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

Abstract

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.

Split form ALE discontinuous Galerkin methods with applications to under-resolved turbulent low-Mach number flows

“…e proposed split form ALE DGSEM is implemented in the open source high order DG solver FLEXI 3 [36]. It provides the necessary framework for the implementation of di erent split forms for high order unstructured meshes, was successfully applied to under-resolved simulations in uid dynamics before [3,15] and shows excellent scaling properties, making it a suitable choice for large-scale simulations, as presented in the next chapter.…”