Truncation effect on Taylor–Aris dispersion in lattice Boltzmann schemes: Accuracy towards stability

Ginzburg, Irina; Roux, Laëtitia

doi:10.1016/j.jcp.2015.07.017

Cited by 27 publications

(15 citation statements)

References 55 publications

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“…As by default, the LBM evolves as a time-marching procedure, the algorithm can be initialized with A = 1 and so maintained until the simulation is about to reach the steadystate criterion; at this point, we switch to A = 0 so that, right after, when the steady-state regime is reached the corresponding time-independent solution supports the consistency properties discussed in this work. This procedure mimics the protocol employed in the flagging of the anti-numerical-diffusion correction popularized in the simulation of time-varying advection-diffusion problems [43,45] .…”

Section: Discussionmentioning

confidence: 99%

“…This distinction is well-established within CFD community. For example, the numerical diffusion phenomenon, which originates from a mixed space/time derivative term of the advective flux, is known to affect time-dependent problems, where it can be cancelled with the inclusion of a anti-numerical-diffusion correction [42][43][44][45] . At steady-state this error does not exist, so the inclusion of such a correction, rather than beneficial, will introduce the exact same numerical diffusion artefact that was designed to eliminate in the first place.…”

Section: Introductionmentioning

confidence: 99%

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Discrete effects on the forcing term for the lattice Boltzmann modeling of steady hydrodynamics

Silva

2020

Computers & Fluids

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This work concerns with the clean inclusion of the forcing term in the lattice Boltzmann method (LBM) for the modeling of non-uniform body forces in steady hydrodynamics. The study is conducted for the two-relaxation-time (TRT) scheme. Here, we consider a simple, but yet sufficiently generic, flow configuration driven by a spatially varying body force based on which we derive the analytical solution of the forced LBM-TRT and compare two force strategies set by first-and second-order expansions. This procedure exactly establishes the macroscopic system satisfied by each force formulation at discrete level. The obtained theoretical results are further verified in two distinct benchmark channel flow problems. Overall, this study shows that the spatial discrete effects posed by the LBM modeling of the force term may come in through two sources. The first one is a defect inherent to LBM, arising from the non-local spatial discretization of the forcing term, and given by the discrete Laplacian of the body force. While it corrupts the discrete momentum balance with a non-linear viscosity dependent term in the single-relaxation-time schemes, this inconsistency is avoided with the TRT scheme, through its free-tunable relaxation degree of freedom . The other error source is unique to the use of second-order force expansions, where its nonzero second-order velocity moment interferes with the discrete momentum balance through a spurious first-order derivative term, leading to several forms of inconsistency in the LBM steady solution. For simulations under the convective scaling it makes the LBM scheme a numerical representation of a differential system distinct from the physical one, whereas under the diffusive scaling it leads to viscosity-dependent numerical errors, which corrupt the otherwise consistent structure of TRT steady-state solutions. In contrast, the defects reported herein are absent with the first-order force expansion scheme operated within the scope of the LBM-TRT model for steady hydrodynamics.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Discrete effects on the forcing term for the lattice Boltzmann modeling of steady hydrodynamics

Silva

2020

Computers & Fluids

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“…28 The numerical simulations in this work will be performed with the steadystate formulation, which enables us to verify all new bounding techniques through a quite arbitrarily, parameter range (physical contrasts, P eclet number), without concerns from stability. 31,32,34,38,60,83 However, the transient MR ADE interface-conjugate has been also developped; 40,42 its update to N-MR is identical with the boundary counterpart, and it is exemplified with the steady-state interfaceconjugate treatment in Sec. III D. The MR interface-conjugate is also formulated 40 for the velocity and normal-stress continuous flow conditions; their release from the tangential stress projection shell becomes possible following the N-MR path.…”

Section: F Summary and Extensionsmentioning

confidence: 99%

“…1. the couple of the TRT bulk equations ( 26), assembled for every bulk link; 2. the local mass-conservation equation ( 28), assembled for every fluid node; 3. the MR closure equation (34), assembled for every wall-cut link or, alternatively, the A-LSOB closure equations assembled innode as provided below. 4. the couple of the MR interface-conjugate equations (36a) and (36b), assembled for every interface-cut link; they replace the couple of bulk equations.…”

Section: E Steady-state Algorithms With the Mr N-mr And A-lsobmentioning

confidence: 99%

“…We address them with the Taylor dispersion Ansatz 34,92 where the adjacent EMM problem combines the parabolic tangential velocity and mass-source fields. We will show that in the presence of the rotated advection, the quartic polynomial solution becomes only available with the hydrodynamic advection-diffusion weights, and it incorporates an anisotropic truncation correction; the latter obeys the spurious non-linear P eclet scale and vanishes only with a particular choice of two remaining free model parameters.…”

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confidence: 99%

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Mass-balance and locality versus accuracy with the new boundary and interface-conjugate approaches in advection-diffusion lattice Boltzmann method

Ginzburg

Silva

2021

Physics of Fluids

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We introduce two new approaches, called A-LSOB and N-MR, for boundary and interface-conjugate conditions on flat or curved surface shapes in the advection-diffusion lattice Boltzmann method (LBM). The Local Second-Order, single-node A-LSOB enhances the existing Dirichlet and Neumann normal boundary treatments with respect to locality, accuracy, and P eclet parametrization. The normal-multi-reflection (N-MR) improves the directional flux schemes via a local release of their nonphysical tangential constraints. The A-LSOB and N-MR restore all first-and second-order derivatives from the nodal non-equilibrium solution, and they are conditioned to be exact on a piece-wise parabolic profile in a uniform arbitrary-oriented tangential velocity field. Additionally, the most compact and accurate single-node parabolic schemes for diffusion and flow in grid-inclined pipes are introduced. In simulations, the global mass-conservation solvability condition of the steady-state, two-relaxation-time (S-TRT) formulation is adjusted with either (i) a uniform mass-source or (ii) a corrective surface-flux. We conclude that (i) the surface-flux counterbalance is more accurate than the bulk one, (ii) the A-LSOB Dirichlet schemes are more accurate than the directional ones in the high P eclet regime, (iii) the directional Neumann advective-diffusive flux scheme shows the best conservation properties and then the best performance both in the tangential no-slip and interface-perpendicular flow, and (iv) the directional non-equilibrium diffusive flux extrapolation is the least conserving and accurate. The error P eclet dependency, Neumann invariance over an additive constant, and truncation isotropy guide this analysis. Our methodology extends from the d2q9 isotropic S-TRT to 3D anisotropic matrix collisions, Robin boundary condition, and the transient LBM.

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A single-relaxation-time lattice Boltzmann model for anisotropic advection-diffusion equation based on the diffusion velocity flux formulation

Perko

2018

Comput Geosci

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Truncation effect on Taylor–Aris dispersion in lattice Boltzmann schemes: Accuracy towards stability

Cited by 27 publications

References 55 publications

Discrete effects on the forcing term for the lattice Boltzmann modeling of steady hydrodynamics

Discrete effects on the forcing term for the lattice Boltzmann modeling of steady hydrodynamics

Mass-balance and locality versus accuracy with the new boundary and interface-conjugate approaches in advection-diffusion lattice Boltzmann method

A single-relaxation-time lattice Boltzmann model for anisotropic advection-diffusion equation based on the diffusion velocity flux formulation

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