Modeling realistic multiphase flows using a non-orthogonal multiple-relaxation-time lattice Boltzmann method

TL;DR

This paper introduces a non-orthogonal MRT-LBM for simulating multiphase flows with high density ratios, demonstrating improved stability, accuracy, and practical applications like droplet impact simulations that align well with experimental data.

Contribution

It develops a simplified non-orthogonal MRT-LBM that enhances portability and stability for multiphase flow simulations at large density ratios.

Findings

The method accurately simulates droplet impact on surfaces at high Reynolds and Weber numbers.

It reproduces experimental phenomena such as minimized contact time on curved surfaces.

The approach shows improved numerical stability and efficiency over classical methods.

Abstract

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.