A new multi-physical particle-based hybrid model for 2D incompressible generalized Newtonian two-phase MHD flow with large density ratio

An accurate and stable weighted-least-squares multi-physical particle-based (WLS-MPP) hybrid model is developed to simulate the incompressible generalized Newtonian two-phase magnetohydrodynamics (MHD) flows, and then it is extended to predict a bubble rising process in shear-thinning MHD flow with large density difference, for the first time. The development of WLS-MPP hybrid model for two-phase MHD flow is derived from that: (a) the weighted-least-squares (WLS) scheme is adopted to approximate the spatial derivatives in incompressible two-phase MHD governing equations; (b) two different stable models from the smoothed particle hydrodynamics (SPH)-based stable techniques (particle shifting technique (PST) and interface repulsive force (IRF)) are introduced and corrected to handle the tensile instability; (c) the continuum surface tension (CST) model is discretized by the WLS when a bubble deformation in Newtonian or non-Newtonian solvent. Moreover, the CPU-based parallel algorithm is designed to reduce the computing cost in the proposed WLS-MPP model. In numerical experiments, several two-phase benchmarks are simulated to test the accuracy and stability of the proposed WLS-MPP hybrid method, including the validity of PST, IRF, and CST. Subsequently, the proposed WLS-MPP is applied to predict deformation of a bubble rising in Newtonian or non-Newtonian two-phase flow under magnetic, the influences of magnetic and density ratios on the complex deformation process are also discussed, and compared with other numerical results. The dynamic process of a bubble rising in non-Newtonian MHD solvent is more complex than that in the case of Newtonian two-phase flow or without magnetic. All the numerical results indicate that the proposed WLS-MPP hybrid model is accurate and robust to simulate generalized Newtonian two-phase MHD flows with large density ratio. © 2024 Elsevier Ltd