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In the classical multiple-relaxation-time (MRT) lattice Boltzmann (LB)method, the transformation matrix is formed by constructing a set of orthogonalbasis vectors. In this paper, a theoretical and numerical study is performed toinvestigate the capability and efficiency of a non-orthogonal MRT-LB model forsimulating multiphase flows. First, a three-dimensional non-orthogonal MRT-LBis proposed. A non-orthogonal MRT collision operator is devised based on a setof non-orthogonal basis vectors, through which the transformation matrix andits inverse matrix are considerably simplified as compared with those of anorthogonal MRT collision operator. Furthermore, through the Chapman-Enskoganalysis, it is theoretically demonstrated that the three-dimensionalnon-orthogonal MRT-LB model can correctly recover the macroscopic equations atthe Navier-Stokes level in the low Mach number limit. Numerical comparisonsbetween the non-orthogonal MRT-LB model and the usual orthogonal MRT-LB modelare made by simulating multiphase flows on the basis of the pseudopotentialmultiphase LB approach. The numerical results show that, in comparison with theusual orthogonal MRT-LB model, the non-orthogonal MRT-LB model can retain thenumerical accuracy while simplifying the implementation.

Three-dimensional non-orthogonal multiple-relaxation-time lattice Boltzmann model for multiphase flows