TY - JOUR
T1 - On the Stability and Accuracy of the BGK, MRT and RLB Boltzmann Schemes for the Simulation of Turbulent Flows
AU - Patrick Nathen, Daniel Gaudlitz, Mathias J. Krause & Nikolaus A. Adams
JO - Communications in Computational Physics
VL - 3
SP - 846
EP - 876
PY - 2018
DA - 2018/03
SN - 23
DO - http://doi.org/10.4208/cicp.OA-2016-0229
UR - https://global-sci.org/intro/article_detail/cicp/10551.html
KW - Lattice Boltzmann, homogeneous isotropic turbulence, wall bounded turbulent flows.
AB - <p style="text-align: justify;">This paper presents an analysis of the stability and accuracy of different Lattice
Boltzmann schemes when employed for direct numerical simulations of turbulent
flows. The Single-Relaxation-Time scheme of Bhatnagar, Gross and Krook (BGK), the
Multi-Relaxation-Time scheme (MRT) and the Regularized Lattice Boltzmann scheme
(RLB) are considered. The stability and accuracy properties of these schemes are investigated
by computing three-dimensional Taylor-Green vortices representing homogeneous
isotropic turbulent flows. Varying Reynolds numbers and grid resolutions were
considered. As expected, the BGK scheme requires sufficiently high grid resolutions
for stable and accurate simulations. Surprisingly, the MRT scheme when used without
any turbulence model fails to obtain mesh convergence for the type of flow considered
here. The RLB scheme allows for stable simulations but exhibits a strong dissipative
behavior. A similar behavior was found when employing the mentioned LBM schemes
for numerical simulations of turbulent channel flows at varying Reynolds numbers
and resolutions. The obtained insights on accuracy and stability of the considered
Lattice Boltzmann methods can become useful especially for the design of effective
turbulence models to be used for high Reynolds number flows.</p>