Effect of the forcing term in the multiple-relaxation-time lattice Boltzmann equation on the shear stress or the strain rate tensor

In this work, the effect of the forcing term (or external force) in the multiple-relaxation-time lattice Boltzmann equation (MRTLBE) on the shear stress or the strain rate tensor is studied theoretically and numerically. Through a Chapman-Enskog analysis and numerical simulations, we show that the shear stress (or the strain rate tensor) derived from the MRTLBE is second-order accurate in space. We then examine the influence of the forcing term on the shear stress or the strain rate tensor, and demonstrate that the forcing term effect must be included when the shear stress or the strain rate tensor is computed with the nonequilibrium part of the distribution function.