Multi-Relaxation Time Lattice Boltzmann Model for Multiphase Flows

Multi-relaxation time (MRT) for Lattice Boltzmann method is gaining renewed attention among researchers in the field. The advantage of such formulation over the widely popular single-time relaxation version, is twofold: better numerical stability and wider span of physical applications, extending to non-isotropic flows. In this work, the numerical advantages of the MRT model versus single-relaxation time (BGK) operator are quantitatively assessed through direct numerical simulations of droplet formation and capillary wave propagation on interphase boundaries. The results show that by proper tuning of the collision operator, and particularly of the higher-order kinetic modes (ghosts), appreciable improvements in stability limits, of the order of 20%, and viscosity limits, of the order of 80%, can be achieved. Moreover, a theoretical analysis accounting for the reasons behind such stability improvement, is also presented.