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Wilde, Dominik; Krämer, Andreas; Küllmer, Knut; Foysi, Holger; Reith, Dirk

doi:10.1002/fld.4457

Cited by 1 publication

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“…These methods rely on off-lattice streaming and polynomial reconstruction of on-lattice populations to match the local velocity and temperature. Given that the latter introduces nonconservative numerical operations, one needs to carefully study and consider effects of the polynomial reconstruction step on the behavior of the scheme [11,15]. To avoid this conservation issue, one could also adapt the shift step by step using only integer-valued shifts that would be chosen, for example, according to the local Ma number or through predefined subdomains in a similar way as for grid refinement patches).…”

Section: Discussionmentioning

confidence: 99%

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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: Discussionmentioning

confidence: 99%

“…Mass, momentum, and energy conservation issues were recently reported in Refs. [11,15]. The latter is currently being investigated in more depth, and corresponding results will be presented in a forthcoming paper.…”

Section: B Error In Equilibrium Momentsmentioning

confidence: 96%