A Parametric Characterization of Spurious Currents in Multiphase Lattice Boltzmann Models
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In the field of multiphase flows, the Lattice Boltzmann Method (LBM) has gained significant relevance due to its mesoscopic nature, which allows the simulation of complex fluid dynamics. Based on kinetic theory, LBM enables the modeling of microscopic liquid-gas interface dynamics without the need for dynamic reconstruction or explicit interface tracking [1,2]. However, one of the well-known drawbacks of multiphase LBM models is the onset of spurious currents. These parasitic currents are small-amplitude, non-physical velocity fields that develop close to the interfaces of steady, static two-phase systems. These arise from the imbalance of discretized forces acting at the interface and persist even when the system should theoretically be at equilibrium, i.e., with zero velocity everywhere [3]. Since spurious currents arise near curved interfaces [2], this work numerically investigates their influence on the velocity field of a static droplet, with the objective of improving model stability and accuracy. In particular, high density ratios are known to significantly amplify spurious currents in multiphase lattice Boltzmann models [1], while surface tension plays a crucial role in interfacial force balance, as described by the Laplace law relating the pressure jump to interface curvature. Accordingly, a parametric analysis is conducted to quantitatively assess the combined effects of density ratio and surface tension on spurious currents. Several multiphase LBM formulations, namely the color-gradient, Shan–Chen, and free-energy models [3], are examined to characterize instability regimes. Regions dominated by spurious currents are identified, and critical parameter thresholds are derived through stability analysis. Furthermore, this study identifies the method that exhibits the most favorable scaling behavior of spurious currents with respect to these key physical parameters. [1] Christopher D. Stiles, Yongqiang Xue, High density ratio lattice Boltzmann method simulations of multicomponent multiphase transport of H2O in air, Computers and Fluids, 2016. [2] Zhangrong Qin, et al. , Spurious currents suppression by accurate difference schemes in multiphase lattice Boltzmann method, Computers and Fluids, 261, 2023. [3] Kevin Connington, Taehun Lee, A review of spurious currents in the lattice Boltzmann method formultiphase flows, Journal of Mechanical Science and Technology, 2012
