Discontinuous Galerkin methods for computational aerodynamics - 3D adaptive flow simulation with the DLR PADGE code. Over the last years, the discontinuous Galerkin method (DGM) has demonstrated its excellence in accurate, high-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.

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  1. Wang, Donghuan; Lian, Yeda; Xiao, Hong: Application of discontinuous Galerkin method in supersonic and hypersonic gas flows (2020)
  2. Ching, Eric J.; Lv, Yu; Gnoffo, Peter; Barnhardt, Michael; Ihme, Matthias: Shock capturing for discontinuous Galerkin methods with application to predicting heat transfer in hypersonic flows (2019)
  3. Bassi, F.; Botti, L.; Colombo, A.; Crivellini, A.; Franchina, N.; Ghidoni, A.: Assessment of a high-order accurate discontinuous Galerkin method for turbomachinery flows (2016)
  4. Kompenhans, Moritz; Rubio, Gonzalo; Ferrer, Esteban; Valero, Eusebio: Comparisons of (p)-adaptation strategies based on truncation- and discretisation-errors for high order discontinuous Galerkin methods (2016)
  5. Izsák, Ferenc: Energy norm error estimates for averaged discontinuous Galerkin methods: multidimensional case (2015)
  6. Giorgiani, Giorgio; Fernández-Méndez, Sonia; Huerta, Antonio: Hybridizable discontinuous Galerkin with degree adaptivity for the incompressible Navier-Stokes equations (2014)
  7. Schoenawa, Stefan; Hartmann, Ralf: Discontinuous Galerkin discretization of the Reynolds-averaged Navier-Stokes equations with the shear-stress transport model (2014)
  8. Crivellini, Andrea; D’Alessandro, Valerio; Bassi, Francesco: A Spalart-Allmaras turbulence model implementation in a discontinuous Galerkin solver for incompressible flows (2013)
  9. Crivellini, Andrea; D’Alessandro, Valerio; Bassi, Francesco: High-order discontinuous Galerkin solutions of three-dimensional incompressible RANS equations (2013)
  10. Renac, Florent; Gérald, Sophie; Marmignon, Claude; Coquel, Frédéric: Fast time implicit-explicit discontinuous Galerkin method for the compressible Navier-Stokes equations (2013)
  11. Rubio, G.; Fraysse, F.; De Vicente, J.; Valero, E.: The estimation of truncation error by (\tau)-estimation for Chebyshev spectral collocation method (2013)
  12. Hartmann, Ralf; Held, Joachim; Leicht, Tobias: Adjoint-based error estimation and adaptive mesh refinement for the RANS and (k-\omega) turbulence model equations (2011)