  Multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is an important
class of LB model with lots of advantages over traditional
single-relaxation-time (SRT) LB model. In addition, the computation of strain
rate 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 LB
model. One is to compute the strain rate tensor by using non-equilibrium parts
of macroscopic moments (Yu formula). The other is to compute the strain rate
tensor by using non-equilibrium parts of density distribution functions (Chai
formula). The mathematical expressions of these two formulas are so different
that we do not know which formula to choose for computing the strain rate
tensor in MRT LB model. In this paper, we study the relationship of these two
formulas. It is found that Yu formula can be deduced from Chai formula in a
particular procedure. However, these two formulas have their own advantages and
disadvantages. Yu formula is more efficient in the computation aspect while
Chai formula can be applied to more lattice patterns of MRT LB models. It is
also found that deducing Yu formula for a particular lattice pattern from Chai
formula is more convenient than the way proposed by Yu et al.
