stable with respect to a weighted L 2 -norm. The results hold for particular boundary conditions including periodic, bounce-back, and bounce-back with flipping of sign boundary conditions. This construction uses the equivalent moment-space definition of BGK-type collision operators and the notion of stability structures as guiding principle for the choice of the equilibrium moments for those moments influencing the error term only but not the order of consistency. The presented structured approach is then applied to the 3D isothermal linearized Euler equations with non-vanishing background velocity. Finally, convergence results in the strong discrete L ∞ -norm highlight the suitability of the structured approach introduced in this manuscript.

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“…The latter source also lists additional memory layout patterns for the LBM. An even more sophisticated alternative is the Esoteric twist (EsoTwist) [49,50] which offers higher geometric flexibility, however, this is not the focus of this work.…”

Section: Memory Layout Patternmentioning

confidence: 99%

A Holistic Scalable Implementation Approach of the Lattice Boltzmann Method for CPU/GPU Heterogeneous Clusters

et al. 2017

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Heterogeneous clusters are a widely utilized class of supercomputers assembled from different types of computing devices, for instance CPUs and GPUs, providing a huge computational potential. Programming them in a scalable way exploiting the maximal performance introduces numerous challenges such as optimizations for different computing devices, dealing with multiple levels of parallelism, the application of different programming models, work distribution, and hiding of communication with computation. We utilize the lattice Boltzmann method for fluid flow as a representative of a scientific computing application and develop a holistic implementation for large-scale CPU/GPU heterogeneous clusters. We review and combine a set of best practices and techniques ranging from optimizations for the particular computing devices to the orchestration of tens of thousands of CPU cores and thousands of GPUs. Eventually, we come up with an implementation using all the available computational resources for the lattice Boltzmann method operators. Our approach shows excellent scalability behavior making it future-proof for heterogeneous clusters of the upcoming architectures on the exaFLOPS scale. Parallel efficiencies of more than 90% are achieved leading to 2604.72 GLUPS utilizing 24,576 CPU cores and 2048 GPUs of the CPU/GPU heterogeneous cluster Piz Daint and computing more than 6.8 × 10 9 lattice cells.

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Esoteric Twist: An Efficient in-Place Streaming Algorithmus for the Lattice Boltzmann Method on Massively Parallel Hardware

Cited by 49 publications

References 28 publications

Under-resolved and large eddy simulations of a decaying Taylor–Green vortex with the cumulant lattice Boltzmann method

Under-resolved and large eddy simulations of a decaying Taylor–Green vortex with the cumulant lattice Boltzmann method

A structured approach to the construction of stable linear Lattice Boltzmann collision operator

A Holistic Scalable Implementation Approach of the Lattice Boltzmann Method for CPU/GPU Heterogeneous Clusters

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