Lattice Boltzmann method for direct numerical simulation of turbulent flows

We present three-dimensional numerical simulations (DNS) of the Kida vortex flow, a prototypical turbulent flow, using a novel high-order lattice Boltzmann model. Extensive comparisons of various global and local statistical quantities obtained with an incompressible flow spectral element solver are reported. It is demonstrated that the lattice Boltzmann method is a promising alternative for DNS as it quantitatively capturesall the computed statistics of fluid turbulence

Elements of the lattice Boltzmann method I: linear advection equation

This paper opens a series of papers aimed at finalizing the development of the lattice Boltzmann method for complex hydrodynamic systems. The lattice Boltzmann method is introduced at the elementary level of the linear advection equation. Details are provided on lifting the target macroscopic equations to a kinetic equation, and, after that, to the fully discrete lattice Boltzmann scheme. The over-relaxation method is put forward as a cornerstone of the second-order temporal discretization, and its enhancement with the use of the entropy estimate is explained in detail. A new asymptotic expansion of the entropy estimate is derived, and implemented in the sample code. It is shown that the lattice Boltzmann method provides a computationally efficient way of numerically solving the advection equation with a controlled amount of numerical dissipation, while retaining positivity

Hydrodynamic and thermodiffusive instability effects on the evolution of laminar planar lean premixed hydrogen flames

ISSN:0022-1120ISSN:1469-764

Entropic lattice Boltzmann method for microflows

A new method for the computation of flows at the micrometer scale is presented. It is based oil the recently introduced minimal entropic kinetic models. Both the thermal and isothermal families of minimal models are presented, and the simplest isothermal entropic lattice Bhatnagar-Gross-Krook (ELBGK) is studied ill detail in order to quantify its relevance for microflow simulations. ELBGK is equipped with boundary conditions which are derived from molecular models (diffusive wall). A map of three-dimensional kinetic equations onto two-dimensional models is established which enables two-dimensional Simulations of quasi-two-dimensional flows. The ELBGK model is studied extensively in the simulation of the two-dimensional Poiseuille channel flow. Results are compared to known analytical and numerical studies of this flow in the setting of the Bhatnagar-Gross-Krook model. The ELBGK is ill quantitative agreement with analytical results in the domain of weak rarefaction (characterized by Knudsen number Kn, the ratio of mean free path to the hydrodynamic scale), up to Kn similar to 0.01, which is the domain of many practical microflows. Moreover, the results qualitatively agree throughout the entire Knudsen number range, demonstrating Knudsen's minimum for the mass flow rate at moderate values of Kn, as well as the logarithmic scaling at large Kn. The present results indicate that ELBM can complement or even replace computationally expensive microscopic simulation techniques such as kinetic Monte Carlo and/or molecular dynamics for low Mach and low Knudsen number hydrodynamics pertinent to microflows