The capability to obtain computer simulations that accurately imitate real flow phenomena has been considered essential to fulfil the European strategic goals of future transportation. This capability, referred here as high-fidelity flow simulation, will allow a cheaper exploration of aeronautical and automotive designs that meet the transport policies dictated by the European agencies. In the last decade, the utilization of unstructured high-order methods has been intensively explored as a promising solution to perform high-fidelity flow simulations.
To exploit all the advantages of unstructured high-order methods for high-fidelity flow simulation in large clusters, it is mandatory to generate meshes composed by a large number of high-quality curved elements that approximate accurately the boundaries of complex domains. In this direction, HiPerMeGaFlowS has resulted in a new formulation to generate curved high-order meshes that feature high-quality and high-accuracy of the geometry approximation. This formulation has been complemented with a new coarse-to-fine approach for distributed meshing in large clusters. Finally, the integration of the high-order solvers with the high-performance curved meshing tool is technological innovation. Nowadays, high-order solvers are used on straight-sided meshes, and they are not integrated with the meshing tools.
The potential of high-order discretizations in flow applications has been proven by various European projects, in particular for the Discontinuous Galerkin (DG) method. Nevertheless, additional research on implicit DG numerical schemes with smaller memory footprints is required. A promising alternative is the emerging Hybridizable Discontinuous Galerkin (HDG) method. Accordingly, in the HiPerMeGaFlowS project a parallel implementation of the Hybridizable Discontinuous Galerkin method and the extension to third-order of an existent Variational Multi-Scale solver have been developed. Both codes have been run on thousands of processors.
A really promising approach to obtain high-fidelity flow results is to perform Implicit Large Eddy Simulation (ILES) with a high-order solver. This approach has proven to predict transition of a turbulent flow around curved domains. However, the difficulty of generating fine curved meshes, and the lack of better parallel implicit DG implementations, have resulted in DG demonstrations of high-order ILES running only in hundreds of processors on simple curved meshes. Accordingly, the high-fidelity flow simulations in thousands of processors using both unstructured high-order solvers on extremely fine curved meshes, and performed in this project, are new results in curved meshing, high-order methods and high-performance scientific computing.
