An unstructured geometrical un-split VOF method for viscoelastic two-phase flows

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. Program Title: DeboRheo CPC Library link to program files: https://doi.org/10.17632/gsgdrjm2md.1 Developer's repository link: https://gitlab.com/deborheo/deborheorelease/ Licensing provisions: GPLv3 Programming language: C++ Nature of problem: DNS of viscoelastic two-phase flows encounters major challenges due to abrupt changes of physical properties and rheological behaviors of the two phases at the fluid interface, and viscoelastic flows characterized with high Weissenberg numbers introduce additional numerical challenges. Solution method: A geometrical unstructured Volume-of-Fluid (VOF) method for handling two-phase flows with a viscoelastic liquid phase, where the latter is modeled by generic rate-type constitutive equations. Appropriate stabilization techniques are included to address the High Weissenberg Number Problem (HWNP).