Linear Analysis on Multiple-relaxation-time Lattice Boltzmann Method

The development of multiple-relaxation-time (MRT) Lattice Boltzmann method (LBM) is a significant contribution in improving the numerical behavior, revealing the math and physics mechanism and extending the application of LBM. However, some of the MRT schemes proposed previously are not physically-consistent. In this work, we take D2Q9 as a example to show how to derive physically-consistent MRT-LBM schemes by eigenvalue decomposition of the collision operator. In addition, the scheme is validated by the equivalence to Navier-Stokes equations and numerical simulations.