On the SRT – MRT Lattice Boltzmann Method: Validity Limits of the Single Relaxation Time for Simulating Single-Phase Flows

Abstract—The multi-relaxation time (MRT) Lattice Boltzmann method (LBM) was developed to overcome several constraints, which are inherent to the more famous single relaxation time (SRT) Bhatnagar–Gross–Krook (LBGK) model. Constraints, such as fixed Prandtl number, fixed ratio between kinematic and bulk viscosity, and Reynolds number limitations undermine the SRT usefulness. Furthermore, the SRT method fails to accurately characterize high viscosity fluids’ behavior near the domain’s walls, an issue which can be circumvented with the MRT method. However, the MRT requires a careful selection of its relaxation parameters for achieving the desired outcome. The ad-hoc nature of this selection makes the method cumbersome, especially for threedimensional (3D) domains. Additionally, it is known that the MRT solution requires about 10% - 15% more computational time than the SRT for the same domain size. Four widely used single-phase flow conditions were explored by using the SRT and the MRT methods. It is shown that the SRT has good accuracy when used for simulating low viscosity fluid cases; however, the SRT exhibits a non-physical velocity jump at the domain surface boundaries when used for simulating high viscosity fluid flows. This issue can be resolved by augmenting the SRT domain’s height, which in turn leads to an increase in the required computational time. The main advantages of the MRT are due to its capability in overcoming the velocity jump in most of the high viscosity fluid cases and in its ability to simulate flows with ultra-low viscosities, which was demonstrated in the characterization of the flow around S822 airfoil with Reynolds number Re≈40,000 .

Index Terms—Lattice boltzmann, multi-relaxation time LBM, LBGK, parabolic flow, S822 airfoil, drag and lift.

Ameer K. Alhilo is with Wayne State University, Detroit, MI, USA and Wasit University, Kut, Iraq.
Wessam F. Hasan is with North Oil Company, Kirkuk, Iraq.
Hassan Farhat is with Wayne State University, Detroit, MI, USA (e-mail: av9328@wayne.edu).

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Cite: Ameer K. Alhilo, Wessam F. Hasan, and Hassan Farhat, "On the SRT – MRT Lattice Boltzmann Method: Validity Limits of the Single Relaxation Time for Simulating Single-Phase Flows," International Journal of Materials, Mechanics and Manufacturing vol. 8, no. 3, pp. 74-83, 2020.

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