Development of the discontinuous Galerkin method for high-resolution, large scale CFD and acoustics in industrial geometries

The recent advent of unstructured high order methods holds the promise of transforming industrial computational fluid dynamics practices. These novel methods combine high precision to high geometrical flexibility, but also provide excellent serial and parallel efficiency up to very large core counts. They also provide many possibilities for adaptive resolution, including accurate non-conformal connections and order adaptation. Due to the combination of these features, these methods are technically better suited for industrial scale resolving computations than the second order finite volume codes that pervade industrial CFD. As this type of computations will be required in the near future, and industrial simulation practices have not yet been firmly established, there is a unique window of opportunity to introduce these novel high-potential methods. Of these methods, the discontinuous Galerkin method is arguably the most mature, in terms of the theoretical framework, its practical deployment and applications. The main objective of this work is the development of this method for tackling scale-resolving simulations of turbomachinery flows. This thesis treats important practical and theoretical steps towards this goal. The first contribution is the study of the stability of the interior penalty method on hybrid meshes. Through the sharp computation of a trace inverse inequality, already available for simplex meshes, for all types of elements, and the generalisation of the coercivity analysis, optimal penalty parameters are found. In particular a specific variant for high aspect ratio meshes, typical for CFD, has been found. A further development concerns the definition of optimal data structures and assembly routines, based on the evaluation of computational performance of algebraic primitives. It has been shown how to define an extremely flexible matrix structure, whilst obtaining very high efficiency. By the reorganisation of assembly routines the increase of computational complexity with interpolation order is largely compensated higher computational efficiency. Both matrix-free GMRES and p-multigrid iterative strategies are furthermore implemented and compared. For the p-multigrid strategy, a generic framework is presented that provides high-quality transfer operators for h- and p-multigrid. Finally, a number of conceptual extensions to the DGM are proposed, namely the practical implementation of a non-conformal method for incompressible flows, as well as the application to frequential formulations, in particular of the Linearised Euler Equations including Perfectly Matched Layers. A first industrial CFD application is shown, which concerns the direct numerical simulation of transitional flow in a low pressure turbine cascade. (FSA 3) -- UCL, 2013