Discontinuous Galerkin methods for computational aerodynamics — 3D adaptive flow simulation with the DLR PADGE code

Abstract Over the last few years, the discontinuous Galerkin method (DGM) has demonstrated its excellence in accurate, higher-order numerical simulations for a wide range of applications in computational physics. However, the development of practical, computationally efficient flow solvers for industrial applications is still in the focus of active research. This paper deals with solving the Navier–Stokes equations describing the motion of three-dimensional, viscous compressible fluids. We present details of the PADGE code under development at the German Aerospace Center (DLR) that is aimed at large-scale applications in aerospace engineering. The discussion covers several advanced aspects like the solution of the Reynolds-averaged Navier–Stokes and k – ω turbulence model equations, a curved boundary representation, anisotropic mesh adaptation for reducing output error and techniques for solving the nonlinear algebraic equations. The performance of the solver is assessed for a set of test cases.