We present an unstructured geometrical Volume-of-Fluid (VOF) method for handling two-phase flows with a viscoelastic liquid phase. The viscoelastic behavior is modeled via generic rate-type constitutive equations. A one-field formulation is employed, which results from conditional volume averaging of the local instantaneous bulk equations and interface jump conditions. The method builds on the 'plicRDF-isoAdvector' geometrical VOF solver that is extended and combined with the modular framework 'DeboRheo' for viscoelastic CFD. A piecewise-linear geometrical interface reconstruction technique on general unstructured meshes is employed for discretizing the viscoelastic stresses across the fluid interface in a numerically consistent and highly accurate way. Because of the numerical challenges posed by the high Weissenberg number problem, we employ an appropriate stabilization approach to the constitutive equation of the viscoelastic phase to increase the robustness of the method at higher fluid elasticity. DeboRheo facilitates a flexible combination of different rheological models with appropriate stabilization methods to address the high Weissenberg number problem. We discuss the theoretical formulation and implementation of the proposed method and demonstrate its effectiveness using numerical examples of viscoelastic flows. The results highlight the method's ability to accurately capture the behavior of viscoelastic fluids in various applications. The proposed method holds promise for furthering our understanding and predictive capabilities of viscoelastic flows in various industrial and natural processes.

翻译：本文提出了一种非结构几何流体体积（VOF）方法，用于处理含有粘弹性液相的两相流。粘弹性行为通过通用率型本构方程进行建模。采用单场公式，该公式由局部瞬时体积方程与界面跳跃条件的条件体积平均导出。该方法基于'plicRDF-isoAdvector'几何VOF求解器进行扩展，并与粘弹性CFD模块化框架'DeboRheo'相结合。采用通用非结构网格上的分段线性几何界面重构技术，以数值一致且高精度的方式离散化流体界面处的粘弹性应力。针对高魏森伯格数问题带来的数值挑战，我们对粘弹性相的本构方程采用适当的稳定化方法，以提高该方法在流体高弹性条件下的鲁棒性。DeboRheo框架支持不同流变模型与适当稳定化方法的灵活组合，以应对高魏森伯格数问题。我们讨论了所提方法的理论公式与实现过程，并通过粘弹性流动数值算例验证了其有效性。结果表明，该方法能够准确捕捉粘弹性流体在各种应用中的行为。该方法的提出有望进一步加深我们对工业和自然过程中粘弹性流动的理解与预测能力。