  In the classical multiple-relaxation-time (MRT) lattice Boltzmann (LB)
method, the transformation matrix is formed by constructing a set of orthogonal
basis vectors. In this paper, a theoretical and numerical study is performed to
investigate the capability and efficiency of a non-orthogonal MRT-LB model for
simulating multiphase flows. First, a three-dimensional non-orthogonal MRT-LB
is proposed. A non-orthogonal MRT collision operator is devised based on a set
of non-orthogonal basis vectors, through which the transformation matrix and
its inverse matrix are considerably simplified as compared with those of an
orthogonal MRT collision operator. Furthermore, through the Chapman-Enskog
analysis, it is theoretically demonstrated that the three-dimensional
non-orthogonal MRT-LB model can correctly recover the macroscopic equations at
the Navier-Stokes level in the low Mach number limit. Numerical comparisons
between the non-orthogonal MRT-LB model and the usual orthogonal MRT-LB model
are made by simulating multiphase flows on the basis of the pseudopotential
multiphase LB approach. The numerical results show that, in comparison with the
usual orthogonal MRT-LB model, the non-orthogonal MRT-LB model can retain the
numerical accuracy while simplifying the implementation.
