# Simplex Space-Time Meshes in Compressible Flow Simulations

## TL;DR

This paper introduces the use of simplex space-time meshes in compressible flow simulations, enabling flexible, efficient, and topology-changing simulations with local temporal refinement, demonstrated through complex 2D and 3D cases.

## Contribution

It presents a finite element formulation for compressible flows on simplex space-time meshes, allowing topology changes and local temporal refinement in simulations.

## Key findings

- Successful simulation of a valve with topology change
- Parallel 3D simulation of piston ring blow-by
- Computational time savings from local temporal refinement

## Abstract

Employing simplex space-time meshes enlarges the scope of compressible flow simulations. The simultaneous discretization of space and time with simplex elements extends the flexibility of unstructured meshes from space to time. In this work, we adopt a finite element formulation for compressible flows to simplex space-time meshes. The method obtained allows, e.g., flow simulations on spatial domains that change topology with time. We demonstrate this with the two-dimensional simulation of compressible flow in a valve that fully closes and opens again. Furthermore, simplex space-time meshes facilitate local temporal refinement. A three-dimensional transient simulation of blow-by past piston rings is run in parallel on 120 cores. The timings point out savings of computation time gained from local temporal refinement in space-time meshes.