The discontinuous galerkin method as an enabling technology for DNS and LES of industrial aeronautical applications

Abstract

To enhance prediction capacities and therefore allowmore advanced aeronautic and aero-propulsive design, new CFD tools are required. State of the art codes are based on second order accurate finite volume methods and are primarily developed for statistical turbulence modeling approaches. Given the limitations of these models, more direct approaches such as DNS or LES are required for the prediction of off-design aerodynamic performance, noise generation, transitional flows… A stumbling block for the industrial use of DNS and LES is the lack of an adequate discretisation strategy. The accurate representation of turbulent flow structures imposes huge resolution and high accuracy requirements, practically unobtainable by industrial codes. Highly accurate academic tools used for the fundamental study of turbulence are on the other hand not able to tackle industrial geometry. The discontinuous Galerkin method is a relatively new discretisation technique, based on a cell-wise independent polynomial interpolation. This provides high accuracy irrespective of grid irregularity, as well as the possibility to locally adapt both mesh and interpolation order, which could be used to significantly improve solver robustness for automated design. DGM finally provides high computational serial and parallel efficiency, direly needed to reduce restitution time to acceptable levels. These characteristics are important assets for industrial DNS and LES. The current contribution illustrates the efforts taken at Cenaero towards proving this potential. Following numerical aspects, the assessment ofDGMforwall-resolved and wall-modeled implicit LES modeling is discussed, thereby illustrating the obtention of high accuracy, on par with academic codes. Finally some practical case studies are included.