A consistent axisymmetric multiphase lattice Boltzmann flux solver for flows with super-large density ratio

Despite the development of numerous axisymmetric models for hydrodynamic fields within the context of Lattice Boltzmann flux solvers, a common challenge remains: the governing equations at the cell centers are often inconsistent with those at the cell interfaces. To solve this problem for the simulation of flow field, this study adopts the kinetic-theory-based axisymmetric lattice Boltzmann method and a consistent finite-volume axisymmetric multiphase lattice Boltzmann flux solver (LBFS) is proposed on the cylindrical coordinates. Through this strategy, the present solver follows the same governing equations both at the cell centers and at the cell interfaces. Specifically, the interface fluxes are numerically reconstructed by the distribution functions and the macroscopic flow variables are tracked at the cell centers. Naturally, the present method does not involve with any complicated velocity gradients which are common in previous axisymmetric LBFS. Due to these striking features, the proposed hydrodynamic model is accurate and stable enough for simulating axisymmetric multiphase flows with superlarge density ratio and large viscosity ratio.