### Abstract

The multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is an important class of LB model with lots of advantages over the traditional single-relaxation-time (SRT) LB model. Generally, the computation of strain rate tensor is crucial for the MRT-LB simulations of some complex flows. At present, only two formulae are available to compute the strain rate tensor in the MRT LB model. One is to compute the strain rate tensor using the non-equilibrium parts of macroscopic moments (Yu formula). The other is to compute the strain rate tensor using the non-equilibrium parts of density distribution functions (Chai formula). The mathematical expressions of these two formulae are so different that we do not know which formula to choose for computing the strain rate tensor in the MRT LB model. To overcome this problem, this paper presents a theoretical study of the relationship between Chai and Yu formulae. The results show that the Yu formula can be deduced from the Chai formula, although they have their own advantages and disadvantages. In particular, the Yu formula is computationally more efficient, while the Chai formula is applicable to more lattice patterns of the MRT LB models. Furthermore, the derivation of the Yu formula in a particular lattice pattern from the Chai formula is more convenient than that proposed by Yu et al.

Original language | English |
---|---|

Pages (from-to) | 2888-2902 |

Number of pages | 15 |

Journal | Computers and Mathematics with Applications |

Volume | 75 |

Issue number | 8 |

DOIs | |

Publication status | Published - 15 Apr 2018 |

### Keywords

- Lattice Boltzmann model
- Multiple relaxation time
- Strain rate tensor

### Cite this

*Computers and Mathematics with Applications*,

*75*(8), 2888-2902. https://doi.org/10.1016/j.camwa.2018.01.019

}

*Computers and Mathematics with Applications*, vol. 75, no. 8, pp. 2888-2902. https://doi.org/10.1016/j.camwa.2018.01.019

**The computation of strain rate tensor in multiple-relaxation-time lattice Boltzmann model.** / Zhang, Wenhuan; Huang, Changsheng; Wang, Yihang; Shi, Baochang; Kuang, Shibo; Chai, Zhenhua.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - The computation of strain rate tensor in multiple-relaxation-time lattice Boltzmann model

AU - Zhang, Wenhuan

AU - Huang, Changsheng

AU - Wang, Yihang

AU - Shi, Baochang

AU - Kuang, Shibo

AU - Chai, Zhenhua

PY - 2018/4/15

Y1 - 2018/4/15

N2 - The multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is an important class of LB model with lots of advantages over the traditional single-relaxation-time (SRT) LB model. Generally, the computation of strain rate tensor is crucial for the MRT-LB simulations of some complex flows. At present, only two formulae are available to compute the strain rate tensor in the MRT LB model. One is to compute the strain rate tensor using the non-equilibrium parts of macroscopic moments (Yu formula). The other is to compute the strain rate tensor using the non-equilibrium parts of density distribution functions (Chai formula). The mathematical expressions of these two formulae are so different that we do not know which formula to choose for computing the strain rate tensor in the MRT LB model. To overcome this problem, this paper presents a theoretical study of the relationship between Chai and Yu formulae. The results show that the Yu formula can be deduced from the Chai formula, although they have their own advantages and disadvantages. In particular, the Yu formula is computationally more efficient, while the Chai formula is applicable to more lattice patterns of the MRT LB models. Furthermore, the derivation of the Yu formula in a particular lattice pattern from the Chai formula is more convenient than that proposed by Yu et al.

AB - The multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is an important class of LB model with lots of advantages over the traditional single-relaxation-time (SRT) LB model. Generally, the computation of strain rate tensor is crucial for the MRT-LB simulations of some complex flows. At present, only two formulae are available to compute the strain rate tensor in the MRT LB model. One is to compute the strain rate tensor using the non-equilibrium parts of macroscopic moments (Yu formula). The other is to compute the strain rate tensor using the non-equilibrium parts of density distribution functions (Chai formula). The mathematical expressions of these two formulae are so different that we do not know which formula to choose for computing the strain rate tensor in the MRT LB model. To overcome this problem, this paper presents a theoretical study of the relationship between Chai and Yu formulae. The results show that the Yu formula can be deduced from the Chai formula, although they have their own advantages and disadvantages. In particular, the Yu formula is computationally more efficient, while the Chai formula is applicable to more lattice patterns of the MRT LB models. Furthermore, the derivation of the Yu formula in a particular lattice pattern from the Chai formula is more convenient than that proposed by Yu et al.

KW - Lattice Boltzmann model

KW - Multiple relaxation time

KW - Strain rate tensor

UR - http://www.scopus.com/inward/record.url?scp=85041966389&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2018.01.019

DO - 10.1016/j.camwa.2018.01.019

M3 - Article

VL - 75

SP - 2888

EP - 2902

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 8

ER -