High-Order Finite Element Method for Non-Newtonian Two-Phase Flows with Moving Interfaces

Abstract

The present work builds upon a computational framework originally developed for Newtonian fluid simulations and subsequently extended to model non-Newtonian two-phase flows with complex interface dynamics. This flexible platform, implemented using modern parallel programming languages, enables the simulation of macro- and microscale phenomena such as bubble approach and coalescence. The methodology employs a one-fluid, high-order Finite Element (FE) interface-tracking method within the Arbitrary Lagrangian-Eulerian (ALE) framework, allowing for mesh motion and adaptive refinement on unstructured meshes. A high-order semi-Lagrangian method is used for stable and accurate advection of both interface and flow variables. The interface between fluids is explicitly discretized using interconnected nodes, enabling precise curvature computation via the Laplace-Beltrami operator and requiring dynamic updates to the interface connectivity during coalescence events. Rigid body dynamics is also incorporated into the framework to model the fluid-solid interaction, enabling the simulation of two-phase systems involving immersed or suspended rigid particles. For further details in the methodology, see [Anjos(2020), Anjos(2021)a, Anjos(2021)b, Santos(2024)]. Results reveal significant interface dynamics and enhanced mixing in the presence of multiple bodies, demonstrating the method’s strong capability to capture the complex Newtonian and non-Newtonian two-phase systems.