DG methods for aerodynamic flow simulations

Abstract

In this talk we will give an overview of recent developments on adaptive higher order Discontinuous Galerkin discretizations for the use in computational aerodynamics at the DLR in Braunschweig, Germany. Finite volume schemes which are currently used in industry are in general bound to 2nd order on unstructured meshes. Discontinuous Galerkin finite element methods can be regarded as a generalization of finite volume method in the sense that the lowest order Discontinuous Galerkin method coincides with a basic 1st order finite volume scheme. However, in contrast to finite volume methods Discontinuous Galerkin methods can be easily extended to higher order on unstructured meshes simply by increasing the polynomial degree and without reconstruction as would be required for finite volume schemes. We will present numerical results demonstrating that higher order discretization schemes are particularly suited for resolving viscous boundary layers. We will show that the use of higher order discretizations can significantly reduce the mesh size and the computational effort for computing numerical flow solutions up to a prescribed accuracy. We demonstrate the use of a posteriori error estimation for estimating the accuracy of the flow solutions in terms of aerodynamical force coefficients. Furthermore, we adopt a goal-oriented (adjoint-based) adaptive mesh refinement specifically tailored to the accurate computation of the force coefficients. The adjoint-based refinement is combined with an anisotropic refinement in order to efficiently resolve anisotropic flow features like boundary layers or shocks. Finally, we give an outlook on future developments on adaptive higher order Discontinuous Galerkin discretizations at the DLR. We also give an overview of the developments planned in the EU project ADIGMA headed by DLR which concentrates the effort of 22 European partners on the development of adaptive higher order methods for aerodynamic applications in industry.