In this work we discuss the implementation and the performance of an in-house viscoelastic two-phase solver, based on a diffuse interface approach. The Phase-Field method is considered and the Cahn-Hilliard equation is employed for describing the transport of a binary fluid system. The interface between the two fluids utilises a continuum approach, which is responsible for smoothing the inherent discontinuities of sharp interface models, facilitating studies that are related to morphological changes of the interface, such as droplet breakup and coalescence. The two-phase solver manages to predict the expected dynamics for all the cases investigated, and exhibits an overall good performance. The numerical implementation is able to predict the expected physical response of the oscillating drop case, while the performance is also validated by examining the droplet deformation case. The corresponding history of the deformation is predicted for several systems considering Newtonian fluids, viscoelastic fluids and combinations of both. Finally, we demonstrate the ability of the solver to capture the complex interfacial patterns of the Rayleigh-Taylor instability for different Atwood numbers when Newtonian fluids are considered. In the two regimes identified, the system is modified to consider viscoelastic fluids and the influence of elasticity is investigated.

在这项工作中，我们将讨论基于扩散接口方法的内部粘弹性两相求解器的实现和性能。考虑了相场法，并采用Cahn-Hilliard方程描述了二元流体系统的输运。两种流体之间的界面采用连续介质方法，该方法可平滑尖锐界面模型的固有不连续性，从而促进与界面形态变化（如液滴破裂和聚结）有关的研究。两阶段求解器设法预测所有研究案例的预期动态，并展现出总体良好的性能。数值实现能够预测振动跌落情况的预期物理响应，通过检查液滴变形情况也可以验证性能。对于考虑牛顿流体，粘弹性流体以及两者的组合的多个系统，可以预测相应的变形历史。最后，当考虑牛顿流体时，我们证明了求解器捕获不同阿特伍德数的瑞利-泰勒不稳定性的复杂界面模式的能力。在确定的两种情况下，对系统进行了修改以考虑粘弹性流体，并研究了弹性的影响。我们证明了当考虑牛顿流体时，求解器能够捕获不同阿特伍德数的瑞利-泰勒不稳定性的复杂界面模式的能力。在确定的两种情况下，对系统进行了修改以考虑粘弹性流体，并研究了弹性的影响。我们证明了当考虑牛顿流体时，求解器能够捕获不同阿特伍德数的瑞利-泰勒不稳定性的复杂界面模式的能力。在确定的两种情况下，对系统进行了修改以考虑粘弹性流体，并研究了弹性的影响。