A magnetic field-coupled semi-Lagrangian meshfree lattice Boltzmann method for two-phase ferrofluid flows

The present work generalizes the semi-Lagrangian meshfree lattice Boltzmann method (SL-M-LBM) for the simulation of two-phase ferrofluid flows. All simulations in the present study are performed in a two-dimensional framework. To achieve a fully coupled treatment of magnetohydrodynamic multiphase flows, the magnetic scalar potential equation is solved together with the hydrodynamic equations and phase-field interface evolution within a single SL-M-LBM framework, whereas this framework is different from many existing magnetic field-based lattice Boltzmann methods (LBMs), where the magnetic field is handled using a separate self-correcting or iterative solver. The magnetic forces are consistently incorporated through the Maxwell stress tensor, enabling accurate capture of magnetically induced droplet deformation, migration, and interaction under externally applied magnetic fields. Our approach combines a semi-Lagrangian scheme with a meshfree framework using moving least squares reconstruction. This allows larger time steps through non-unity Courant–Friedrichs–Lewy numbers, stable evaluation of Lagrangian temporal derivatives, and fully meshfree simulations with flexible, non-uniform node distributions. A number of benchmark tests are carried out to validate the accuracy and robustness of the proposed method for two-phase ferrofluid flows subjected to an external magnetic field. The validated model is subsequently used to investigate pressure-driven ferrofluid droplet passing through a constricted throat under magnetic field. The numerical results demonstrate that droplet deformation and migration are sensitive to the magnetic field orientation, with two representative orientations examined at α=0° and α=90°. Furthermore, a systematic parametric study is conducted to examine the effects of the magnetic Bond number (Bom), the capillary number (Ca), the density ratio (ρr), and constriction-to-droplet ratio (γ) on droplet transport behavior. These results give a quantitative understanding in the magnetically controlled ferrofluid droplet transport in constricted geometries.