On the Stability and Accuracy of the BGK, MRT and RLB Boltzmann Schemes for the Simulation of Turbulent Flows (Communications in Computational Physics, 2018)
This paper presents an analysis of the stability and accuracy of different LatticeBoltzmann schemes when employed for direct numerical simulations of turbulentflows. The Single-Relaxation-Time scheme of Bhatnagar, Gross and Krook (BGK), theMulti-Relaxation-Time scheme (MRT) and the Regularized Lattice Boltzmann scheme(RLB) are considered. The stability and accuracy properties of these schemes are investigatedby computing three-dimensional Taylor-Green vortices representing homogeneousisotropic turbulent flows. Varying Reynolds numbers and grid resolutions wereconsidered. As expected, the BGK scheme requires sufficiently high grid resolutionsfor stable and accurate simulations. Surprisingly, the MRT scheme when used withoutany turbulence model fails to obtain mesh convergence for the type of flow consideredhere. The RLB scheme allows for stable simulations but exhibits a strong dissipativebehavior. A similar behavior was found when employing the mentioned LBM schemesfor numerical simulations of turbulent channel flows at varying Reynolds numbersand resolutions. The obtained insights on accuracy and stability of the consideredLattice Boltzmann methods can become useful especially for the design of effectiveturbulence models to be used for high Reynolds number flows.
Keywords: Lattice Boltzmann; homogeneous isotropic turbulence; wall bounded turbulent flows.