Theoretical and numerical analysis of the lattice kinetic scheme for complex-flow simulations

The lattice kinetic scheme (LKS) is a modified version of the classical single relaxation time lattice Boltzmann method. Although used for many applications, especially when large variations in viscosity are involved, a thorough analysis of the scheme has not been provided yet. In the context of this work, the macroscopic behavior of this scheme is evaluated through the Chapman-Enskog analysis. It is shown that the additional degree of freedom provided in the scheme allows for an independent control of higher-order moments. These results are further corroborated by numerical simulations. The behavior of this numerical scheme is studied for selected external and internal flows to clarify the effect of the free parameter on the different moments of the distribution function. It is shown that it is more stable than SRT (single relaxation time) when confronted to fully periodic under-resolved simulations (especially for λ≈1). It can also help minimize the error coming from the viscosity-dependence of the wall position when combined with the bounce-back approach; although still present, viscosity-dependence of the wall position is reduced. Furthermore, as shown through the multiscale analysis, specific choices of the free parameter can cancel out the leading-order error. Overall, the LKS is shown to be a useful and efficient alternative to the SRT method for simulating numerically complex flows.