An improved multiphase lattice Boltzmann flux solver for three-dimensional flows with large density ratio and high Reynolds number

An improved multiphase lattice Boltzmann flux solver (MLBFS) is proposed in this work for effective simulation of three-dimensional (3D) multiphase flows with large density ratio and high Reynolds number. As a finite volume scheme, the MLBFS originally proposed in 27 applies the finite volume method to solve for macroscopic flow variables directly. The fluxes are reconstructed locally at each cell interface by using the standard LBM solutions. Due to the modeling error of the standard LBM, the reconstructed fluxes deviate from those in the Navier-Stokes equations; and to compensate this error, a complex tensor is introduced in the original MLBFS. However, the computation of the tensor introduces additional complexity and usually needs a relatively thicker interface thickness to maintain numerical stability, which makes the solver be complex and inefficient in the 3D case. To remove this drawback, in this work, a theoretical analysis to the formulations obtained from the Chapman-Enskog expansion is conducted. It is shown that the modeling error can be effectively removed by modifying the computation of the equilibrium density distribution function. With this improvement, the proposed 3D MLBFS not only avoids the calculation of the compensation tensor but also is able to maintain numerical stability with very thin interface thickness. Several benchmark cases, including the challenging droplet impacting on a dry surface, head-on collisions of binary droplets and droplet splashing on a thin film with density ratio 1000 and Reynolds number up to 3000, are studied to validate the proposed solver. The obtained results agree well with the published data.