Towards a better understanding of wall-driven square cavity flows using the lattice Boltzmann method

An, Byungjin; Mellibovsky, Fernando; Bergadà, Josep M.; Sang, Weimin

doi:10.1016/j.apm.2020.01.057

Cited by 10 publications

(11 citation statements)

References 41 publications

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“…The lattice Boltzmann method has been shown a valid approach to even more complex fluid dynamic problems than those tackled here, such as involving heat transfer [17], non-Newtonian fluids [18], hydrology applications [19], porous media [20] or fluid-solid interfaces [21] among others, and is subject to constant ongoing development for its applications to new fields [22][23][24][25][26][27]. The numerical method has been coded in-house and extensively tested in the past [1][2][3], where thorough mesh-independence studies were undertaken. Based on the previous experience and comprehensive mesh convergence analysis, the square cavity has been resolved with a uniform Cartesian mesh of 1024 1024…”

Section: U V P X Y T Re U V P X Y T Re M U V P X Y T Re U V P X Y T R...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…A systematical research on the transitional dynamics of several 2D wall-driven cavity flows was performed in several previous studies [1][2][3]. In particular, in [2,3] we took into consideration the flow within a square enclosure driven by the tangential motion of two opposing walls, with equal speed, in parallel and antiparallel directions. The purpose was to unfold the whole bifurcation diagram, to locate all occurring bifurcations, to analyse the physics encoded behind each one of them and to discuss their bearing over the flow field.…”

Section: Introductionmentioning

confidence: 99%

“…Here we undertake a thorough systematic analysis of this problem, with special attention in regards to the first Hopf and Neimark-Sacker bifurcations, the onset of chaos, the symmetry disruption and the energy cascade, which serve to link the different vortical structures that appear in the flow to their corresponding frequency peaks and associated energy. Since the present study is an extension of authors' previous work, the in-house code validation and the resolution study will not be repeated in the present manuscript, but can be found in [1][2][3].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Square Cavity Flow Driven by Two Mutually Facing Sliding Walls

Bergadà²,

Sang

et al. 2022

SSRN Journal

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Section: U V P X Y T Re U V P X Y T Re M U V P X Y T Re U V P X Y T R...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Square Cavity Flow Driven by Two Mutually Facing Sliding Walls

Bergadà²,

Sang

et al. 2022

SSRN Journal

Self Cite

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“…A complete description of gas microflows involved in the micro/nano-electro-mechanical systems (MEMS/NEMS) [1] remains a challenge for many researchers during the last decades. Lid-driven cavity flow is one of the classical benchmark problems of computational fluid dynamics (CFD) [2][3][4][5]. Such flow has been analyzed by various computational methods like the Navier-Stokes-Fourier equations (NSF) [6,7], Direct Simulation Monte Carlo (DSMC) [7][8][9][10] and moment equations approach [6,10,11].…”

Section: Introductionmentioning

confidence: 99%

Numerical Study of Gas Microflow within a Triangular Lid-driven Cavity

Elguennouni¹,

Hssikou²,

Baliti³

et al. 2020

Adv. sci. technol. eng. syst. j.

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A rarefied gas flow is modeled inside two cases of triangular lid-driven microcavity using single (SRT) and multi-relaxation time (MRT) lattice Boltzmann approaches. In the first one, the right angle is in the top-left corner and the upper wall moves with positive horizontal velocity. However, in the second case, the right angle is in the bottom-left corner and the bottom wall moves with negative horizontal velocity. Unlike the classical form of square cavities, widely treated in the literature, the triangular form has a diagonal wall that affects the flow motion. At the moving wall, diffuse scattering boundary condition (DSBC) is employed while at the stationary sides, a combination of bounce-back and specular reflection boundary conditions (BSBC) is used. The computations are primarily performed in the slip and early transition regimes. The rarefaction effect, given by the Knudsen number (Kn) value, on the profiles of velocity components, is examined for both approaches. This study proves that for the higher values of Kn, the SRT-LBM approach cannot provide accurate results, particularly, near the inclined wall. However, the MRT-LBM approach confirms its validity even in the transition regime. A comparison with Direct Simulation Monte Carlo (DSMC) results for horizontal velocity contours shows the efficiency of the MRT-LBM approach than the SRT-LBM one which breaks down for rarefied flows.

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A modified lattice Boltzmann approach based on radial basis function approximation for the non‐uniform rectangular mesh

Hu,

Bergadà,

et al. 2024

Numerical Methods in Fluids

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We have presented a novel lattice Boltzmann approach for the non‐uniform rectangular mesh based on the radial basis function approximation (RBF‐LBM). The non‐uniform rectangular mesh is a good option for local grid refinement, especially for the wall boundaries and flow areas with intensive change of flow quantities. Which allows, the total number of grid cells to be reduced and so the computational cost, therefore improving the computational efficiency. But the grid structure of the non‐uniform rectangular mesh is no longer applicable to the classic lattice Boltzmann method (CLBM), which is based on the famous BGK collision‐streaming evolution. This is why the present study is inspired by the idea of the interpolation‐supplemented LBM (ISLBM) methodology. The ISLBM algorithm is improved in the present manuscript and developed into a novel LBM approach through the radial basis function approximation instead of the Lagrangian interpolation scheme. The new approach is validated for both steady states and unsteady periodic solutions. The comparison between the radial basis function approximation and the Lagrangian interpolation is discussed. It is found that the novel approach has a good performance on computational accuracy and efficiency. Proving that the non‐uniform rectangular mesh allows grid refinement while obtaining precise flow predictions.

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Towards a better understanding of wall-driven square cavity flows using the lattice Boltzmann method

Cited by 10 publications

References 41 publications

Square Cavity Flow Driven by Two Mutually Facing Sliding Walls

Square Cavity Flow Driven by Two Mutually Facing Sliding Walls

Numerical Study of Gas Microflow within a Triangular Lid-driven Cavity

A modified lattice Boltzmann approach based on radial basis function approximation for the non‐uniform rectangular mesh

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