DNS and LES of decaying isotropic turbulence with and without frame rotation using lattice Boltzmann method

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LES of turbulent square jet flow using an MRT lattice Boltzmann model (2006, background): “…discrete time tn 2 dtN0 is fðxi þ edt; tn þ dtÞ fðxi; tnÞ ¼ Xðxi; tnÞ ¼ M 1 Ŝ ½m mðeqÞ ; ð1Þ where M is a Q · Q matrix which linearly transforms the distribution functions f 2 V to the velocity moments m 2M: m ¼ M f; f ¼ M 1 m. ð2Þ We use the bold-face symbols to denote column vectors as the…”
Coupled lattice Boltzmann method and discrete element modelling of particle transport in turbulent fluid flows: Computational issues (2007, methodology): “Following this approach, the filtered form of the LB equation is expressed as [10] f̃i (x + ei t, t + t) = f̃i (x, t) − 1 ∗ [ f̃i (x, t) − f̃ eq i (x, t)] (i = 0, .”
Lattice Boltzmann methods for multiphase flow and phase-change heat transfer (2015, methodology): “, in the case of calculating the strain rate tensor using the second-order moment of the non-equilibrium distribution function, which is often required in the LB simulations of non-Newtonian flows [154-157] and in the LB-based simulations of turbulent flows [158, 159].”
Consistent initial conditions for lattice Boltzmann simulations (2006, methodology): “And second, more importantly, such scheme would be of little use in the cases such as decaying homogeneous isotropic turbulence [16–18], in which the initial velocity is a random field.”