An incompressible smoothed particle hydrodynamics (ISPH) method is developed for the modeling of multiphase Newtonian and inelastic non‐Newtonian flows at low density ratios. This new method is the multiphase extension of Xenakis et al, J. Non‐Newtonian Fluid Mech., 218, 1‐15, which has been shown to be stable and accurate, with a virtually noise‐free pressure field for single‐phase non‐Newtonian flows. For the validation of the method a semi‐analytical solution of a two‐phase Newtonian/non‐Newtonian (inelastic) Poiseuille flow is derived. The developed method is also compared with the benchmark multiphase case of the Rayleigh Taylor instability and a submarine landslide, thereby demonstrating capability in both Newtonian/Newtonian and Newtonian/non‐Newtonian two‐phase applications. Comparisons with analytical solutions, experimental and previously published results are conducted and show that the proposed methodology can accurately predict the free‐surface and interface profiles of complex incompressible multi‐phase flows at low‐density ratios relevant, for example, to geophysical environmental applications.

中文翻译：

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牛顿/非牛顿多相流的不可压缩光滑粒子流体力学方案，包括两相非弹性泊松流的半解析解

开发了一种不可压缩的平滑粒子流体动力学（ISPH）方法，用于在低密度比下模拟多相牛顿流和非弹性非牛顿流。这种新方法是Xenakis等人（J.Non-Newtonian Fluid Mech。，218，1-15）的多相扩展，已被证明是稳定和准确的，并且对于单相非接触流体几乎没有噪声。牛顿流。为了验证该方法，推导了两阶段牛顿/非牛顿（非弹性）泊瓦斯流的半解析解。还将开发的方法与瑞利泰勒不稳定性的基准多相情况和海底滑坡进行了比较，从而证明了牛顿/牛顿和牛顿/非牛顿两相应用的能力。与分析解决方案的比较，