Investigation of stability and hydrodynamics of different lattice Boltzmann models.

*(English)*Zbl 1113.82044Summary: Stability and hydrodynamic behaviors of different lattice Boltzmann models including the lattice Boltzmann equation (LBE), the differential lattice Boltzmann equation (DLBE), the interpolation-supplemented lattice Boltzmann method (ISLBM) and the Taylor series expansion- and least square-based lattice Boltzmann method (TLLBM) are studied in detail. Our work is based on the von Neumann linearized stability analysis under a uniform flow condition. The local stability and hydrodynamic (dissipation) behaviors are studied by solving the evolution operator of the linearized lattice Boltzmann equations numerically. Our investigation shows that the LBE schemes with interpolations, such as DLBE, ISLBM and TLLBM, improve the numerical stability by increasing hyper-viscosities at large wave numbers (small scales). It was found that these interpolated LBE schemes with the upwind interpolations are more stable than those with central interpolations because of much larger hyper-viscosities.

##### MSC:

82C20 | Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics |

82C40 | Kinetic theory of gases in time-dependent statistical mechanics |

76P05 | Rarefied gas flows, Boltzmann equation in fluid mechanics |

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\textit{X. D. Niu} et al., J. Stat. Phys. 117, No. 3--4, 665--680 (2004; Zbl 1113.82044)

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