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Modeling realistic multiphase flows using a non-orthogonal multiple-relaxation-time lattice Boltzmann method
In this paper, we develop a three-dimensional multiple-relaxation-time
lattice Boltzmann method (MRT-LBM) based on a set of non-orthogonal basis
vectors. Compared with the classical MRT-LBM based on a set of orthogonal basis
vectors, the present non-orthogonal MRT-LBM simplifies the transformation
between the discrete velocity space and the moment space, and exhibits better
portability across different lattices. The proposed method is then extended to
multiphase flows at large density ratio with tunable surface tension, and its
numerical stability and accuracy are well demonstrated by some benchmark cases.
Using the proposed method, a practical case of a fuel droplet impacting on a
dry surface at high Reynolds and Weber numbers is simulated and the evolution
of the spreading film diameter agrees well with the experimental data.
Furthermore, another realistic case of a droplet impacting on a
super-hydrophobic wall with a cylindrical obstacle is reproduced, which
confirms the experimental finding of Liu \textit{et al.} [``Symmetry breaking
in drop bouncing on curved surfaces," Nature communications 6, 10034 (2015)]
that the contact time is minimized when the cylinder radius is comparable with
the droplet cylinder.Comment: 19 pages, 11 figure
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