Fluid-structure interaction with the entropic lattice Boltzmann method

Dorschner, Benedikt; Karlin, Iliya V.

doi:10.1103/physreve.97.023305

Cited by 28 publications

(17 citation statements)

References 68 publications

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“…Deviation of the (eq) xyy moment of (a) the second-order and (b) entropic discrete EDFs from their continuous counterpart as a function of the Mach number (Ma) for a streamwise shift of U x = δ x /δ t and different spanwise Mach numbers: Bottom to top ( ) 0.173, ( ) 0.346, and ( ) 0.519. appropriate shift. This explains why compressible flows can be simulated using low-order velocity discretizations, which are usually restricted in terms of velocity and/or temperature ranges [1][2][3]11,66]. Nevertheless, in order to properly recover the macroscopic behavior of Navier-Stokes-Fourier equations, it is mandatory to have velocity-and temperature-dependent shift velocities which will eventually require (nonconservative) space interpolation.…”

Section: B Error In Equilibrium Momentsmentioning

confidence: 99%

Extensive analysis of the lattice Boltzmann method on shifted stencils

et al. 2019

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Standard lattice Boltzmann methods (LBMs) are based on a symmetric discretization of the phase space, which amounts to study the evolution of particle distribution functions (PDFs) in a reference frame at rest. This choice induces a number of limitations when the simulated flow speed gets closer to the sound speed, such as velocity-dependent transport coefficients. The latter issue is usually referred to as a Galilean invariance defect. To restore the Galilean invariance of LBMs, it was proposed to study the evolution of PDFs in a comoving reference frame by relying on asymmetric shifted lattices [N. Frapolli, S. S. Chikatamarla, and I. V. Karlin, Phys. Rev. Lett. 117, 010604 (2016)]. From the numerical viewpoint, this corresponds to overcoming the rather restrictive Courant-Friedrichs-Lewy conditions on standard LBMs and modeling compressible flows while keeping memory consumption and processing costs to a minimum (therefore using the standard first-neighbor stencils). In the present work systematic physical error evaluations and stability analyses are conducted for different discrete equilibrium distribution functions (EDFs) and collision models. Thanks to them, it is possible to (1) better understand the effect of this solution on both physics and stability, (2) assess its viability as a way to extend the validity range of LBMs, and (3) quantify the importance of the reference state as compared to other parameters such as the equilibrium state and equilibration path. The results clearly show that, in theory, the concept of shifted lattices allows the scheme to deal with arbitrarily high values of the nondimensional velocity. Furthermore, just like the zero-Mach flow for the standard stencils, it is observed that setting the shift velocity to the fluid velocity results in optimal physical and numerical properties. In addition, a detailed analysis of the obtained results shows that the properties of different collision models and EDFs remain unchanged under the shift of stencil. In other words, by introducing a velocity shift in the stencil, the optimal operating point, in terms of physics and numerics, will also be shifted by the same vector regardless of the EDF or collision model considered. Eventually, while limited to the D2Q9 stencil with the nine possible first-neighbor shifts, the present study and corresponding conclusions can be extended to other stencils and velocity shifts in a straightforward manner.

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Section: B Error In Equilibrium Momentsmentioning

confidence: 99%

Extensive analysis of the lattice Boltzmann method on shifted stencils

et al. 2019

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“…Hence, one may prefer to rely on KBC models to improve the numerical stability of LBMs at a low CPU cost. These collision models are based on an approximation to the minimization problem, and use an analytic formula for the computation of the dynamic relaxation time [12][13][14][15][16][17][18]. They can further decouple the relaxation of shear modes from acoustic and ghost modes, hence, freeing themselves from the generation of spurious vortices induced by the use of a varying shear viscosity in underre-solved conditions.…”

Section: Introductionmentioning

confidence: 99%

Comprehensive comparison of collision models in the lattice Boltzmann framework: Theoretical investigations

2019

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Over the last decades, several types of collision models have been proposed to extend the validity domain of the lattice Boltzmann method (LBM), each of them being introduced in its own formalism. The present article proposes a formalism that describes all these methods within a common mathematical framework, and in this way allows us to draw direct links between them. Here, the focus is put on single and multirelaxation time collision models in either their raw moment, central moment, cumulant or regularized form. In parallel with that, several bases (non orthogonal, orthogonal, Hermite) are considered for the polynomial expansion of populations. General relationships between moments are first derived to understand how moment spaces are related to each other. In addition, a review of collision models further sheds light on collision models that can be rewritten in a linear matrix form. More quantitative mathematical studies are then carried out by comparing explicit expressions for the post collision populations. Thanks to this, it is possible to deduce the impact of both the polynomial basis (raw, Hermite, central, central Hermite, cumulant) and the inclusion of regularization steps on isothermal LBMs. Extensive results are provided for the D1Q3, D2Q9, and D3Q27 lattices, the latter being further extended to the D3Q19 velocity discretization. Links with the most common two and multirelaxation time collision models are also provided for the sake of completeness. The present work ends by emphasizing the importance of an accurate representation of the equilibrium state, independently of the choice of moment space. As an addition to the theoretical purpose of the present article, general instructions are provided to help the reader with the implementation of the most complicated collision models.

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“…The majority of these modified LB schemes were developed and proposed with the aim of extending the stability domain of the solver in order to access higher Reynolds and/or Mach numbers at reasonable costs. They include (but are not limited to) approaches such as the entropic lattice Boltzmann method (ELBM) [10][11][12][13][14][15][16][17][18] , the multiple relaxation (MRT) [19][20][21][22][23][24][25][26][27][28][29][30][31] , the central moments (CM) or cascaded LBM [32][33][34][35][36][37][38][39] , the regularized (RLBM) [40][41][42][43][44][45][46][47][48][49][50] and the Cumulant method [51][52][53][54] . In addition to these collision models, several numerical discretizations have been used to numerically solve the lattice Boltzamnn equation, see for example [55]…”

Section: Introductionmentioning

confidence: 99%

Stability of the lattice kinetic scheme and choice of the free relaxation parameter

et al. 2019

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The lattice kinetic scheme (LKS), a modified version of the classical single relaxation time (SRT) lattice Boltzmann (LB) method, was initially developed as a suitable numerical approach for non-Newtonian flow simulations and a way to reduce memory consumption of the original SRT approach. The better performances observed for non-Newtonian flows are mainly due to the additional degree of freedom allowing an independent control over the relaxation of higher-order moments, independently from the fluid viscosity. Although widely applied to fluid flow simulations, yet no theoretical analysis of LKS has been performed. The present work focuses on a systematic von Neumann analysis of the linearized collision operator. Thanks to this analysis, the effect of the modified collision operator on the stability domain and spectral behavior of the scheme are clarified. Results obtained in this study show that correct choices of the "second relaxation coefficient" lead, to a certain extent, to more consistent dispersion and dissipation for large values of the first relaxation coefficient. Furthermore, appropriate values of this parameter can lead to a larger linear stability domain. At moderate and low values of the viscosity, larger values of the free parameter are observed to increase dissipation of kinetic modes, while leaving the acoustic modes untouched and having a less pronounced effect on the convective mode. This increased dissipation leads in general to less pronounced sources of non-linear instability, thus improving the stability of the LKS.

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Fluid-structure interaction with the entropic lattice Boltzmann method

Cited by 28 publications

References 68 publications

Extensive analysis of the lattice Boltzmann method on shifted stencils

Extensive analysis of the lattice Boltzmann method on shifted stencils

Comprehensive comparison of collision models in the lattice Boltzmann framework: Theoretical investigations

Stability of the lattice kinetic scheme and choice of the free relaxation parameter

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