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High-Performance Curved Meshing and Unstructured High-Order Galerkin Solvers for High-Fidelity Flow Simulation

Periodic Reporting for period 1 - HiPerMeGaFlowS (High-Performance Curved Meshing and Unstructured High-Order Galerkin Solvers for High-Fidelity Flow Simulation)

Reporting period: 2015-04-01 to 2017-03-31

High-fidelity flow simulation is one of the main goals to pursue in the research towards exascale computing. This capability will allow a cheaper exploration of aeronautical and automotive designs that fulfill energy consumption and noise emissions policies of the European agencies. In this project, the integration of three high-performance tools will be studied as a promising alternative to perform high-fidelity flow simulations. Specifically, a parallel curved unstructured mesh generator will be integrated with two different parallel high-order stabilized Galerkin solvers. We expect that the novel research required on the development and combination of these high-performance tools will provide the physical, numerical, and geometrical accuracy required to perform high-fidelity flow simulations on complex domains defined by industrial computer-aided design models. Furthermore, the project is of major interest in high-performance computing since we expect to improve the scalability of implicit flow solvers by increasing the accuracy for a given computational cost, favoring computation to data transfer, and increasing the ratio of operations that scale linearly with the number of mesh elements. The combined tools will be deployed in a large cluster to obtain flow simulations of practical interest for the aeronautical and automotive industries.
O1 High-performance computing for high-quality curved meshing from CAD geometries. The goal of generating in parallel high-quality curved meshes from CAD models on thousands of processors has been fulfilled. To this end, a new formulation for the curved meshing problem based on quality and disparity measures has been proposed. This formulation leads to curved meshes with continuity of the normal vector on the smooth surfaces of the domain boundary. Furthemore, it leads to meshes that super-converge exponentially to the target geometry. In addition, a parallel algorithm has been proposed and implemented. The meshing tool has been integrated with the high-order simulation tools developed during the HiPerMeGaFlowS project.

O2 High-performance computing for high-order unstructured Galerkin solvers. The goal to develop two different high-performance unstructured high-order flow solvers has been accomplished. First, a parallel implementation of the HDG method has been developed to run in thousands of processors. Second, an existing high-performance SUPG solver has been extended to high-order. In this manner, both solvers now can run on the large curved meshes provided by the methods proposed in this project. Both solvers have been integrated together with the high-performance curved meshing tool developed during the duration of the HiPerMeGaFlowS project.

O3 High-fidelity flow simulations on large high-performance clusters. The goal of performing ILES and RANS runs on large curved meshes with both high-order solvers on thousands of processors has been reached. The simulations have been performed for curved objects immersed in a flow stream, such as blade and a complex topography. The flow features obtained with these simulations has been proved to match the quantitative and qualitative behaviour of the experimental results in turbulence transition available in the literature. In addition, these simulations have been used to compare the advantages of the obtained curved meshes, which feature a proper continuity of the normal vector, with the standard meshes.

As planned the fellow has performed scientific dissemination in international conferences and peer reviewed publications in high impact peer reviewed journals and conferences. Furthermore, he has been involved in different public engagement activities:
- Inclusion of the project information, progress and results in several dissemination activities: Spanish news, website, YouTube channel, talks for high-school students, short courses.
- Participation in MareNostrum open day event, which are aimed to the general public.
- Cooperation with other Universities and research centers.
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.
Flow solution on: (a,c) a standard straight-sided mesh and (b,d) our parallel curved subdivision