Non-orthogonal multiple-relaxation-time lattice Boltzmann method: theory and its application in multiphase flows

A three-dimensional multiple-relaxation-time lattice Boltzmann method (MRT-LBM) is constructed based on a series of non-orthogonal moments. Compared with the widely used orthogonal-moments-based MRT-LBM, the present formulation simplifies the mapping between the discrete velocity space and the moment space, and exhibits better flexibility across different lattices. The proposed method is then extended to simulate multiphase flows with large density ratio and tunable surface tension, and validated via benchmark cases. Finally, we present simulations of several practical and challenging problems using the non-orthogonal MRT-LBM to highlight its capability for simulating realistic multiphase flows.