关键词: structure function, factorization, cofactor, relative prime, gcd, combination, algebraic division, Fermat’s Last Theorem, isotropic turbulent flow, mesoscopic modelling, intermittency, high-order statistics, lattice Boltzmann method (LBM), self-similarity

Abstract: The lattice Boltzmann method (LBM) is coupled with the multiple-relaxationtime (MRT) collision model and the three-dimensional 19-discrete-velocity (D3Q19) model to resolve intermittent behaviors on small scales in isotropic turbulent flows. The highorder scaling exponents of the velocity structure functions, the probability distribution functions of Lagrangian accelerations, and the local energy dissipation rates are investigated. The self-similarity of the space-time velocity structure functions is explored using the extended self-similarity (ESS) method, which was originally developed for velocity spatial structure functions. The scaling exponents of spatial structure functions at up to ten orders are consistent with the experimental measurements and theoretical results, implying that the LBM can accurately resolve the intermittent behaviors. This validation provides a solid basis for using the LBM to study more complex processes that are sensitive to small scales in turbulent flows, such as the relative dispersion of pollutants and mesoscale structures of preferential concentration of heavy particles suspended in turbulent flows.

Key words: factorization, cofactor, relative prime, gcd, combination, algebraic division, Fermat’s Last Theorem, lattice Boltzmann method (LBM), mesoscopic modelling, self-similarity, isotropic turbulent flow, high-order statistics, structure function, intermittency