Accuracy and Numerical Stabilty Analysis of Lattice Boltzmann Method with Multiple Relaxation Time for Incompressible Flows

Pradipto, None; Purqon, Acep

doi:10.1088/1742-6596/877/1/012035

Cited by 5 publications

(9 citation statements)

References 13 publications

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“…The LBM is a Navier-Stokes flow solver that discretizes space into a Cartesian lattice and time into discrete time steps [1][2][3][4]. For each point on the lattice, density ρ and velocity u of the flow are computed from so-called density distribution functions (DDFs) f i (also called fluid populations).…”

Section: A Lbm-overviewmentioning

confidence: 99%

“…b is a constant called exponent bias and n m is the number of bits in the mantissa (values in Table II). The precision is log 10 (2 n m +1 ) decimal digits 3 and the truncation error is…”

Section: Overviewmentioning

confidence: 99%

“…The lattice Boltzmann method (LBM) [1][2][3][4] is a powerful tool to simulate fluid flow. The parallel nature of the underlying algorithm has led to (multi-)GPU implementations , becoming a popular choice as speedup can be up to two orders of magnitude compared to CPUs at similar power consumption.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2022

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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.

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Section: A Lbm-overviewmentioning

confidence: 99%

“…b is a constant called exponent bias and n m is the number of bits in the mantissa (values in Table II). The precision is log 10 (2 n m +1 ) decimal digits 3 and the truncation error is…”

Section: Overviewmentioning

confidence: 99%

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

et al. 2022

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“…Subsequently, the LBM with a D3Q19 discrete velocity model was applied to obtain the permeability of the three-dimensional digital cores with fractures. The lattice Bhatnagar-Gross-Krook collision approximation was applied to simplify the quantitation (Pradipto and Purqon, 2017). Grain walls were considered as non-slip solid surfaces, and a fixed pressure gradient of 0.00005 was set across the cores.…”

Section: Methodsmentioning

confidence: 99%

Effects of microfractures on permeability in carbonate rocks based on digital core technology

Liu

Zhang

Li³

et al. 2022

Adv. Geo-Energy Res.

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Carbonate reservoirs develop many different types of microfractures that play an important role in increasing the effective reservoir space and permeability. Thus, the qualitative and quantitative characterisation of the effect of microfractures on permeability in rocks is essential. In this study, a quantitative method for evaluating the impact of different microfracture parameters on carbonate rock permeability was proposed. Lattice Boltzmann simulations were carried on two carbonate digital cores with different types of artificially added microfractures. Based on the simulation results, a partial least squares regression analysis was used to investigate the impact of microfractures on the permeability of the cores. Increases in the fracture length, aperture, and density were found to linearly increase the permeability of the carbonate rocks, and as the fracture length increased to penetrate the whole core, an exponential increase in permeability was observed. Additionally, the effect of microfractures on the digital core permeability was more significant in cores with high permeability compared to that in low-permeability cores. Although both fractures and matrix permeability contribute to the permeability of the digital cores, the former were found to have a greater effect on the permeability.

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“…In recent decades, the lattice Boltzmann method (LBM) [1,2] has been developed into a promising and successful alternative to the conventional computational fluid dynamics (CFD) method, particularly for incompressible flows [3], porous-media flows [4], magnetohydrodynamics [5], and single-and multi-phase fluid flows [6]; more recently see [7][8][9][10][11]. Different from the traditional CFD, the LBM models the fluid as a group of fictive particles by using discrete distribution functions [1].…”

Section: Introductionmentioning

confidence: 99%

Mass-Conserved Wall Treatment of the Non-Equilibrium Extrapolation Boundary Condition in Lattice Boltzmann Method

Feng

Lim

2018

Energies

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In lattice Boltzmann simulations, the widely used non-equilibrium extrapolation method for velocity and pressure boundary conditions can cause a constant mass leakage under certain circumstances, particularly when an external force field is imposed on the fluid domain. The non-equilibrium distribution function at the boundary uses a first-order extrapolation method on the corresponding data of adjacent fluid nodes. In addition, based on this extrapolation method, the macroscopic velocity and density at the boundary nodes are obtained. Therefore, the corresponding equilibrium component of the distribution function can be calculated explicitly. Regarding the no-slip wall boundary condition, we found that the mass leakage primarily results from the extrapolation scheme for the density term in the equilibrium component of the distribution function at the boundary node. In this study, a mass-conserved wall treatment method is developed to correct the existing density term for guaranteeing the conservation of mass. Several benchmark test cases were simulated and compared to prove the justification of the newly developed mass-conserved boundary condition, and the results show a good agreement with those in the existing literature.

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Accuracy and Numerical Stabilty Analysis of Lattice Boltzmann Method with Multiple Relaxation Time for Incompressible Flows

Cited by 5 publications

References 13 publications

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

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

Effects of microfractures on permeability in carbonate rocks based on digital core technology

Mass-Conserved Wall Treatment of the Non-Equilibrium Extrapolation Boundary Condition in Lattice Boltzmann Method

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