A finite element method for two-phase flow with material viscous interface

TL;DR

This paper develops a finite element method for simulating two-phase flows with viscous interfaces, addressing complex interactions and ensuring stability, with numerical assessments of its performance and an iterative solution approach.

Contribution

It introduces a novel unfitted finite element discretization for two-phase flows with viscous interfaces and analyzes its stability and efficiency.

Findings

Method is stable across various parameters.

Iterative splitting improves computational efficiency.

Numerical results validate the approach.

Abstract

This paper studies a model of two-phase flow with an immersed material viscous interface and a finite element method for numerical solution of the resulting system of PDEs. The interaction between the bulk and surface media is characterized by no-penetration and slip with friction interface conditions. The system is shown to be dissipative and a model stationary problem is proved to be well-posed. The finite element method applied in this paper belongs to a family of unfitted discretizations. The performance of the method when model and discretization parameters vary is assessed. Moreover, an iterative procedure based on the splitting of the system into bulk and surface problems is introduced and studied numerically.