A Three-Dimensional Mass-Conserved Multiphase Lattice Boltzmann Flux Solver for Incompressible Flows with Large Density and Viscosity Ratios

Abstract

Multiphase lattice Boltzmann flux solver (MLBFS) uses the finite volume method to solve Navier-Stokes (NS) and Cahn-Hilliard (CH) equations. However, instead of macroscopic fluxes, the corresponding mesoscopic fluxes, defined using a local lattice Boltzmann method, are evaluated at cell faces. Since the development of the original three-dimensional (3D) MLBFS [16], several improvements have been made in it, including modification of CH equation to conserve the mass, determination of CH mesoscopic fluxes to eliminate the weighted essentially non-oscillatory scheme, and simplification of mesoscopic fluxes to improve the computational efficiency. However, these improvements have been implemented and studied in two-dimensional or axisymmetric MLBFS. In this study, MLBFS (based on the mentioned improvements) has been extended to 3D flows and applied to simulate three incompressible multiphase benchmark cases with large density and viscosity ratios up to 1000 and 100, respectively. The results of benchmark cases (Laplace law, bubble rising, and drop impact on a dry surface) agree well with previous credential data. Our simulations show the original CH equation considerably reduces the bubble/drop mass, while the modified CH equation conserves it completely. According to results, using the simplified mesoscopic fluxes (instead of the original ones) saves about 13% of computational time.