2018
DOI: 10.1103/physreve.97.053303
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Abstract: Lattice Boltzmann (LB) models used for the computation of fluid flows represented by the Navier-Stokes (NS) equations on standard lattices can lead to non-Galilean-invariant (GI) viscous stress involving cubic velocity errors. This arises from the dependence of their third-order diagonal moments on the first-order moments for standard lattices, and strategies have recently been introduced to restore Galilean invariance without such errors using a modified collision operator involving corrections to either the … Show more

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Cited by 21 publications
(23 citation statements)
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References 54 publications
(98 reference statements)
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“…Corrections to eliminate these errors will then be derived in what follows. The analysis for a 3D LBE formulation given above follows the approach presented in Premnath and Banjeree [44] and Hajabdollahi and Premnath [45], which was adopted for constructing a rectangular LB algorithm recently [26].…”
Section: Equilibria and Sources: Central Moments And Raw Momentsmentioning
confidence: 99%
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“…Corrections to eliminate these errors will then be derived in what follows. The analysis for a 3D LBE formulation given above follows the approach presented in Premnath and Banjeree [44] and Hajabdollahi and Premnath [45], which was adopted for constructing a rectangular LB algorithm recently [26].…”
Section: Equilibria and Sources: Central Moments And Raw Momentsmentioning
confidence: 99%
“…The structures of the non-equilibrium moments can then be obtained from Equation (20a-f) after substituting for the time derivatives of the conserved moments by means of terms related to the spatial derivatives using Equation (18a-d) and simplifying the resulting equations by retaining terms of O(u 3 i ) (following Hajabdollahi and Premnath [45]). The off-diagonal second order non-equilibrium moments n…”
Section: And Nmentioning
confidence: 99%
“…Using the standard D3Q27 lattice, the problem can be removed by a modification of the relaxation rate [47] or the equilibrium moments [21]. This correction is usually applied in the cumulant method and has also been included into some central moment methods [19]. However, in their recent work Coreixas and co-workers analysed cumulant methods omitting the correction [20].…”
Section: Galilean Invariance Correctionmentioning
confidence: 99%
“…(A. 19) In what follows, we omit equations for cumulants which can be obtained by permuting indices in the listed equations. The first few cumulants are seen to be identical to the first few central moments: and so on by permuting indices.…”
Section: Appendix A3: Forward Cumulant Transformationmentioning
confidence: 99%
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