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.

中文翻译：

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一种基于多物理粒子的新型二维不可压缩广义牛顿两相 MHD 流大密度比混合模型


建立了一种精确稳定的加权最小二乘法多物理粒子基 （WLS-MPP） 混合模型来模拟不可压缩的广义牛顿两相磁流体动力学 （MHD） 流动，并首次扩展为预测具有大密度差异的剪切稀化 MHD 流中的气泡上升过程。两相 MHD 流的 WLS-MPP 混合模型的发展由以下因素推导：（a） 采用加权最小二乘 （WLS） 方案来逼近不可压缩两相 MHD 控制方程中的空间导数;（b） 引入并修正了基于平滑粒子流体动力学 （SPH） 的稳定技术中的两种不同的稳定模型（粒子偏移技术 （PST） 和界面排斥力 （IRF））来处理拉伸不稳定性;（c） 当气泡在牛顿或非牛顿溶剂中发生变形时，连续体表面张力 （CST） 模型被 WLS 离散化。此外，在所提出的 WLS-MPP 模型中，基于 CPU 的并行算法旨在降低计算成本。在数值实验中，模拟了几个两阶段基准，以测试所提出的 WLS-MPP 混合方法的准确性和稳定性，包括 PST 、 IRF 和 CST 的有效性。随后，将所提出的 WLS-MPP 应用于预测磁作用下牛顿或非牛顿两相流中气泡上升的变形，讨论了磁比和密度比对复杂变形过程的影响，并与其他数值结果进行了比较。气泡在非牛顿 MHD 溶剂中上升的动力学过程比在牛顿两相流或无磁性的情况下更复杂。 所有数值结果表明，所提出的 WLS-MPP 混合模型对广义牛顿两相 MHD 流具有准确和鲁棒性，具有较大的密度比。