On the development, verification, and validation of a discontinuous Galerkin solver for the Navier–Stokes equations

Abstract

We present maDG, a newly developed code designed for the efficient parallel implicit solution of the 3D unstructured nodal discontinuous Galerkin discretization of the unsteady compressible Navier–Stokes equations. The code is being developed to provide an efficient, modular, and maintainable software platform for studying algorithmic and modeling issues arising in high-resolution CFD. In this paper we address some issues pertinent to the software architecture and testing implementation used towards the goal of implicit time integration of discontinuous Galerkin (DG) approximations.This effort is largely inspired by the life work of Antony Jameson and by his legendary FLO codes, which for more than four decades have provided a unique platform for the development of CFD methods, and enabled path-breaking advances in aerodynamics. We dedicate this paper to Antony on the occasion of his 85th birthday, with the utmost gratitude for his teaching and his friendship.