Journal of Shanghai Jiao Tong University (Science) ›› 2020, Vol. 25 ›› Issue (2): 177-185.doi: 10.1007/s12204-020-2158-3

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Derivations of Exact Lattice Boltzmann Evolution Equation

YE Huanfeng (叶欢锋), KUANG Bo (匡波), YANG Yanhua (杨燕华)   

  1. (1. School of Nuclear Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China; 2. National Energy Key Laboratory of Nuclear Power Software, Beijing 102209, China)
  • 出版日期:2020-04-01 发布日期:2020-04-01
  • 通讯作者: YE Huanfeng (叶欢锋) E-mail:huanfye@163.com

Derivations of Exact Lattice Boltzmann Evolution Equation

YE Huanfeng (叶欢锋), KUANG Bo (匡波), YANG Yanhua (杨燕华)   

  1. (1. School of Nuclear Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China; 2. National Energy Key Laboratory of Nuclear Power Software, Beijing 102209, China)
  • Online:2020-04-01 Published:2020-04-01
  • Contact: YE Huanfeng (叶欢锋) E-mail:huanfye@163.com

摘要: A comparative analysis on the schemes for exact lattice Boltzmann (LB) evolution equation is presented in this paper. It includes two classical exact LB schemes, i.e., B¨osch-Karlin (BK) scheme and He-Luo (HL) scheme, and the present Taylor-expansion (TE) scheme. TE scheme originates from the extension of BK scheme. The mathematical mechanism and the equilibrium distribution evolution behind these exact schemes have been detailedly addressed. After that, an analysis is carried out to discuss the cause of the LB equation difference among the schemes, which offers an insight of the exactness in these schemes and brings up their continuity precondition. At last, the schemes are systematically addressed for their pros and cons in the further development of LB equations.

关键词: lattice Boltzmann (LB) method, exact LB evolution equation, Taylor-expansion (TE) scheme

Abstract: A comparative analysis on the schemes for exact lattice Boltzmann (LB) evolution equation is presented in this paper. It includes two classical exact LB schemes, i.e., B¨osch-Karlin (BK) scheme and He-Luo (HL) scheme, and the present Taylor-expansion (TE) scheme. TE scheme originates from the extension of BK scheme. The mathematical mechanism and the equilibrium distribution evolution behind these exact schemes have been detailedly addressed. After that, an analysis is carried out to discuss the cause of the LB equation difference among the schemes, which offers an insight of the exactness in these schemes and brings up their continuity precondition. At last, the schemes are systematically addressed for their pros and cons in the further development of LB equations.

Key words: lattice Boltzmann (LB) method, exact LB evolution equation, Taylor-expansion (TE) scheme

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