An improved multiphase lattice Boltzmann flux solver for the simulation of incompressible flow with large density ratio and complex interface
Liuming Yang, C. Shu, Zhen Chen, Guoxiang Hou, Yan Wang
Abstract
The recently developed multiphase lattice Boltzmann flux solver (MLBFS) overcomes the limitations in the multiphase lattice Boltzmann method (MLBM), such as the coupled time step and mesh step, uniform meshes, and complex distribution functions (DFs) treatment at the boundary. Unlike the original MLBFS deduced from the standard lattice Boltzmann method, an improved multiphase lattice Boltzmann flux solver (IMLBFS) is proposed based on the Chapman–Enskog analysis of the MLBM which has a source term stemming from the density contrast and surface tension force. In this way, the surface tension force is considered when reconstructing the numerical interface fluxes, which gives the present method stronger physical basis. As a result, the IMLBFS is more stable than the MLBFS. Moreover, the IMLBFS simplifies the process of reconstructing interface fluxes and avoids the complicated calculation of the source term in the MLBM. Some moments of the DFs and source terms are directly given as macroscopic variables to avoid additional computations and storage. This strategy ensures that the IMLBFS even has higher computational efficiency than the MLBFS. To test the proposed IMBFS for large-density-ratio flows, complex interfacial changes and high Reynolds number (up to 10 000), several typical problems are studied, including the static Laplace law, the droplet spreading on a flat surface, the unsteady Rayleigh–Taylor instability, the bubble rising under buoyancy, and the droplet splashing on a thin film. Simulations suggest that the present method predicts smaller spurious velocities, and it is more stable and efficient than the original MLBFS.