Unified magnetic multiphase lattice Boltzmann flux solver for ferrofluid flows with large density and viscosity ratios

In this paper, a unified magnetic multiphase lattice Boltzmann flux solver (UMMLBFS) is developed for simulating ferrofluid multiphase flows. The method begins by establishing consistent relationships between the macroscopic governing equations and the corresponding mesoscopic equations for the flow field, the phase field, and the magnetic field. The fluxes in the macroscopic governing equations are then derived from the mesoscopic distribution functions. These macroscopic governing equations are discretized using the finite volume method, with the fluxes at the cell interface computed based on the established mesoscopic–macroscopic relationships. In this way, it enables a unified and coherent solution strategy for coupling the flow field, the phase field, and the magnetic field. To evaluate the stability and accuracy of the proposed solver, five test examples, including a static cylinder in a magnetic field, the deformation of a ferrofluid droplet, the merging of two bubbles in a ferrofluid under a magnetic field, the Rosensweig instability of ferrofluid on a smooth surface, and the spreading of a ferrofluid droplet on a flat surface under a magnetic field, are simulated. The results indicate that the UMMLBFS achieves enhanced stability and accuracy in simulating ferrofluid multiphase flows compared to the non-unified method. Additionally, it performs robustly across a wide range of density ratios (1.975–850.7) and viscosity ratios (20–279.3), with excellent mass conservation properties.