Phase-field lattice Boltzmann method with two-relaxation-time model for dendrite growth of a binary alloy with melt convection

2021 ◽  
Vol 186 ◽  
pp. 110070
Author(s):  
Shinji Sakane ◽  
Tomohiro Takaki
Keyword(s):  
Relaxation Time ◽  
Lattice Boltzmann Method ◽  
Binary Alloy ◽  
Phase Field ◽  
Lattice Boltzmann ◽  
Dendrite Growth ◽  
Time Model ◽  
Melt Convection ◽  
Boltzmann Method

Improving the Stability of the Multiple-Relaxation-Time Lattice Boltzmann Method by a Viscosity Counteracting Approach

2015 ◽  
Vol 8 (1) ◽  
pp. 37-51 ◽  
Author(s):  
Chunze Zhang ◽  
Yongguang Cheng ◽  
Shan Huang ◽  
Jiayang Wu
Keyword(s):  
Reynolds Number ◽  
Relaxation Time ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Numerical Instability ◽  
Time Model ◽  
Multiple Relaxation Time ◽  
The Stability ◽  
Boltzmann Method ◽  
Accuracy And Stability

AbstractNumerical instability may occur when simulating high Reynolds number flows by the lattice Boltzmann method (LBM). The multiple-relaxation-time (MRT) model of the LBM can improve the accuracy and stability, but is still subject to numerical instability when simulating flows with large single-grid Reynolds number (Reynolds number/grid number). The viscosity counteracting approach proposed recently is a method of enhancing the stability of the LBM. However, its effectiveness was only verified in the single-relaxation-time model of the LBM (SRT-LBM). This paper aims to propose the viscosity counteracting approach for the multiple-relaxation-time model (MRT-LBM) and analyze its numerical characteristics. The verification is conducted by simulating some benchmark cases: the two-dimensional (2D) lid-driven cavity flow, Poiseuille flow, Taylor-Green vortex flow and Couette flow, and three-dimensional (3D) rectangular jet. Qualitative and Quantitative comparisons show that the viscosity counteracting approach for the MRT-LBM has better accuracy and stability than that for the SRT-LBM.

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