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Multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is an importantclass of LB model with lots of advantages over traditionalsingle-relaxation-time (SRT) LB model. In addition, the computation of strainrate tensor is crucial in MRT-LB simulations of some complex flows. Up to now,there are only two formulas to compute the strain rate tensor in the MRT LBmodel. One is to compute the strain rate tensor by using non-equilibrium partsof macroscopic moments (Yu formula). The other is to compute the strain ratetensor by using non-equilibrium parts of density distribution functions (Chaiformula). The mathematical expressions of these two formulas are so differentthat we do not know which formula to choose for computing the strain ratetensor in MRT LB model. In this paper, we study the relationship of these twoformulas. It is found that Yu formula can be deduced from Chai formula in aparticular procedure. However, these two formulas have their own advantages anddisadvantages. Yu formula is more efficient in the computation aspect whileChai formula can be applied to more lattice patterns of MRT LB models. It isalso found that deducing Yu formula for a particular lattice pattern from Chaiformula is more convenient than the way proposed by Yu et al.

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