Investigation on different discrete velocity quadrature rules in gas-kinetic unified algorithm solving Boltzmann model equation

2018 ◽  
Vol 75 (11) ◽  
pp. 4179-4200 ◽  
Author(s):  
Wen-Qiang Hu ◽  
Zhi-Hui Li
Keyword(s):  
Model Equation ◽  
Quadrature Rules ◽  
Discrete Velocity ◽  
Unified Algorithm ◽  
Boltzmann Model

scholarly journals Gas-kinetic unified algorithm for hypersonic aerothermodynamics covering various flow regimes solving Boltzmann model equation

2015 ◽  
Vol 64 (22) ◽  
pp. 224703
Author(s):  
Li Zhi-Hui ◽  
Peng Ao-Ping ◽  
Fang Fang ◽  
Li Si-Xin ◽  
Zhang Shun-Yu
Keyword(s):  
Model Equation ◽  
Flow Regimes ◽  
Unified Algorithm ◽  
Boltzmann Model

An Implicit Scheme for Solving Unsteady Boltzmann Model Equation

2019 ◽  
Vol 12 (2) ◽  
pp. 594-606
Author(s):  
Xiaowei Li，Chunxin Li，Dan Zhang and Zhihui Li
Keyword(s):  
Model Equation ◽  
Implicit Scheme ◽  
Boltzmann Model

scholarly journals dugksFoam: An open source OpenFOAM solver for the Boltzmann model equation

2017 ◽  
Vol 213 ◽  
pp. 155-164 ◽  
Author(s):  
Lianhua Zhu ◽  
Songze Chen ◽  
Zhaoli Guo
Keyword(s):  
Open Source ◽  
Model Equation ◽  
Boltzmann Model

scholarly journals Discrete Velocity Boltzmann Model for Quasi-Incompressible Hydrodynamics

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 993
Author(s):  
Oleg Ilyin
Keyword(s):  
Cross Sections ◽  
Lattice Boltzmann ◽  
Present Model ◽  
Test Problems ◽  
Hydrodynamic Equations ◽  
Interacting Particles ◽  
Closed Expression ◽  
Discrete Velocity ◽  
H Theorem ◽  
Boltzmann Model

In this paper, we consider the development of the two-dimensional discrete velocity Boltzmann model on a nine-velocity lattice. Compared to the conventional lattice Boltzmann approach for the present model, the collision rules for the interacting particles are formulated explicitly. The collisions are tailored in such a way that mass, momentum and energy are conserved and the H-theorem is fulfilled. By applying the Chapman–Enskog expansion, we show that the model recovers quasi-incompressible hydrodynamic equations for small Mach number limit and we derive the closed expression for the viscosity, depending on the collision cross-sections. In addition, the numerical implementation of the model with the on-lattice streaming and local collision step is proposed. As test problems, the shear wave decay and Taylor–Green vortex are considered, and a comparison of the numerical simulations with the analytical solutions is presented.

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