Since viscoelastic two-phase flows arise in various industrial and natural processes, developing accurate and efficient software for their detailed numerical simulation is a highly relevant and challenging research task. We present a geometrical unstructured Volume-of-Fluid (VOF) method for handling two-phase flows with viscoelastic liquid phase, where the latter is modeled via generic rate-type constitutive equations and a one-field description is derived by 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 computational fluid dynamics (CFD). A piecewise-linear geometrical interface reconstruction technique on general unstructured meshes is employed for discretizing the viscoelastic stresses across the fluid interface. DeboRheo facilitates a flexible combination of different rheological models with appropriate stabilization methods to address the high Weissenberg number problem.

翻译：由于粘弹性两相流广泛存在于工业与自然过程中，开发精确高效的数值模拟软件已成为极具现实意义与挑战性的研究课题。本文提出一种用于处理粘弹性液相两相流的非结构化几何流体体积（VOF）方法，其中粘弹性相通过通用率型本构方程建模，并通过对局部瞬态体方程与界面跳跃条件进行条件体积平均推导出单场描述。该方法建立在plicRDF-isoAdvector几何VOF求解器基础上，结合粘弹性计算流体力学（CFD）模块化框架DeboRheo进行扩展。采用适用于非结构化网格的分段线性几何界面重构技术，实现对流体界面处粘弹性应力的离散化处理。DeboRheo框架支持不同流变模型与相应稳定化方法的灵活组合，以有效应对高韦森伯格数问题。