# Simplex space-time meshes in two-phase flow simulations

## TL;DR

This paper introduces a space-time finite element method with local temporal refinement for two-phase flow simulations, enabling high-resolution modeling of interfaces with complex local effects.

## Contribution

It extends existing methods to include adaptive temporal refinement based on interface position, creating tetrahedral and pentatope meshes for improved accuracy and efficiency.

## Key findings

- Effective local temporal refinement improves interface resolution.
- Method handles complex effects like surface tension and property jumps.
- Enhanced computational efficiency in two-phase flow simulations.

## Abstract

In this paper, we present the numerical solution of two-phase flow problems of engineering significance with a space-time finite element method that allows for local temporal refinement. Our basis is the method presented in [3], which allows for arbitrary temporal refinement in preselected regions of the mesh. It has been extended to adaptive temporal refinement that is governed by a quantity that is part of the solution process, namely, the interface position in two-phase flow. Due to local effects such as surface tension, jumps in material properties, etc., the interface can, in general, be considered a region that requires high flexibility and high resolution, both in space and in time. The new method, which leads to tetrahedral (for 2D problems) and pentatope (for 3D problems) meshes, offers an efficient yet accurate approach to the underlying two-phase flow problems.