An axisymmetric multiple-relaxation-time lattice Boltzmann scheme

作者：Xie, Wenjun^*

来源：Journal of Computational Physics, 2015, 281: 55-66.

DOI：10.1016/j.jcp.2014.10.019

• Lattice Boltzmann method
• Axisymmetric
• Multiple-relaxation-time
• Compressible

A multiple-relaxation-time (MRT) lattice Boltzmann (LB) scheme developedfor axisymmetric flowsrecovers the complete continuity and Navier-Stokes equations. This scheme follows the strategy of the standard D2Q9 model by using a single particle distribution function and a simple "collision-streaming" updating rule. The extra terms related to axisymmetry in the macroscopic equations are recovered by adding source terms into the LB equation, which are simple and involveno gradients. The compressible effect retained in the Navier-Stokes equations is recovered by introducing a term related to the reversed transformation matrix for MRT collision operator, so as to produce a correct bulk viscosity, making it suitable for compressible flows with high frequency and low Mach number. The validity of the scheme is demonstrated by testing the Hagen-Poiseuille flow and 3D Womersley flow, as well as the standing acoustic waves in a closed cylindrical chamber. The numerical experiments show desirable stability at low viscosities, enabling to simulate a standing ultrasound field in centimeters space.

• 出版日期2015-1-15
• 单位西北工业大学