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

New unstructured high order methods hold the promise of transforming industrial ?CFD practices. Their combination of high precision, high geometrical flexibility ?and parallel efficiency, make them much better suited for unsteady scale resolving ?simulations (DNS, LES, ...) of turbulent industrial flows than current industrial codes. ?As industrial practices for this type of simulations have not yet been established, ?there is an opportunity to increase simulation reliability and resolution capacity by ?introducing these novel high-potential methods.
?The main objective of this work is the practical development of the discontinuous ?Galerkin method, arguably the most mature high-order discretisation, for the scaleresolving ?simulations of turbomachinery flows. ?First optimal interior penalty parameters, adapted to hybrid and high aspect ratio ?meshes, typical for CFD, have been developed. This includes the development of a ?sharp trace inverse inequality for all types of elements, as well as the generalisation ?of the coercivity analysis.
?Based on algebraic primitives performance, a flexible yet extremely efficient blockedmatrix ?structure is defined, as well as reorganised assembly routines that compensate ?the increase of computational complexity of the high-order quadrature. Different ?iterative strategies have implemented and compared, and a generic framework is ?presented that provides high-quality transfer operators for h- and p-multigrid.
?Some extensions of the DGM towards low Reynolds incompressible flows and ?frequential acoustics are furthermore developed and analysed. ?The capacities of the developed platform are demonstrated by the direct numerical ?simulation of the transitional flow on a low-pressure turbine.