Boltzmann–BGK approach to simulating weakly compressible 3D turbulence: comparison between lattice Boltzmann and gas kinetic methods

Abstract

Recently, the so-called gas-kinetic method (GKM) based on the Boltzmann-BGK equation has been successfully used in a variety of high Mach-number shock and laminar flow calculations. In this paper, we study the viability of extending the applicability of GKM to simulate turbulent flows. We evaluate the capability of GKM by making detailed comparisons against the lattice Boltzmann method and a Navier–Stokes solver. We perform three-dimensional direct numerical simulations (DNS) of decaying isotropic turbulence with the three methods and compare the evolution of kinetic energy, dissipation rate, and energy spectrum. Details of various macroscopic flow variables of interest are also examined. Further, the decay exponent calculated from the GKM is compared with the published results. The agreement in all categories considered is quite good. The results clearly demonstrate the potential promise of GKM for turbulence simulations over a broad range of Mach numbers.

Acknowledgment

This work was supported by AFOSR (MURI) grant no. FA9550-04-1-0425 (Program Manager: Dr. John Schmisseur).

Notes

1. The velocity obtained in LBM (U _LBM) is related to the physical velocity (U _P ) as

One sets in the LBM R = 1 and T = 1/3 for convenience (assumes that the temperature fluctuations are small). This in turn requires that Δ x/Δ t = 1 in the LBM.

One can alternatively proceed by making use of the relation