In this work, a robust corrected weakly compressible smoothed particle hydrodynamics scheme combined with several improved interface treatments (CWCSPH-IT) is proposed to investigate viscous or viscoelastic two-phase flows of high density ratios. The proposed viscoelastic two-phase CWCSPH-IT model is mainly derived from three aspects: (a) a combined elastic stress approximation in the momentum equation based on the weighted idea is proposed; (b) the transition region near the interface of two fluids is regarded as a weak polymer fluid by approximating the relaxation time with a Shepard interpolation which handles the discontinuity of elastic stress near the interface; and (c) a new mixed boundary treatment is proposed to treat the wall boundary in a viscoelastic flow. Moreover, a weighted color gradient scheme is adopted to handle the surface tension near the phase interface, and a particle shifting technique is used to regularize particle distributions and enhance numerical stability. Several two-phase benchmark problems are simulated to test the validity and reliability of the proposed CWCSPH-IT. Subsequently, the proposed particle scheme is adopted to simulate the droplet rising in viscous/viscoelastic matrix fluid with high density ratios. Further, the stable dimple shape of a polymer drop falling in a low-density matrix, and the complex overshooting, oscillation and breakup phenomena of a drop in a high-viscoelasticity shear fluid are numerically investigated. The comparison between the SPH and other reliable reference results demonstrates the ability of the present viscoelastic two-phase scheme in modeling complex viscous or viscoelastic multi-phase problems.

在这项工作中，提出了一种稳健的修正弱可压缩平滑粒子流体动力学方案，结合几种改进的界面处理（CWCSPH-IT）来研究高密度比的粘性或粘弹性两相流。所提出的粘弹性两相CWCSPH-IT模型主要来源于三个方面：(a)提出了基于加权思想的动量方程中的组合弹性应力近似；(b) 通过使用处理界面附近弹性应力不连续性的 Shepard 插值近似松弛时间，将两种流体界面附近的过渡区域视为弱聚合物流体；(c) 提出了一种新的混合边界处理方法来处理粘弹性流中的壁边界。而且，采用加权颜色梯度方案来处理相界面附近的表面张力，并使用粒子移动技术来规范粒子分布并增强数值稳定性。模拟了几个两阶段基准问题，以测试所提出的 CWCSPH-IT 的有效性和可靠性。随后，采用所提出的粒子方案来模拟具有高密度比的粘性/粘弹性基质流体中的液滴上升。此外，数值研究了落在低密度基体中的聚合物液滴的稳定凹坑形状，以及液滴在高粘弹性剪切流体中的复杂超调、振荡和破碎现象。