Current status of Lattice Boltzmann Methods applied to aerodynamic, aeroacoustic, and thermal flows

Sharma, Keerti Vardhan; Straka, Róbert; Tavares, Frederico W.

doi:10.1016/j.paerosci.2020.100616

Cited by 47 publications

(19 citation statements)

References 193 publications

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“…The lattice Boltzmann (LB) methods, which arise as minimally discretized numerical schemes of the Boltzmann transport equation-a cornerstone formulation in kinetic theory, have attracted much attention in recent decades [1][2][3][4][5]. As a mesoscopic approach, these methods have enriched the variety of computational fluid dynamics (CFD) techniques that are being developed and has been applied to a wide range of fluid flows successfully [6][7][8][9]. This involves the evolution of the distribution of the particle populations by a collision step, which is then followed by lock-step advection along discrete directions-referred to as the streaming step.…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Central Moment Lattice Boltzmann Method on a Cuboid Lattice for Anisotropic and Inhomogeneous Flows

Yahia

Schupbach

Premnath

2021

Fluids

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Lattice Boltzmann (LB) methods are usually developed on cubic lattices that discretize the configuration space using uniform grids. For efficient computations of anisotropic and inhomogeneous flows, it would be beneficial to develop LB algorithms involving the collision-and-stream steps based on orthorhombic cuboid lattices. We present a new 3D central moment LB scheme based on a cuboid D3Q27 lattice. This scheme involves two free parameters representing the ratios of the characteristic particle speeds along the two directions with respect to those in the remaining direction, and these parameters are referred to as the grid aspect ratios. Unlike the existing LB schemes for cuboid lattices, which are based on orthogonalized raw moments, we construct the collision step based on the relaxation of central moments and avoid the orthogonalization of moment basis, which leads to a more robust formulation. Moreover, prior cuboid LB algorithms prescribe the mappings between the distribution functions and raw moments before and after collision by using a moment basis designed to separate the trace of the second order moments (related to bulk viscosity) from its other components (related to shear viscosity), which lead to cumbersome relations for the transformations. By contrast, in our approach, the bulk and shear viscosity effects associated with the viscous stress tensor are naturally segregated only within the collision step and not for such mappings, while the grid aspect ratios are introduced via simpler pre- and post-collision diagonal scaling matrices in the above mappings. These lead to a compact approach, which can be interpreted based on special matrices. It also results in a modular 3D LB scheme on the cuboid lattice, which allows the existing cubic lattice implementations to be readily extended to those based on the more general cuboid lattices. To maintain the isotropy of the viscous stress tensor of the 3D Navier–Stokes equations using the cuboid lattice, corrections for eliminating the truncation errors resulting from the grid anisotropy as well as those from the aliasing effects are derived using a Chapman–Enskog analysis. Such local corrections, which involve the diagonal components of the velocity gradient tensor and are parameterized by two grid aspect ratios, augment the second order moment equilibria in the collision step. We present a numerical study validating the accuracy of our approach for various benchmark problems at different grid aspect ratios. In addition, we show that our 3D cuboid central moment LB method is numerically more robust than its corresponding raw moment formulation. Finally, we demonstrate the effectiveness of the 3D cuboid central moment LB scheme for the simulations of anisotropic and inhomogeneous flows and show significant savings in memory storage and computational cost when used in lieu of that based on the cubic lattice.

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Section: Introductionmentioning

confidence: 99%

Three-Dimensional Central Moment Lattice Boltzmann Method on a Cuboid Lattice for Anisotropic and Inhomogeneous Flows

Yahia

Schupbach

Premnath

2021

Fluids

View full text Add to dashboard Cite

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“…Substituting (B 33) and (B 34) into (B 32), we get the heat flux q in the energy equation (B 31) as a combination of the Fourier law and the Appendix C. Thermodynamic data for benchmarks Data useful for reproducing the benchmarks in § 4 is provided here for reference. The data source is the publicly accessible GRI-Mech 3.0 mechanism (Smith et al 1999) and it is calculated by the open source code Cantera (Goodwin et al 2018)…”

Section: Declaration Of Interestsmentioning

confidence: 99%

“…Thermodynamic data necessary for the simulations such as the specific heats, molecular masses and transport coefficients including dynamic viscosity, thermal conductivity and the Stefan-Maxwell diffusivities were obtained from the publicly accessible GRI-Mech 3.0 mechanism (Smith et al 1999). The lattice Boltzmann code was coupled to the open source code Cantera (Goodwin et al 2018) which is capable of parsing the GRI-Mech mechanism data file.…”

Section: Overview Of Numerical Implementationmentioning

confidence: 99%

“…, Q − 1, fitting into a regular space-filling lattice, with the kinetic equation for the populations f i (x, t) following a simple algorithm of 'stream along links c i and collide at the nodes x in discrete time t'. Since its inception (Higuera & Jiménez 1989;Higuera, Succi & Benzi 1989), LBM has evolved into a versatile tool for the simulation of complex flows including transitional flows (Dorschner, Chikatamarla & Karlin 2017), flows in complex moving geometries (Dorschner et al 2016), compressible flows (Yan et al 2013;Frapolli, Chikatamarla & Karlin 2016b;Dorschner, Bösch & Karlin 2018;Gan et al 2018;Lin & Luo 2018), multiphase flows (Mazloomi, Chikatamarla & Karlin 2015Wöhrwag et al 2018), rarefied gas (Shan, Yuan & Chen 2006) and nanoflow (Montessori et al 2016;Montemore et al 2017), to mention a few recent instances; see Succi (2018), Krüger et al (2017) and Sharma, Straka & Tavares (2020) for a discussion of LBM and its application areas.…”

Section: Introductionmentioning

confidence: 99%

“…2017), to mention a few recent instances; see Succi (2018), Krüger et al. (2017) and Sharma, Straka & Tavares (2020) for a discussion of LBM and its application areas.…”

Section: Introductionmentioning

confidence: 99%

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