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

Abstract

Multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is an important class of LB model with lots of advantages over traditional singlerelaxation-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 nonequilibrium 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 * Corresponding author, Tel and Fax: +86 574 87608744.