14-velocity and 18-velocity multiple-relaxation-time lattice Boltzmann models for three-dimensional incompressible flows

TL;DR

This paper introduces 14-velocity and 18-velocity MRT lattice Boltzmann models for 3D incompressible flows, demonstrating improved accuracy and stability over existing models through simulations of classical flow problems.

Contribution

The paper develops new 14-velocity and 18-velocity MRT LB models for 3D incompressible flows, enhancing accuracy and stability compared to previous models.

Findings

Models recover 3D incompressible Navier-Stokes equations at low Mach numbers.

Simulation results agree with analytical and numerical solutions.

Models outperform existing models in accuracy and stability.

Abstract

In this paper, 14-velocity and 18-velocity multiple-relaxation-time (MRT) lattice Boltzmann (LB) models are proposed for three-dimensional incompressible flows. These two models are constructed based on the incompressible LBGK model proposed by He et al. (Chin. Phys., 2004, 13: 40-46) and the MRT LB model proposed by d'Humi\`{e}res et al. (Philos. Trans. R. Soc., A, 2002, 360: 437-451), which have advantages in the computational efficiency and stability, respectively. Through the Chapman-Enskog analysis, the models can recover to three-dimensional incompressible Navier-Stokes equations in the low Mach number limit. To verify the present models, the steady Poiseuille flow, unsteady pulsatile flow and lid-driven cavity flow in three dimensions are simulated. The simulation results agree well with the analytical solutions or the existing numerical results. Moreover, it is found that the present models show higher accuracy than d'Humi\`{e}res et al. model and better stability than He et al. model.