Towards a Discontinuous Galerkin solver for scale-resolving simulations of moderate Reynolds number flows, and application to industrial cases

Due to the continuously increasing economical and environmental constraints, the standard industrial CFD methods (mostly Reynolds Averaged Navier-Stokes equations, RANS) are no longer sufficient to answer the design requirements of the industry, in particular when off-design performance and noise need to be predicted. Therefore, scale-resolving simulations, where the full (Direct Numerical Simulation, DNS) or at least a significant portion (Large-Eddy Simulation, LES) of the turbulence spectrum is resolved, are required. However, as these simulations require a nearly flawless representation of very small turbulent structures, current industrial solvers require huge computational resources in order to provide sufficient accuracy. The discontinuous Galerkin method (DGM) could alleviate this to a large extent as it seems to bridge the gap between the flexibility of industrial codes and the accuracy of academic solvers. During this thesis, the flexibility and the parallel efficiency of a DGM solver has been improved to tackle the large requirements of DNS and LES. The method was subsequently assessed for DNS and LES based on canonical benchmarks. Due to its interesting dissipation and dispersion properties, DGM seems to offer an accuracy similar to pseudo-spectral (PS) solvers for DNS. As the dissipation targets only the smallest scales, the method seems well suited to use an implicit LES approach. This approach has been validated on the simulation of homogeneous isotropic turbulence and on the channel flow at several Reynolds numbers. Finally, the method has been successfully applied on industrial cases, including a low pressure turbine blade, airfoil profiles and a high Mach number jet flow, thereby showing the maturity of the method.