A Hybridized Discontinuous Galerkin Solver for High-Speed Compressible Flow

Georg May,Thierry Magin,Ajay Rangarajan,Koen Devesse

doi:10.3390/aerospace8110322

Abstract

We present a high-order consistent compressible flow solver, based on a hybridized discontinuous Galerkin (HDG) discretization, for applications covering subsonic to hypersonic flow. In the context of high-order discretization, this broad range of applications presents unique difficulty, especially at the high-Mach number end. For instance, if a high-order discretization is to efficiently resolve shock and shear layers, it is imperative to use adaptive methods. Furthermore, high-Enthalpy flow requires non-trivial physical modeling. The aim of the present paper is to present the key enabling technologies. We discuss efficient discretization methods, including anisotropic metric-based adaptation, as well as the implementation of flexible modeling using object-oriented programming and algorithmic differentiation. We present initial verification and validation test cases focusing on external aerodynamics.

Highlights

We proved in a previous publication that, with appropriate treatment of boundary conditions, the hybridized discontinuous Galerkin (HDG) discretization (17) is adjoint consistent [42,48]
We present numerical results using the modeling approach, discretization, and adaptation discussed in preceding Sections
We presented design and initial verification of a high-order, HDG-based solver for high-speed flows, and, more broadly, flows requiring non-trivial physical modeling

Summary

Introduction

Higher order consistent methods promise superior resolution at reduced number of degrees-of-freedom (DoF), provided the solution is (locally) smooth enough [9]

Objectives

Results

Conclusion