Linear stability and isotropy properties of athermal regularized lattice Boltzmann methods

Wissocq, Gauthier; Coreixas, Christophe; Boussuge, Jean‐François

doi:10.1103/physreve.102.053305

Cited by 32 publications

(71 citation statements)

References 80 publications

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“…Hydrodynamic equations (40,41) are coupled to thermal effects Eqs. (42,43,44) through the perfect gas EOS = , = and heat capacities = /( −1) and = /( −1). Then, combining Eqs.…”

Section: Unified Model On Standard Latticementioning

confidence: 99%

“…(40,41) with any choice among Eqs. (42,43,44) and assuming a constant and values one gets the kinetic tensor and pressure equations,…”

Section: Unified Model On Standard Latticementioning

confidence: 99%

“…While Eqs. (42,43,44) are equivalent, their discretized counterparts may lead to highly different stability and accuracy properties. The entropy equation in non-conservative format being mainly an advection equation with source terms, it is easily discretized and leads to robust results, explaining this choice of energy variable, widely present in the LB literature 13,[22][23][24] .…”

Section: Thermal Couplingmentioning

confidence: 99%

“…Numerical experiments showed better stability properties for Ma 1.7 simulations than with the usual evaluation, however, no measurable difference was observed for lower Ma numbers when using . This change formally introduces a O (Δ ) error in the stress tensor, which is of the order of the leading numerical error already introduced by the non-BGK collision kernel 17,26,42 .…”

Section: Non-equilibrium Reconstructionmentioning

confidence: 99%

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A unified hybrid lattice-Boltzmann method for compressible flows: Bridging between pressure-based and density-based methods

et al. 2021

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A unified expression for high-speed compressible segregated consistent lattice Boltzmann methods, namely, pressure-based and improved density-based methods, is given. It is theoretically proved that in the absence of forcing terms, these approaches are strictly identical and can be recast in a unique form. An important result is that the difference with classical density-based methods lies in the addition of fourth-order term in the equilibrium function. It is also shown that forcing terms used to balance numerical errors in both original pressure-based and improved density-based methods can be written in a generalized way. A hybrid segregated efficient lattice-Boltzmann for compressible flow based on this unified model, equipped with a recursive regularization kernel, is proposed and successfully assessed on a wide set of test cases with and without shock waves.

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“…Hydrodynamic equations (40,41) are coupled to thermal effects Eqs. (42,43,44) through the perfect gas EOS = , = and heat capacities = /( −1) and = /( −1). Then, combining Eqs.…”

Section: Unified Model On Standard Latticementioning

confidence: 99%

“…(40,41) with any choice among Eqs. (42,43,44) and assuming a constant and values one gets the kinetic tensor and pressure equations,…”

Section: Unified Model On Standard Latticementioning

confidence: 99%

Section: Thermal Couplingmentioning

confidence: 99%

Section: Non-equilibrium Reconstructionmentioning

confidence: 99%

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A unified hybrid lattice-Boltzmann method for compressible flows: Bridging between pressure-based and density-based methods

et al. 2021

Self Cite

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“…With this procedure, we introduce ghost Reynolds numbers [34] for each moment order larger than one. Hence with the scan over the parameter space induced by bold-italicς, we test values of possible ghost Reynolds numbers, which in terms of (3.11) appear as controllable bulk [64] and hyper viscosities [37,40]. Based on that, three-dimensional BF-stability maps are obtained and gathered in figure 5, where the x-, y-, z-coordinate axes correspond to ςq,μ, ςe, ςε,Π, respectively.…”

Section: Numerical Resultsmentioning

confidence: 99%

Linear and brute force stability of orthogonal moment multiple-relaxation-time lattice Boltzmann methods applied to homogeneous isotropic turbulence

Simonis

Haussmann

Kronberg

et al. 2021

Phil. Trans. R. Soc. A.

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Multiple-relaxation-time (MRT) lattice Boltzmann methods (LBM) based on orthogonal moments exhibit lattice Mach number dependent instabilities in diffusive scaling. The present work renders an explicit formulation of stability sets for orthogonal moment MRT LBM. The stability sets are defined via the spectral radius of linearized amplification matrices of the MRT collision operator with variable relaxation frequencies. Numerical investigations are carried out for the three-dimensional Taylor–Green vortex benchmark at Reynolds number 1600. Extensive brute force computations of specific relaxation frequency ranges for the full test case are opposed to the von Neumann stability set prediction. Based on that, we prove numerically that a scan over the full wave space, including scaled mean flow variations, is required to draw conclusions on the overall stability of LBM in turbulent flow simulations. Furthermore, the von Neumann results show that a grid dependence is hardly possible to include in the notion of linear stability for LBM. Lastly, via brute force stability investigations based on empirical data from a total number of 22 696 simulations, the existence of a deterministic influence of the grid resolution is deduced. This article is part of the theme issue ‘Progress in mesoscale methods for fluid dynamics simulation’.

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Lattice Boltzmann model for diffusion equation with reduced truncation errors: Applications to Gaussian filtering and image processing

Ilyin

2023

Applied Mathematics and Computation

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Linear stability and isotropy properties of athermal regularized lattice Boltzmann methods

Cited by 32 publications

References 80 publications

A unified hybrid lattice-Boltzmann method for compressible flows: Bridging between pressure-based and density-based methods

A unified hybrid lattice-Boltzmann method for compressible flows: Bridging between pressure-based and density-based methods

Linear and brute force stability of orthogonal moment multiple-relaxation-time lattice Boltzmann methods applied to homogeneous isotropic turbulence

Lattice Boltzmann model for diffusion equation with reduced truncation errors: Applications to Gaussian filtering and image processing

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