A simplified lattice Boltzmann flux solver for multiphase flows with large density ratio

Abstract

AbstractUnlike the conventional multiphase lattice Boltzmann method (LBM), the recently developed finite volume‐based multiphase lattice Boltzmann flux solver (MLBFS) is free from the limitation of the uniform mesh, the coupled time step and mesh spacing, and the high virtual memories. In the MLBFS, the macroscopic equations recovered from the LBM are discretized by the finite volume method while the fluxes at the cell interfaces are evaluated based on the local application of LBM. The interfacial fluxes are calculated only by the distribution functions. However, the code implementation involving too many distribution functions is still not simple enough. And the computation of the distribution functions will still cost relatively large computational resources. We notice that some moments of the distribution functions can be directly simplified as the macroscopic variables. Therefore, to further simplify the code implementation and improve the computational efficiency of the MLBFS, we propose a simplified MLBFS which reconstructs the fluxes with the combination of the distribution functions and the macroscopic variables. Naturally, we can expect that the simplified method can improve the computational efficiency while maintaining the numerical accuracy and reliability of the original MLBFS. Numerical experiments of the Laplace law, the Rayleigh–Taylor instability, the bubble rising under buoyancy and the droplet splashing on a liquid film are conducted to evaluate the simplified MLBFS. Results show that our method can save up to 18.32% of the original computational time. The simplified method is superior to the original one especially for the cases with a large number of girds.