Speaker
Description
The numerical simulation of viscoelastic two-phase flows involves complex free boundary dynamics and faces major challenges, such as the High Weissenberg Number Problem and the loss of positive definiteness of the conformation tensor.
In this presentation, we introduce an energy-stable numerical framework designed to address these issues. First, we discuss energy-stable, positivity-preserving discretizations for viscoelastic fluid models and highlight novel convergence results. Second, we extend these approaches to the two-phase setting using a parametric finite element method (PFEM) for the coupled bulk-interface system, ensuring unconditional solvability and energy stability. We discuss the preservation of physical and geometric structures by incorporating global Lagrange multipliers to guarantee exact volume conservation and energy dissipation. We demonstrate the robustness of the proposed methods with numerical experiments.