Pseudoentropic derivation of the regularized lattice Boltzmann method

Krämer, Andreas; Wilde, Dominik; Küllmer, Knut; Reith, Dirk; Foysi, Holger

doi:10.1103/physreve.100.023302

Cited by 23 publications

(14 citation statements)

References 69 publications

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“…Lee et al used the benchmark for their low-dissipation solver based on OpenFOAM [87]. The same benchmark was also used in several studies using different variants of the lattice Boltzmann scheme [88][89][90], the semi-Lagrangian off-lattice Boltzmann method [3], the lattice kinetic scheme [91] and GKS [92,93].…”

Section: Three-dimensional Taylor-green Vortexmentioning

confidence: 99%

“…In a recent paper Krämer et al [89] used the Taylor-Green vortex test case for the investigation of a regularized LBM method (RLBM) derived from a pseudoentropy maximization and the KBC method named after Karlin, Bösch and Chikatamarla [24]. Both methods apply regularization to non-hydrodynamic moments in order to improve the stability of the lattice Boltzmann scheme.…”

Section: Comparison To Regularized and Kbc Lattice Boltzmann Modelsmentioning

confidence: 99%

“…We note that this is not necessary in the current case, but it is shown here for fairness as the other two methods are explicitly designed for maximum stability. We use the original data from [89] which was computed on a grid with 80 3 nodes and compare them to our results for the same resolution. The advection correction (KF3) is not used here since it requires finite differences and would render the comparison unfair.…”

Section: Comparison To Regularized and Kbc Lattice Boltzmann Modelsmentioning

confidence: 99%

“…Comparison between the K17 and K17L method with two other recent lattice Boltzmann methods: the regularized LBM (RLBM) and the KBC method. The data for the latter two methods were supplied by the authors of [89]. The RLBM and KBC methods were designed to maximize stability, while the K17 method maximizes accuracy.…”

Section: Vortical Structuresmentioning

confidence: 99%

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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: Three-dimensional Taylor-green Vortexmentioning

confidence: 99%

Section: Comparison To Regularized and Kbc Lattice Boltzmann Modelsmentioning

confidence: 99%

Section: Comparison To Regularized and Kbc Lattice Boltzmann Modelsmentioning

confidence: 99%

Section: Vortical Structuresmentioning

confidence: 99%

See 2 more Smart Citations

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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“…Throughout the 100,000 time steps of the simulation, maximum velocity and enstrophy are measured. The enstrophy, a measure for the turbulent energy dissipation in the system with respect to the resolved flow quantities [8,12], increases as turbulence intensity increases in the regarded volume.…”

Section: Air Flowmentioning

confidence: 99%

Designing Air Flow with Surrogate-Assisted Phenotypic Niching

Hagg

Wilde

Asteroth

et al. 2020

Parallel Problem Solving From Nature – PPSN XVI

Self Cite

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In complex, expensive optimization domains we often narrowly focus on finding high performing solutions, instead of expanding our understanding of the domain itself. But what if we could quickly understand the complex behaviors that can emerge in said domains instead? We introduce surrogate-assisted phenotypic niching, a quality diversity algorithm which allows to discover a large, diverse set of behaviors by using computationally expensive phenotypic features. In this work we discover the types of air flow in a 2D fluid dynamics optimization problem. A fast GPU-based fluid dynamics solver is used in conjunction with surrogate models to accurately predict fluid characteristics from the shapes that produce the air flow. We show that these features can be modeled in a data-driven way while sampling to improve performance, rather than explicitly sampling to improve feature models. Our method can reduce the need to run an infeasibly large set of simulations while still being able to design a large diversity of air flows and the shapes that cause them. Discovering diversity of behaviors helps engineers to better understand expensive domains and their solutions.

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