Speaker
Thomas Frachon, KTH Royal Institut of Technology
Abstract
Multiphase flow simulations present significant computational challenges due to several key factors. The evolving interface undergoes large deformations and topological changes, with its evolution directly coupled to bulk-surface partial differential equations. Additionally, geometric quantities such as the mean curvature vector must be accurately computed. The convection-diffusion equation modeling surfactant transport, when coupled to the Navier-Stokes equations, introduces substantial nonlinearities and complexity. Moreover, both equations involve quantities that must be conserved throughout the simulation.
In this talk, I will present an unfitted finite element method for simulating two-phase flows in the presence of insoluble surfactants. The proposed method conserves surfactant mass, defines a mesh that is non-conforming with respect to the evolving interface separating immiscible fluids, and accurately approximates weak and strong discontinuities across the evolving geometry.