Fitted front tracking methods for two-phase incompressible Navier--Stokes flow: Eulerian and ALE finite element discretizations

TL;DR

This paper introduces novel fitted finite element methods for simulating two-phase incompressible Navier--Stokes flow, utilizing Eulerian and ALE formulations with interface approximation, demonstrating accuracy, robustness, and efficiency through numerical experiments.

Contribution

The paper develops and compares new fitted finite element approaches for two-phase flow, avoiding interface remeshing and enhancing computational stability.

Findings

Both Eulerian and ALE methods show high accuracy in simulations.

The methods maintain mesh quality without remeshing.

Numerical experiments confirm robustness and efficiency.

Abstract

We investigate novel fitted finite element approximations for two-phase Navier--Stokes flow. In particular, we consider both Eulerian and Arbitrary Lagrangian--Eulerian (ALE) finite element formulations. The moving interface is approximated with the help of parametric piecewise linear finite element functions. The bulk mesh is fitted to the interface approximation, so that standard bulk finite element spaces can be used throughout. The meshes describing the discrete interface in general do not deteriorate in time, which means that in numerical simulations a smoothing or a remeshing of the interface mesh is not necessary. We present several numerical experiments, including convergence experiments and benchmark computations, for the introduced numerical methods, which demonstrate the accuracy and robustness of the proposed algorithms. We also compare the accuracy and efficiency of the Eulerian and ALE formulations.