# FLEXI: A high order discontinuous Galerkin framework for hyperbolic-parabolic conservation laws

arXiv: https://arxiv.org/abs/1910.02858 · HTML: https://mlsanity.com/paper/1910.02858/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Oct 2019.

## Built on by (most cited first, 7 of 7)

- [Deep Reinforcement Learning for Turbulence Modeling in Large Eddy Simulations](https://mlsanity.com/paper/2206.11038/) (2022)
- [Deep Reinforcement Learning for Computational Fluid Dynamics on HPC Systems](https://mlsanity.com/paper/2205.06502/) (2022)
- [Toward Discretization-Consistent Closure Schemes for Large Eddy Simulation Using Reinforcement Learning](https://mlsanity.com/paper/2309.06260/) (2023)
- [Harnessing Equivariance: Modeling Turbulence with Graph Neural Networks](https://mlsanity.com/paper/2504.07741/) (2025)
- [Gym-preCICE: Reinforcement Learning Environments for Active Flow Control](https://mlsanity.com/paper/2305.02033/) (2023)
- [Plug-and-Play Benchmarking of Reinforcement Learning Algorithms for Large-Scale Flow Control](https://mlsanity.com/paper/2601.15015/) (2026)
- [Invariant Control Strategies for Active Flow Control using Graph Neural Networks](https://mlsanity.com/paper/2503.22775/) (2025)

## Abstract (arXiv)

High order (HO) schemes are attractive candidates for the numerical solution of multiscale problems occurring in fluid dynamics and related disciplines. Among the HO discretization variants, discontinuous Galerkin schemes offer a collection of advantageous features which have lead to a strong increase in interest in them and related formulations in the last decade. The methods have matured sufficiently to be of practical use for a range of problems, for example in direct numerical and large eddy simulation of turbulence. However, in order to take full advantage of the potential benefits of these methods, all steps in the simulation chain must be designed and executed with HO in mind. Especially in this area, many commercially available closed-source solutions fall short. In this work, we therefor present the FLEXI framework, a HO consistent, open-source simulation tool chain for solving the compressible Navier-Stokes equations in a high performance computing setting. We describe the numerical algorithms and implementation details and give an overview of the features and capabilities of all parts of the framework. Beyond these technical details, we also discuss the important, but often overlooked issues of code stability, reproducibility and user-friendliness. The benefits gained by developing an open-source framework are discussed, with a particular focus on usability for the open-source community. We close with sample applications that demonstrate the wide range of use cases and the expandability of FLEXI and an overview of current and future developments.