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Two-Relaxation-Time Regularized Lattice Boltzmann Model for Navier-Stokes Equations

Two-Relaxation-Time Regularized Lattice Boltzmann Model for Navier-Stokes Equations

Year:    2025

Author:    Yuan Yu, Zuojian Qin, Siwei Chen, Shi Shu, Haizhuan Yuan

Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 2 : pp. 489–516

Abstract

In this paper, we develop a two-relaxation-time regularized lattice Boltzmann (TRT-RLB) model for simulating weakly compressible isothermal flows, which demonstrates superior stability and accuracy over existing models such as the regularized lattice Boltzmann (RLB) and two-relaxation-time (TRT) models. In this model, a free relaxation parameter, $\tau_{s,2},$ is employed to relax the regularized non-equilibrium third-order terms. Chapman-Enskog analysis reveals that our model can accurately recover the Navier-Stokes equations. Theoretical analysis and numerical experiments both confirm the model’s ability to eliminate non-physical numerical slip associated with the half-way bounce-back scheme. Our simulations of the double shear layer problem and Taylor-Green vortex flow exhibit pronounced advantages in terms of stability and accuracy, even under super-high Reynolds numbers as high as ${\rm Re}=10^7.$ Additionally, the simulation of creeping flow around a square cylinder showcases the model’s precision in computing ultra-low Reynolds numbers down to ${\rm Re}=10^{−7}.$ This robust capability confirms the proposed model as a highly effective and adaptable tool in computational fluid dynamics.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2024-0203

Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 2 : pp. 489–516

Published online:    2025-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    28

Keywords:    Regularized lattice Boltzmann two-relaxation-time high-Reynolds number creeping flow numerical slip.

Author Details

Yuan Yu

Zuojian Qin

Siwei Chen

Shi Shu

Haizhuan Yuan